[{"data":1,"prerenderedAt":12190},["ShallowReactive",2],{"TNqVEtX5OY":3,"VyF3Mmj32r":10604,"N9m89Rcq0G":10830},{"title":4,"description":5,"body":6,"_type":10602,"_id":10603},"Ray Traversal","The ray traversal process identifies and handles intersections between a ray\nand geometries in an acceleration structure.",{"type":7,"children":8,"toc":10577},"root",[9,17,22,117,124,134,139,148,153,180,3069,3213,4451,4677,5283,5330,5692,5818,5914,7078,7333,7338,7346,7356,7373,7406,7448,7463,7468,7494,7499,7540,7545,7552,7557,7593,7605,7633,7643,7648,7653,7659,7741,7790,7833,7839,7873,7892,7898,7916,7921,7927,7939,8626,8844,8855,8881,8904,8939,8959,8965,8982,8999,9024,9029,9045,9055,9061,9076,9081,9108,9120,9133,9166,9207,9244,9249,9268,9286,9322,9327,9344,9364,9369,9378,9391,9412,9425,9437,9912,9917,9922,9928,9944,10000,10005,10038,10127,10137,10143,10160,10165,10170,10214,10291,10308,10313,10331,10342,10389,10406,10411,10416,10427,10489,10522,10572],{"type":10,"tag":11,"props":12,"children":14},"element","h1",{"id":13},"ray-traversal",[15],{"type":16,"value":4},"text",{"type":10,"tag":18,"props":19,"children":20},"p",{},[21],{"type":16,"value":5},{"type":10,"tag":18,"props":23,"children":24},{},[25,27,32,34,41,43,50,52,62,64,70,72,76,78,84,86,92,94,104,106,111,112,115],{"type":16,"value":26},"Ray traversal cannot be started by a Vulkan API command directly - a shader\n",{"type":10,"tag":28,"props":29,"children":31},"normative",{"type":30},"must",[],{"type":16,"value":33}," execute\n",{"type":10,"tag":35,"props":36,"children":38},"code",{"className":37},[],[39],{"type":16,"value":40},"OpRayQueryProceedKHR",{"type":16,"value":42},"\nor\na ",{"type":10,"tag":44,"props":45,"children":47},"a",{"href":46},"/404#glossary-pipeline-trace-ray",[48],{"type":16,"value":49},"pipeline trace ray",{"type":16,"value":51}," instruction\n.\nWhen the ",{"type":10,"tag":44,"props":53,"children":55},{"href":54},"/man/VkPhysicalDeviceRayTracingPipelineFeaturesKHR#features-rayTracingPipeline",[56],{"type":10,"tag":35,"props":57,"children":59},{"className":58},[],[60],{"type":16,"value":61},"rayTracingPipeline",{"type":16,"value":63}," feature\nis enabled, ",{"type":10,"tag":35,"props":65,"children":67},{"className":66},[],[68],{"type":16,"value":69},"OpTraceRayKHR",{"type":16,"value":71}," ",{"type":10,"tag":28,"props":73,"children":75},{"type":74},"can",[],{"type":16,"value":77}," be used for ",{"type":10,"tag":44,"props":79,"children":81},{"href":80},"/chapters/ray-tracing#ray-tracing",[82],{"type":16,"value":83},"ray tracing",{"type":16,"value":85},"\nin a ",{"type":10,"tag":44,"props":87,"children":89},{"href":88},"/chapters/pipelines#pipelines-ray-tracing",[90],{"type":16,"value":91},"ray tracing pipeline",{"type":16,"value":93},".\nWhen the ",{"type":10,"tag":44,"props":95,"children":97},{"href":96},"/man/VkPhysicalDeviceRayQueryFeaturesKHR#features-rayQuery",[98],{"type":10,"tag":35,"props":99,"children":101},{"className":100},[],[102],{"type":16,"value":103},"rayQuery",{"type":16,"value":105}," feature is enabled,\n",{"type":10,"tag":35,"props":107,"children":109},{"className":108},[],[110],{"type":16,"value":40},{"type":16,"value":71},{"type":10,"tag":28,"props":113,"children":114},{"type":74},[],{"type":16,"value":116}," be used in any shader stage.",{"type":10,"tag":118,"props":119,"children":121},"h2",{"id":120},"ray-intersection-candidate-determination",[122],{"type":16,"value":123},"Ray Intersection Candidate Determination",{"type":10,"tag":18,"props":125,"children":126},{},[127,129,132],{"type":16,"value":128},"Once tracing begins, rays are first tested against instances in a top-level\nacceleration structure.\nA ray that intersects an instance will be transformed into the space of the\ninstance to continue traversal within that instance; therefore the transform\nmatrix stored in the instance ",{"type":10,"tag":28,"props":130,"children":131},{"type":30},[],{"type":16,"value":133}," be invertible.",{"type":10,"tag":18,"props":135,"children":136},{},[137],{"type":16,"value":138},"In case multiple instances are intersected by a ray, the ray transformation\ninto the space of the instance is invariant under the order in which these\ninstances are encountered in the top-level acceleration structure.",{"type":10,"tag":140,"props":141,"children":142},"note",{},[143],{"type":10,"tag":18,"props":144,"children":145},{},[146],{"type":16,"value":147},"Applying multiple forward and reverse transforms to a ray to transition from\none instance to another could result in accumulated errors.\nThus an implementation should behave as if the ray is transformed from the\norigin for each instance independently.",{"type":10,"tag":18,"props":149,"children":150},{},[151],{"type":16,"value":152},"Next, rays are tested against geometries in a bottom-level acceleration\nstructure to determine if a hit occurred between them, initially based only\non their geometric properties (i.e. their vertices).\nThe implementation performs similar operations to that of rasterization, but\nwith the effective viewport determined by the parameters of the ray, and the\ngeometry transformed into a space determined by that viewport.",{"type":10,"tag":18,"props":154,"children":155},{},[156,158,168,170,178],{"type":16,"value":157},"The vertices of each primitive are transformed from acceleration structure\nspace ",{"type":10,"tag":159,"props":160,"children":161},"em",{},[162],{"type":10,"tag":163,"props":164,"children":165},"sub",{},[166],{"type":16,"value":167},"as",{"type":16,"value":169}," to ray space ",{"type":10,"tag":159,"props":171,"children":172},{},[173],{"type":10,"tag":163,"props":174,"children":175},{},[176],{"type":16,"value":177},"r",{"type":16,"value":179}," according to the ray origin and direction as\nfollows:",{"type":10,"tag":181,"props":182,"children":185},"span",{"className":183},[184],"katex-display",[186],{"type":10,"tag":181,"props":187,"children":190},{"className":188},[189],"katex",[191,1147],{"type":10,"tag":181,"props":192,"children":195},{"className":193},[194],"katex-mathml",[196],{"type":10,"tag":197,"props":198,"children":201},"math",{"xmlns":199,"display":200},"http://www.w3.org/1998/Math/MathML","block",[202],{"type":10,"tag":203,"props":204,"children":205},"semantics",{},[206,1140],{"type":10,"tag":207,"props":208,"children":209},"mrow",{},[210,325,330,976],{"type":10,"tag":207,"props":211,"children":212},{},[213,220,320],{"type":10,"tag":214,"props":215,"children":217},"mo",{"fence":216},"true",[218],{"type":16,"value":219},"(",{"type":10,"tag":221,"props":222,"children":226},"mtable",{"rowspacing":223,"columnalign":224,"columnspacing":225},"0.16em","center","1em",[227,260,291],{"type":10,"tag":228,"props":229,"children":230},"mtr",{},[231],{"type":10,"tag":232,"props":233,"children":234},"mtd",{},[235],{"type":10,"tag":236,"props":237,"children":240},"mstyle",{"scriptlevel":238,"displaystyle":239},"0","false",[241],{"type":10,"tag":207,"props":242,"children":243},{},[244,250,256],{"type":10,"tag":245,"props":246,"children":247},"mi",{},[248],{"type":16,"value":249},"x",{"type":10,"tag":245,"props":251,"children":253},{"mathvariant":252},"normal",[254],{"type":16,"value":255},"_",{"type":10,"tag":245,"props":257,"children":258},{},[259],{"type":16,"value":177},{"type":10,"tag":228,"props":261,"children":262},{},[263],{"type":10,"tag":232,"props":264,"children":265},{},[266],{"type":10,"tag":236,"props":267,"children":268},{"scriptlevel":238,"displaystyle":239},[269],{"type":10,"tag":207,"props":270,"children":271},{},[272,278,283,287],{"type":10,"tag":273,"props":274,"children":275},"mtext",{},[276],{"type":16,"value":277}," ",{"type":10,"tag":245,"props":279,"children":280},{},[281],{"type":16,"value":282},"y",{"type":10,"tag":245,"props":284,"children":285},{"mathvariant":252},[286],{"type":16,"value":255},{"type":10,"tag":245,"props":288,"children":289},{},[290],{"type":16,"value":177},{"type":10,"tag":228,"props":292,"children":293},{},[294],{"type":10,"tag":232,"props":295,"children":296},{},[297],{"type":10,"tag":236,"props":298,"children":299},{"scriptlevel":238,"displaystyle":239},[300],{"type":10,"tag":207,"props":301,"children":302},{},[303,307,312,316],{"type":10,"tag":273,"props":304,"children":305},{},[306],{"type":16,"value":277},{"type":10,"tag":245,"props":308,"children":309},{},[310],{"type":16,"value":311},"z",{"type":10,"tag":245,"props":313,"children":314},{"mathvariant":252},[315],{"type":16,"value":255},{"type":10,"tag":245,"props":317,"children":318},{},[319],{"type":16,"value":177},{"type":10,"tag":214,"props":321,"children":322},{"fence":216},[323],{"type":16,"value":324},")",{"type":10,"tag":214,"props":326,"children":327},{},[328],{"type":16,"value":329},"=",{"type":10,"tag":207,"props":331,"children":332},{},[333,337,972],{"type":10,"tag":214,"props":334,"children":335},{"fence":216},[336],{"type":16,"value":219},{"type":10,"tag":221,"props":338,"children":340},{"rowspacing":223,"columnalign":339,"columnspacing":225},"center center center",[341,554,763],{"type":10,"tag":228,"props":342,"children":343},{},[344,407,481],{"type":10,"tag":232,"props":345,"children":346},{},[347],{"type":10,"tag":236,"props":348,"children":349},{"scriptlevel":238,"displaystyle":239},[350],{"type":10,"tag":207,"props":351,"children":352},{},[353,357,361,375,379,384,389,394,398,403],{"type":10,"tag":245,"props":354,"children":355},{},[356],{"type":16,"value":44},{"type":10,"tag":245,"props":358,"children":359},{"mathvariant":252},[360],{"type":16,"value":255},{"type":10,"tag":362,"props":363,"children":364},"msup",{},[365,369],{"type":10,"tag":245,"props":366,"children":367},{},[368],{"type":16,"value":249},{"type":10,"tag":370,"props":371,"children":372},"mn",{},[373],{"type":16,"value":374},"2",{"type":10,"tag":214,"props":376,"children":377},{"stretchy":239},[378],{"type":16,"value":219},{"type":10,"tag":370,"props":380,"children":381},{},[382],{"type":16,"value":383},"1",{"type":10,"tag":214,"props":385,"children":386},{},[387],{"type":16,"value":388},"−",{"type":10,"tag":245,"props":390,"children":391},{},[392],{"type":16,"value":393},"c",{"type":10,"tag":214,"props":395,"children":396},{"stretchy":239},[397],{"type":16,"value":324},{"type":10,"tag":214,"props":399,"children":400},{},[401],{"type":16,"value":402},"+",{"type":10,"tag":245,"props":404,"children":405},{},[406],{"type":16,"value":393},{"type":10,"tag":232,"props":408,"children":409},{},[410],{"type":10,"tag":236,"props":411,"children":412},{"scriptlevel":238,"displaystyle":239},[413],{"type":10,"tag":207,"props":414,"children":415},{},[416,420,424,428,432,436,440,444,448,452,456,460,464,469,473,477],{"type":10,"tag":245,"props":417,"children":418},{},[419],{"type":16,"value":44},{"type":10,"tag":245,"props":421,"children":422},{"mathvariant":252},[423],{"type":16,"value":255},{"type":10,"tag":245,"props":425,"children":426},{},[427],{"type":16,"value":249},{"type":10,"tag":245,"props":429,"children":430},{},[431],{"type":16,"value":44},{"type":10,"tag":245,"props":433,"children":434},{"mathvariant":252},[435],{"type":16,"value":255},{"type":10,"tag":245,"props":437,"children":438},{},[439],{"type":16,"value":282},{"type":10,"tag":214,"props":441,"children":442},{"stretchy":239},[443],{"type":16,"value":219},{"type":10,"tag":370,"props":445,"children":446},{},[447],{"type":16,"value":383},{"type":10,"tag":214,"props":449,"children":450},{},[451],{"type":16,"value":388},{"type":10,"tag":245,"props":453,"children":454},{},[455],{"type":16,"value":393},{"type":10,"tag":214,"props":457,"children":458},{"stretchy":239},[459],{"type":16,"value":324},{"type":10,"tag":214,"props":461,"children":462},{},[463],{"type":16,"value":388},{"type":10,"tag":245,"props":465,"children":466},{},[467],{"type":16,"value":468},"s",{"type":10,"tag":245,"props":470,"children":471},{},[472],{"type":16,"value":44},{"type":10,"tag":245,"props":474,"children":475},{"mathvariant":252},[476],{"type":16,"value":255},{"type":10,"tag":245,"props":478,"children":479},{},[480],{"type":16,"value":311},{"type":10,"tag":232,"props":482,"children":483},{},[484],{"type":10,"tag":236,"props":485,"children":486},{"scriptlevel":238,"displaystyle":239},[487],{"type":10,"tag":207,"props":488,"children":489},{},[490,494,498,502,506,510,514,518,522,526,530,534,538,542,546,550],{"type":10,"tag":245,"props":491,"children":492},{},[493],{"type":16,"value":44},{"type":10,"tag":245,"props":495,"children":496},{"mathvariant":252},[497],{"type":16,"value":255},{"type":10,"tag":245,"props":499,"children":500},{},[501],{"type":16,"value":249},{"type":10,"tag":245,"props":503,"children":504},{},[505],{"type":16,"value":44},{"type":10,"tag":245,"props":507,"children":508},{"mathvariant":252},[509],{"type":16,"value":255},{"type":10,"tag":245,"props":511,"children":512},{},[513],{"type":16,"value":311},{"type":10,"tag":214,"props":515,"children":516},{"stretchy":239},[517],{"type":16,"value":219},{"type":10,"tag":370,"props":519,"children":520},{},[521],{"type":16,"value":383},{"type":10,"tag":214,"props":523,"children":524},{},[525],{"type":16,"value":388},{"type":10,"tag":245,"props":527,"children":528},{},[529],{"type":16,"value":393},{"type":10,"tag":214,"props":531,"children":532},{"stretchy":239},[533],{"type":16,"value":324},{"type":10,"tag":214,"props":535,"children":536},{},[537],{"type":16,"value":402},{"type":10,"tag":245,"props":539,"children":540},{},[541],{"type":16,"value":468},{"type":10,"tag":245,"props":543,"children":544},{},[545],{"type":16,"value":44},{"type":10,"tag":245,"props":547,"children":548},{"mathvariant":252},[549],{"type":16,"value":255},{"type":10,"tag":245,"props":551,"children":552},{},[553],{"type":16,"value":282},{"type":10,"tag":228,"props":555,"children":556},{},[557,634,690],{"type":10,"tag":232,"props":558,"children":559},{},[560],{"type":10,"tag":236,"props":561,"children":562},{"scriptlevel":238,"displaystyle":239},[563],{"type":10,"tag":207,"props":564,"children":565},{},[566,570,574,578,582,586,590,594,598,602,606,610,614,618,622,626,630],{"type":10,"tag":273,"props":567,"children":568},{},[569],{"type":16,"value":277},{"type":10,"tag":245,"props":571,"children":572},{},[573],{"type":16,"value":44},{"type":10,"tag":245,"props":575,"children":576},{"mathvariant":252},[577],{"type":16,"value":255},{"type":10,"tag":245,"props":579,"children":580},{},[581],{"type":16,"value":249},{"type":10,"tag":245,"props":583,"children":584},{},[585],{"type":16,"value":44},{"type":10,"tag":245,"props":587,"children":588},{"mathvariant":252},[589],{"type":16,"value":255},{"type":10,"tag":245,"props":591,"children":592},{},[593],{"type":16,"value":282},{"type":10,"tag":214,"props":595,"children":596},{"stretchy":239},[597],{"type":16,"value":219},{"type":10,"tag":370,"props":599,"children":600},{},[601],{"type":16,"value":383},{"type":10,"tag":214,"props":603,"children":604},{},[605],{"type":16,"value":388},{"type":10,"tag":245,"props":607,"children":608},{},[609],{"type":16,"value":393},{"type":10,"tag":214,"props":611,"children":612},{"stretchy":239},[613],{"type":16,"value":324},{"type":10,"tag":214,"props":615,"children":616},{},[617],{"type":16,"value":402},{"type":10,"tag":245,"props":619,"children":620},{},[621],{"type":16,"value":468},{"type":10,"tag":245,"props":623,"children":624},{},[625],{"type":16,"value":44},{"type":10,"tag":245,"props":627,"children":628},{"mathvariant":252},[629],{"type":16,"value":255},{"type":10,"tag":245,"props":631,"children":632},{},[633],{"type":16,"value":311},{"type":10,"tag":232,"props":635,"children":636},{},[637],{"type":10,"tag":236,"props":638,"children":639},{"scriptlevel":238,"displaystyle":239},[640],{"type":10,"tag":207,"props":641,"children":642},{},[643,647,651,662,666,670,674,678,682,686],{"type":10,"tag":245,"props":644,"children":645},{},[646],{"type":16,"value":44},{"type":10,"tag":245,"props":648,"children":649},{"mathvariant":252},[650],{"type":16,"value":255},{"type":10,"tag":362,"props":652,"children":653},{},[654,658],{"type":10,"tag":245,"props":655,"children":656},{},[657],{"type":16,"value":282},{"type":10,"tag":370,"props":659,"children":660},{},[661],{"type":16,"value":374},{"type":10,"tag":214,"props":663,"children":664},{"stretchy":239},[665],{"type":16,"value":219},{"type":10,"tag":370,"props":667,"children":668},{},[669],{"type":16,"value":383},{"type":10,"tag":214,"props":671,"children":672},{},[673],{"type":16,"value":388},{"type":10,"tag":245,"props":675,"children":676},{},[677],{"type":16,"value":393},{"type":10,"tag":214,"props":679,"children":680},{"stretchy":239},[681],{"type":16,"value":324},{"type":10,"tag":214,"props":683,"children":684},{},[685],{"type":16,"value":402},{"type":10,"tag":245,"props":687,"children":688},{},[689],{"type":16,"value":393},{"type":10,"tag":232,"props":691,"children":692},{},[693],{"type":10,"tag":236,"props":694,"children":695},{"scriptlevel":238,"displaystyle":239},[696],{"type":10,"tag":207,"props":697,"children":698},{},[699,703,707,711,715,719,723,727,731,735,739,743,747,751,755,759],{"type":10,"tag":245,"props":700,"children":701},{},[702],{"type":16,"value":44},{"type":10,"tag":245,"props":704,"children":705},{"mathvariant":252},[706],{"type":16,"value":255},{"type":10,"tag":245,"props":708,"children":709},{},[710],{"type":16,"value":282},{"type":10,"tag":245,"props":712,"children":713},{},[714],{"type":16,"value":44},{"type":10,"tag":245,"props":716,"children":717},{"mathvariant":252},[718],{"type":16,"value":255},{"type":10,"tag":245,"props":720,"children":721},{},[722],{"type":16,"value":311},{"type":10,"tag":214,"props":724,"children":725},{"stretchy":239},[726],{"type":16,"value":219},{"type":10,"tag":370,"props":728,"children":729},{},[730],{"type":16,"value":383},{"type":10,"tag":214,"props":732,"children":733},{},[734],{"type":16,"value":388},{"type":10,"tag":245,"props":736,"children":737},{},[738],{"type":16,"value":393},{"type":10,"tag":214,"props":740,"children":741},{"stretchy":239},[742],{"type":16,"value":324},{"type":10,"tag":214,"props":744,"children":745},{},[746],{"type":16,"value":388},{"type":10,"tag":245,"props":748,"children":749},{},[750],{"type":16,"value":468},{"type":10,"tag":245,"props":752,"children":753},{},[754],{"type":16,"value":44},{"type":10,"tag":245,"props":756,"children":757},{"mathvariant":252},[758],{"type":16,"value":255},{"type":10,"tag":245,"props":760,"children":761},{},[762],{"type":16,"value":249},{"type":10,"tag":228,"props":764,"children":765},{},[766,843,916],{"type":10,"tag":232,"props":767,"children":768},{},[769],{"type":10,"tag":236,"props":770,"children":771},{"scriptlevel":238,"displaystyle":239},[772],{"type":10,"tag":207,"props":773,"children":774},{},[775,779,783,787,791,795,799,803,807,811,815,819,823,827,831,835,839],{"type":10,"tag":273,"props":776,"children":777},{},[778],{"type":16,"value":277},{"type":10,"tag":245,"props":780,"children":781},{},[782],{"type":16,"value":44},{"type":10,"tag":245,"props":784,"children":785},{"mathvariant":252},[786],{"type":16,"value":255},{"type":10,"tag":245,"props":788,"children":789},{},[790],{"type":16,"value":249},{"type":10,"tag":245,"props":792,"children":793},{},[794],{"type":16,"value":44},{"type":10,"tag":245,"props":796,"children":797},{"mathvariant":252},[798],{"type":16,"value":255},{"type":10,"tag":245,"props":800,"children":801},{},[802],{"type":16,"value":311},{"type":10,"tag":214,"props":804,"children":805},{"stretchy":239},[806],{"type":16,"value":219},{"type":10,"tag":370,"props":808,"children":809},{},[810],{"type":16,"value":383},{"type":10,"tag":214,"props":812,"children":813},{},[814],{"type":16,"value":388},{"type":10,"tag":245,"props":816,"children":817},{},[818],{"type":16,"value":393},{"type":10,"tag":214,"props":820,"children":821},{"stretchy":239},[822],{"type":16,"value":324},{"type":10,"tag":214,"props":824,"children":825},{},[826],{"type":16,"value":388},{"type":10,"tag":245,"props":828,"children":829},{},[830],{"type":16,"value":468},{"type":10,"tag":245,"props":832,"children":833},{},[834],{"type":16,"value":44},{"type":10,"tag":245,"props":836,"children":837},{"mathvariant":252},[838],{"type":16,"value":255},{"type":10,"tag":245,"props":840,"children":841},{},[842],{"type":16,"value":282},{"type":10,"tag":232,"props":844,"children":845},{},[846],{"type":10,"tag":236,"props":847,"children":848},{"scriptlevel":238,"displaystyle":239},[849],{"type":10,"tag":207,"props":850,"children":851},{},[852,856,860,864,868,872,876,880,884,888,892,896,900,904,908,912],{"type":10,"tag":245,"props":853,"children":854},{},[855],{"type":16,"value":44},{"type":10,"tag":245,"props":857,"children":858},{"mathvariant":252},[859],{"type":16,"value":255},{"type":10,"tag":245,"props":861,"children":862},{},[863],{"type":16,"value":282},{"type":10,"tag":245,"props":865,"children":866},{},[867],{"type":16,"value":44},{"type":10,"tag":245,"props":869,"children":870},{"mathvariant":252},[871],{"type":16,"value":255},{"type":10,"tag":245,"props":873,"children":874},{},[875],{"type":16,"value":311},{"type":10,"tag":214,"props":877,"children":878},{"stretchy":239},[879],{"type":16,"value":219},{"type":10,"tag":370,"props":881,"children":882},{},[883],{"type":16,"value":383},{"type":10,"tag":214,"props":885,"children":886},{},[887],{"type":16,"value":388},{"type":10,"tag":245,"props":889,"children":890},{},[891],{"type":16,"value":393},{"type":10,"tag":214,"props":893,"children":894},{"stretchy":239},[895],{"type":16,"value":324},{"type":10,"tag":214,"props":897,"children":898},{},[899],{"type":16,"value":402},{"type":10,"tag":245,"props":901,"children":902},{},[903],{"type":16,"value":468},{"type":10,"tag":245,"props":905,"children":906},{},[907],{"type":16,"value":44},{"type":10,"tag":245,"props":909,"children":910},{"mathvariant":252},[911],{"type":16,"value":255},{"type":10,"tag":245,"props":913,"children":914},{},[915],{"type":16,"value":249},{"type":10,"tag":232,"props":917,"children":918},{},[919],{"type":10,"tag":236,"props":920,"children":921},{"scriptlevel":238,"displaystyle":239},[922],{"type":10,"tag":207,"props":923,"children":924},{},[925,929,933,944,948,952,956,960,964,968],{"type":10,"tag":245,"props":926,"children":927},{},[928],{"type":16,"value":44},{"type":10,"tag":245,"props":930,"children":931},{"mathvariant":252},[932],{"type":16,"value":255},{"type":10,"tag":362,"props":934,"children":935},{},[936,940],{"type":10,"tag":245,"props":937,"children":938},{},[939],{"type":16,"value":311},{"type":10,"tag":370,"props":941,"children":942},{},[943],{"type":16,"value":374},{"type":10,"tag":214,"props":945,"children":946},{"stretchy":239},[947],{"type":16,"value":219},{"type":10,"tag":370,"props":949,"children":950},{},[951],{"type":16,"value":383},{"type":10,"tag":214,"props":953,"children":954},{},[955],{"type":16,"value":388},{"type":10,"tag":245,"props":957,"children":958},{},[959],{"type":16,"value":393},{"type":10,"tag":214,"props":961,"children":962},{"stretchy":239},[963],{"type":16,"value":324},{"type":10,"tag":214,"props":965,"children":966},{},[967],{"type":16,"value":402},{"type":10,"tag":245,"props":969,"children":970},{},[971],{"type":16,"value":393},{"type":10,"tag":214,"props":973,"children":974},{"fence":216},[975],{"type":16,"value":324},{"type":10,"tag":207,"props":977,"children":978},{},[979,983,1136],{"type":10,"tag":214,"props":980,"children":981},{"fence":216},[982],{"type":16,"value":219},{"type":10,"tag":221,"props":984,"children":985},{"rowspacing":223,"columnalign":224,"columnspacing":225},[986,1034,1085],{"type":10,"tag":228,"props":987,"children":988},{},[989],{"type":10,"tag":232,"props":990,"children":991},{},[992],{"type":10,"tag":236,"props":993,"children":994},{"scriptlevel":238,"displaystyle":239},[995],{"type":10,"tag":207,"props":996,"children":997},{},[998,1002,1006,1017,1021,1026,1030],{"type":10,"tag":245,"props":999,"children":1000},{},[1001],{"type":16,"value":249},{"type":10,"tag":245,"props":1003,"children":1004},{"mathvariant":252},[1005],{"type":16,"value":255},{"type":10,"tag":207,"props":1007,"children":1008},{},[1009,1013],{"type":10,"tag":245,"props":1010,"children":1011},{},[1012],{"type":16,"value":44},{"type":10,"tag":245,"props":1014,"children":1015},{},[1016],{"type":16,"value":468},{"type":10,"tag":214,"props":1018,"children":1019},{},[1020],{"type":16,"value":388},{"type":10,"tag":245,"props":1022,"children":1023},{},[1024],{"type":16,"value":1025},"o",{"type":10,"tag":245,"props":1027,"children":1028},{"mathvariant":252},[1029],{"type":16,"value":255},{"type":10,"tag":245,"props":1031,"children":1032},{},[1033],{"type":16,"value":249},{"type":10,"tag":228,"props":1035,"children":1036},{},[1037],{"type":10,"tag":232,"props":1038,"children":1039},{},[1040],{"type":10,"tag":236,"props":1041,"children":1042},{"scriptlevel":238,"displaystyle":239},[1043],{"type":10,"tag":207,"props":1044,"children":1045},{},[1046,1050,1054,1058,1069,1073,1077,1081],{"type":10,"tag":273,"props":1047,"children":1048},{},[1049],{"type":16,"value":277},{"type":10,"tag":245,"props":1051,"children":1052},{},[1053],{"type":16,"value":282},{"type":10,"tag":245,"props":1055,"children":1056},{"mathvariant":252},[1057],{"type":16,"value":255},{"type":10,"tag":207,"props":1059,"children":1060},{},[1061,1065],{"type":10,"tag":245,"props":1062,"children":1063},{},[1064],{"type":16,"value":44},{"type":10,"tag":245,"props":1066,"children":1067},{},[1068],{"type":16,"value":468},{"type":10,"tag":214,"props":1070,"children":1071},{},[1072],{"type":16,"value":388},{"type":10,"tag":245,"props":1074,"children":1075},{},[1076],{"type":16,"value":1025},{"type":10,"tag":245,"props":1078,"children":1079},{"mathvariant":252},[1080],{"type":16,"value":255},{"type":10,"tag":245,"props":1082,"children":1083},{},[1084],{"type":16,"value":282},{"type":10,"tag":228,"props":1086,"children":1087},{},[1088],{"type":10,"tag":232,"props":1089,"children":1090},{},[1091],{"type":10,"tag":236,"props":1092,"children":1093},{"scriptlevel":238,"displaystyle":239},[1094],{"type":10,"tag":207,"props":1095,"children":1096},{},[1097,1101,1105,1109,1120,1124,1128,1132],{"type":10,"tag":273,"props":1098,"children":1099},{},[1100],{"type":16,"value":277},{"type":10,"tag":245,"props":1102,"children":1103},{},[1104],{"type":16,"value":311},{"type":10,"tag":245,"props":1106,"children":1107},{"mathvariant":252},[1108],{"type":16,"value":255},{"type":10,"tag":207,"props":1110,"children":1111},{},[1112,1116],{"type":10,"tag":245,"props":1113,"children":1114},{},[1115],{"type":16,"value":44},{"type":10,"tag":245,"props":1117,"children":1118},{},[1119],{"type":16,"value":468},{"type":10,"tag":214,"props":1121,"children":1122},{},[1123],{"type":16,"value":388},{"type":10,"tag":245,"props":1125,"children":1126},{},[1127],{"type":16,"value":1025},{"type":10,"tag":245,"props":1129,"children":1130},{"mathvariant":252},[1131],{"type":16,"value":255},{"type":10,"tag":245,"props":1133,"children":1134},{},[1135],{"type":16,"value":311},{"type":10,"tag":214,"props":1137,"children":1138},{"fence":216},[1139],{"type":16,"value":324},{"type":10,"tag":1141,"props":1142,"children":1144},"annotation",{"encoding":1143},"application/x-tex",[1145],{"type":16,"value":1146},"\\left(\n\\begin{array}{c}\nx\\_{r} \\\\\\\ny\\_{r}\\\\\\\nz\\_{r}\n\\end{array}\n\\right) =\n\\left(\n\\begin{matrix}\na\\_x^2(1-c) + c & a\\_xa\\_y(1-c) - sa\\_z & a\\_xa\\_z(1-c) + sa\\_y \\\\\\\na\\_xa\\_y(1-c) + sa\\_z & a\\_y^2(1-c) + c & a\\_ya\\_z(1-c) - sa\\_x \\\\\\\na\\_xa\\_z(1-c) - sa\\_y & a\\_ya\\_z(1-c) + sa\\_x & a\\_z^2(1-c) + c\n\\end{matrix}\n\\right)\n\\left(\n\\begin{array}{c}\nx\\_{as} - o\\_x \\\\\\\ny\\_{as} - o\\_y \\\\\\\nz\\_{as} - o\\_z\n\\end{array}\n\\right)",{"type":10,"tag":181,"props":1148,"children":1151},{"className":1149,"ariaHidden":216},[1150],"katex-html",[1152,1472],{"type":10,"tag":181,"props":1153,"children":1156},{"className":1154},[1155],"base",[1157,1163,1457,1462,1468],{"type":10,"tag":181,"props":1158,"children":1162},{"className":1159,"style":1161},[1160],"strut","height:3.6em;vertical-align:-1.55em;",[],{"type":10,"tag":181,"props":1164,"children":1167},{"className":1165},[1166],"minner",[1168,1242,1403],{"type":10,"tag":181,"props":1169,"children":1172},{"className":1170},[1171],"mopen",[1173],{"type":10,"tag":181,"props":1174,"children":1178},{"className":1175},[1176,1177],"delimsizing","mult",[1179],{"type":10,"tag":181,"props":1180,"children":1184},{"className":1181},[1182,1183],"vlist-t","vlist-t2",[1185,1230],{"type":10,"tag":181,"props":1186,"children":1189},{"className":1187},[1188],"vlist-r",[1190,1223],{"type":10,"tag":181,"props":1191,"children":1195},{"className":1192,"style":1194},[1193],"vlist","height:2.05em;",[1196],{"type":10,"tag":181,"props":1197,"children":1199},{"style":1198},"top:-4.05em;",[1200,1206],{"type":10,"tag":181,"props":1201,"children":1205},{"className":1202,"style":1204},[1203],"pstrut","height:5.6em;",[],{"type":10,"tag":181,"props":1207,"children":1209},{"style":1208},"width:0.875em;height:3.600em;",[1210],{"type":10,"tag":1211,"props":1212,"children":1217},"svg",{"xmlns":1213,"width":1214,"height":1215,"viewBox":1216},"http://www.w3.org/2000/svg","0.875em","3.600em","0 0 875 3600",[1218],{"type":10,"tag":1219,"props":1220,"children":1222},"path",{"d":1221},"M863,9c0,-2,-2,-5,-6,-9c0,0,-17,0,-17,0c-12.7,0,-19.3,0.3,-20,1\nc-5.3,5.3,-10.3,11,-15,17c-242.7,294.7,-395.3,682,-458,1162c-21.3,163.3,-33.3,349,\n-36,557 l0,84c0.2,6,0,26,0,60c2,159.3,10,310.7,24,454c53.3,528,210,\n949.7,470,1265c4.7,6,9.7,11.7,15,17c0.7,0.7,7,1,19,1c0,0,18,0,18,0c4,-4,6,-7,6,-9\nc0,-2.7,-3.3,-8.7,-10,-18c-135.3,-192.7,-235.5,-414.3,-300.5,-665c-65,-250.7,-102.5,\n-544.7,-112.5,-882c-2,-104,-3,-167,-3,-189\nl0,-92c0,-162.7,5.7,-314,17,-454c20.7,-272,63.7,-513,129,-723c65.3,\n-210,155.3,-396.3,270,-559c6.7,-9.3,10,-15.3,10,-18z",[],{"type":10,"tag":181,"props":1224,"children":1227},{"className":1225},[1226],"vlist-s",[1228],{"type":16,"value":1229},"​",{"type":10,"tag":181,"props":1231,"children":1233},{"className":1232},[1188],[1234],{"type":10,"tag":181,"props":1235,"children":1238},{"className":1236,"style":1237},[1193],"height:1.55em;",[1239],{"type":10,"tag":181,"props":1240,"children":1241},{},[],{"type":10,"tag":181,"props":1243,"children":1246},{"className":1244},[1245],"mord",[1247],{"type":10,"tag":181,"props":1248,"children":1250},{"className":1249},[221],[1251,1257,1399],{"type":10,"tag":181,"props":1252,"children":1256},{"className":1253,"style":1255},[1254],"arraycolsep","width:0.5em;",[],{"type":10,"tag":181,"props":1258,"children":1261},{"className":1259},[1260],"col-align-c",[1262],{"type":10,"tag":181,"props":1263,"children":1265},{"className":1264},[1182,1183],[1266,1388],{"type":10,"tag":181,"props":1267,"children":1269},{"className":1268},[1188],[1270,1383],{"type":10,"tag":181,"props":1271,"children":1273},{"className":1272,"style":1194},[1193],[1274,1308,1346],{"type":10,"tag":181,"props":1275,"children":1277},{"style":1276},"top:-4.21em;",[1278,1283],{"type":10,"tag":181,"props":1279,"children":1282},{"className":1280,"style":1281},[1203],"height:3em;",[],{"type":10,"tag":181,"props":1284,"children":1286},{"className":1285},[1245],[1287,1293,1299],{"type":10,"tag":181,"props":1288,"children":1291},{"className":1289},[1245,1290],"mathnormal",[1292],{"type":16,"value":249},{"type":10,"tag":181,"props":1294,"children":1297},{"className":1295,"style":1296},[1245],"margin-right:0.02778em;",[1298],{"type":16,"value":255},{"type":10,"tag":181,"props":1300,"children":1302},{"className":1301},[1245],[1303],{"type":10,"tag":181,"props":1304,"children":1306},{"className":1305,"style":1296},[1245,1290],[1307],{"type":16,"value":177},{"type":10,"tag":181,"props":1309,"children":1311},{"style":1310},"top:-3.01em;",[1312,1316],{"type":10,"tag":181,"props":1313,"children":1315},{"className":1314,"style":1281},[1203],[],{"type":10,"tag":181,"props":1317,"children":1319},{"className":1318},[1245],[1320,1326,1332,1337],{"type":10,"tag":181,"props":1321,"children":1324},{"className":1322},[1323],"mspace",[1325],{"type":16,"value":277},{"type":10,"tag":181,"props":1327,"children":1330},{"className":1328,"style":1329},[1245,1290],"margin-right:0.03588em;",[1331],{"type":16,"value":282},{"type":10,"tag":181,"props":1333,"children":1335},{"className":1334,"style":1296},[1245],[1336],{"type":16,"value":255},{"type":10,"tag":181,"props":1338,"children":1340},{"className":1339},[1245],[1341],{"type":10,"tag":181,"props":1342,"children":1344},{"className":1343,"style":1296},[1245,1290],[1345],{"type":16,"value":177},{"type":10,"tag":181,"props":1347,"children":1349},{"style":1348},"top:-1.81em;",[1350,1354],{"type":10,"tag":181,"props":1351,"children":1353},{"className":1352,"style":1281},[1203],[],{"type":10,"tag":181,"props":1355,"children":1357},{"className":1356},[1245],[1358,1363,1369,1374],{"type":10,"tag":181,"props":1359,"children":1361},{"className":1360},[1323],[1362],{"type":16,"value":277},{"type":10,"tag":181,"props":1364,"children":1367},{"className":1365,"style":1366},[1245,1290],"margin-right:0.04398em;",[1368],{"type":16,"value":311},{"type":10,"tag":181,"props":1370,"children":1372},{"className":1371,"style":1296},[1245],[1373],{"type":16,"value":255},{"type":10,"tag":181,"props":1375,"children":1377},{"className":1376},[1245],[1378],{"type":10,"tag":181,"props":1379,"children":1381},{"className":1380,"style":1296},[1245,1290],[1382],{"type":16,"value":177},{"type":10,"tag":181,"props":1384,"children":1386},{"className":1385},[1226],[1387],{"type":16,"value":1229},{"type":10,"tag":181,"props":1389,"children":1391},{"className":1390},[1188],[1392],{"type":10,"tag":181,"props":1393,"children":1395},{"className":1394,"style":1237},[1193],[1396],{"type":10,"tag":181,"props":1397,"children":1398},{},[],{"type":10,"tag":181,"props":1400,"children":1402},{"className":1401,"style":1255},[1254],[],{"type":10,"tag":181,"props":1404,"children":1407},{"className":1405},[1406],"mclose",[1408],{"type":10,"tag":181,"props":1409,"children":1411},{"className":1410},[1176,1177],[1412],{"type":10,"tag":181,"props":1413,"children":1415},{"className":1414},[1182,1183],[1416,1446],{"type":10,"tag":181,"props":1417,"children":1419},{"className":1418},[1188],[1420,1441],{"type":10,"tag":181,"props":1421,"children":1423},{"className":1422,"style":1194},[1193],[1424],{"type":10,"tag":181,"props":1425,"children":1426},{"style":1198},[1427,1431],{"type":10,"tag":181,"props":1428,"children":1430},{"className":1429,"style":1204},[1203],[],{"type":10,"tag":181,"props":1432,"children":1433},{"style":1208},[1434],{"type":10,"tag":1211,"props":1435,"children":1436},{"xmlns":1213,"width":1214,"height":1215,"viewBox":1216},[1437],{"type":10,"tag":1219,"props":1438,"children":1440},{"d":1439},"M76,0c-16.7,0,-25,3,-25,9c0,2,2,6.3,6,13c21.3,28.7,42.3,60.3,\n63,95c96.7,156.7,172.8,332.5,228.5,527.5c55.7,195,92.8,416.5,111.5,664.5\nc11.3,139.3,17,290.7,17,454c0,28,1.7,43,3.3,45l0,9\nc-3,4,-3.3,16.7,-3.3,38c0,162,-5.7,313.7,-17,455c-18.7,248,-55.8,469.3,-111.5,664\nc-55.7,194.7,-131.8,370.3,-228.5,527c-20.7,34.7,-41.7,66.3,-63,95c-2,3.3,-4,7,-6,11\nc0,7.3,5.7,11,17,11c0,0,11,0,11,0c9.3,0,14.3,-0.3,15,-1c5.3,-5.3,10.3,-11,15,-17\nc242.7,-294.7,395.3,-681.7,458,-1161c21.3,-164.7,33.3,-350.7,36,-558\nl0,-144c-2,-159.3,-10,-310.7,-24,-454c-53.3,-528,-210,-949.7,\n-470,-1265c-4.7,-6,-9.7,-11.7,-15,-17c-0.7,-0.7,-6.7,-1,-18,-1z",[],{"type":10,"tag":181,"props":1442,"children":1444},{"className":1443},[1226],[1445],{"type":16,"value":1229},{"type":10,"tag":181,"props":1447,"children":1449},{"className":1448},[1188],[1450],{"type":10,"tag":181,"props":1451,"children":1453},{"className":1452,"style":1237},[1193],[1454],{"type":10,"tag":181,"props":1455,"children":1456},{},[],{"type":10,"tag":181,"props":1458,"children":1461},{"className":1459,"style":1460},[1323],"margin-right:0.2778em;",[],{"type":10,"tag":181,"props":1463,"children":1466},{"className":1464},[1465],"mrel",[1467],{"type":16,"value":329},{"type":10,"tag":181,"props":1469,"children":1471},{"className":1470,"style":1460},[1323],[],{"type":10,"tag":181,"props":1473,"children":1475},{"className":1474},[1155],[1476,1480,2709,2714],{"type":10,"tag":181,"props":1477,"children":1479},{"className":1478,"style":1161},[1160],[],{"type":10,"tag":181,"props":1481,"children":1483},{"className":1482},[1166],[1484,1536,2657],{"type":10,"tag":181,"props":1485,"children":1487},{"className":1486},[1171],[1488],{"type":10,"tag":181,"props":1489,"children":1491},{"className":1490},[1176,1177],[1492],{"type":10,"tag":181,"props":1493,"children":1495},{"className":1494},[1182,1183],[1496,1525],{"type":10,"tag":181,"props":1497,"children":1499},{"className":1498},[1188],[1500,1520],{"type":10,"tag":181,"props":1501,"children":1503},{"className":1502,"style":1194},[1193],[1504],{"type":10,"tag":181,"props":1505,"children":1506},{"style":1198},[1507,1511],{"type":10,"tag":181,"props":1508,"children":1510},{"className":1509,"style":1204},[1203],[],{"type":10,"tag":181,"props":1512,"children":1513},{"style":1208},[1514],{"type":10,"tag":1211,"props":1515,"children":1516},{"xmlns":1213,"width":1214,"height":1215,"viewBox":1216},[1517],{"type":10,"tag":1219,"props":1518,"children":1519},{"d":1221},[],{"type":10,"tag":181,"props":1521,"children":1523},{"className":1522},[1226],[1524],{"type":16,"value":1229},{"type":10,"tag":181,"props":1526,"children":1528},{"className":1527},[1188],[1529],{"type":10,"tag":181,"props":1530,"children":1532},{"className":1531,"style":1237},[1193],[1533],{"type":10,"tag":181,"props":1534,"children":1535},{},[],{"type":10,"tag":181,"props":1537,"children":1539},{"className":1538},[1245],[1540],{"type":10,"tag":181,"props":1541,"children":1543},{"className":1542},[221],[1544,1923,1927,1931,2290,2294,2298],{"type":10,"tag":181,"props":1545,"children":1547},{"className":1546},[1260],[1548],{"type":10,"tag":181,"props":1549,"children":1551},{"className":1550},[1182,1183],[1552,1912],{"type":10,"tag":181,"props":1553,"children":1555},{"className":1554},[1188],[1556,1907],{"type":10,"tag":181,"props":1557,"children":1559},{"className":1558,"style":1194},[1193],[1560,1683,1795],{"type":10,"tag":181,"props":1561,"children":1562},{"style":1276},[1563,1567],{"type":10,"tag":181,"props":1564,"children":1566},{"className":1565,"style":1281},[1203],[],{"type":10,"tag":181,"props":1568,"children":1570},{"className":1569},[1245],[1571,1576,1581,1630,1635,1640,1645,1651,1655,1660,1665,1669,1674,1678],{"type":10,"tag":181,"props":1572,"children":1574},{"className":1573},[1245,1290],[1575],{"type":16,"value":44},{"type":10,"tag":181,"props":1577,"children":1579},{"className":1578,"style":1296},[1245],[1580],{"type":16,"value":255},{"type":10,"tag":181,"props":1582,"children":1584},{"className":1583},[1245],[1585,1590],{"type":10,"tag":181,"props":1586,"children":1588},{"className":1587},[1245,1290],[1589],{"type":16,"value":249},{"type":10,"tag":181,"props":1591,"children":1594},{"className":1592},[1593],"msupsub",[1595],{"type":10,"tag":181,"props":1596,"children":1598},{"className":1597},[1182],[1599],{"type":10,"tag":181,"props":1600,"children":1602},{"className":1601},[1188],[1603],{"type":10,"tag":181,"props":1604,"children":1607},{"className":1605,"style":1606},[1193],"height:0.8141em;",[1608],{"type":10,"tag":181,"props":1609,"children":1611},{"style":1610},"top:-3.063em;margin-right:0.05em;",[1612,1617],{"type":10,"tag":181,"props":1613,"children":1616},{"className":1614,"style":1615},[1203],"height:2.7em;",[],{"type":10,"tag":181,"props":1618,"children":1624},{"className":1619},[1620,1621,1622,1623],"sizing","reset-size6","size3","mtight",[1625],{"type":10,"tag":181,"props":1626,"children":1628},{"className":1627},[1245,1623],[1629],{"type":16,"value":374},{"type":10,"tag":181,"props":1631,"children":1633},{"className":1632},[1171],[1634],{"type":16,"value":219},{"type":10,"tag":181,"props":1636,"children":1638},{"className":1637},[1245],[1639],{"type":16,"value":383},{"type":10,"tag":181,"props":1641,"children":1644},{"className":1642,"style":1643},[1323],"margin-right:0.2222em;",[],{"type":10,"tag":181,"props":1646,"children":1649},{"className":1647},[1648],"mbin",[1650],{"type":16,"value":388},{"type":10,"tag":181,"props":1652,"children":1654},{"className":1653,"style":1643},[1323],[],{"type":10,"tag":181,"props":1656,"children":1658},{"className":1657},[1245,1290],[1659],{"type":16,"value":393},{"type":10,"tag":181,"props":1661,"children":1663},{"className":1662},[1406],[1664],{"type":16,"value":324},{"type":10,"tag":181,"props":1666,"children":1668},{"className":1667,"style":1643},[1323],[],{"type":10,"tag":181,"props":1670,"children":1672},{"className":1671},[1648],[1673],{"type":16,"value":402},{"type":10,"tag":181,"props":1675,"children":1677},{"className":1676,"style":1643},[1323],[],{"type":10,"tag":181,"props":1679,"children":1681},{"className":1680},[1245,1290],[1682],{"type":16,"value":393},{"type":10,"tag":181,"props":1684,"children":1685},{"style":1310},[1686,1690],{"type":10,"tag":181,"props":1687,"children":1689},{"className":1688,"style":1281},[1203],[],{"type":10,"tag":181,"props":1691,"children":1693},{"className":1692},[1245],[1694,1699,1704,1709,1714,1719,1724,1729,1734,1739,1743,1748,1752,1757,1762,1766,1771,1775,1780,1785,1790],{"type":10,"tag":181,"props":1695,"children":1697},{"className":1696},[1323],[1698],{"type":16,"value":277},{"type":10,"tag":181,"props":1700,"children":1702},{"className":1701},[1245,1290],[1703],{"type":16,"value":44},{"type":10,"tag":181,"props":1705,"children":1707},{"className":1706,"style":1296},[1245],[1708],{"type":16,"value":255},{"type":10,"tag":181,"props":1710,"children":1712},{"className":1711},[1245,1290],[1713],{"type":16,"value":249},{"type":10,"tag":181,"props":1715,"children":1717},{"className":1716},[1245,1290],[1718],{"type":16,"value":44},{"type":10,"tag":181,"props":1720,"children":1722},{"className":1721,"style":1296},[1245],[1723],{"type":16,"value":255},{"type":10,"tag":181,"props":1725,"children":1727},{"className":1726,"style":1329},[1245,1290],[1728],{"type":16,"value":282},{"type":10,"tag":181,"props":1730,"children":1732},{"className":1731},[1171],[1733],{"type":16,"value":219},{"type":10,"tag":181,"props":1735,"children":1737},{"className":1736},[1245],[1738],{"type":16,"value":383},{"type":10,"tag":181,"props":1740,"children":1742},{"className":1741,"style":1643},[1323],[],{"type":10,"tag":181,"props":1744,"children":1746},{"className":1745},[1648],[1747],{"type":16,"value":388},{"type":10,"tag":181,"props":1749,"children":1751},{"className":1750,"style":1643},[1323],[],{"type":10,"tag":181,"props":1753,"children":1755},{"className":1754},[1245,1290],[1756],{"type":16,"value":393},{"type":10,"tag":181,"props":1758,"children":1760},{"className":1759},[1406],[1761],{"type":16,"value":324},{"type":10,"tag":181,"props":1763,"children":1765},{"className":1764,"style":1643},[1323],[],{"type":10,"tag":181,"props":1767,"children":1769},{"className":1768},[1648],[1770],{"type":16,"value":402},{"type":10,"tag":181,"props":1772,"children":1774},{"className":1773,"style":1643},[1323],[],{"type":10,"tag":181,"props":1776,"children":1778},{"className":1777},[1245,1290],[1779],{"type":16,"value":468},{"type":10,"tag":181,"props":1781,"children":1783},{"className":1782},[1245,1290],[1784],{"type":16,"value":44},{"type":10,"tag":181,"props":1786,"children":1788},{"className":1787,"style":1296},[1245],[1789],{"type":16,"value":255},{"type":10,"tag":181,"props":1791,"children":1793},{"className":1792,"style":1366},[1245,1290],[1794],{"type":16,"value":311},{"type":10,"tag":181,"props":1796,"children":1797},{"style":1348},[1798,1802],{"type":10,"tag":181,"props":1799,"children":1801},{"className":1800,"style":1281},[1203],[],{"type":10,"tag":181,"props":1803,"children":1805},{"className":1804},[1245],[1806,1811,1816,1821,1826,1831,1836,1841,1846,1851,1855,1860,1864,1869,1874,1878,1883,1887,1892,1897,1902],{"type":10,"tag":181,"props":1807,"children":1809},{"className":1808},[1323],[1810],{"type":16,"value":277},{"type":10,"tag":181,"props":1812,"children":1814},{"className":1813},[1245,1290],[1815],{"type":16,"value":44},{"type":10,"tag":181,"props":1817,"children":1819},{"className":1818,"style":1296},[1245],[1820],{"type":16,"value":255},{"type":10,"tag":181,"props":1822,"children":1824},{"className":1823},[1245,1290],[1825],{"type":16,"value":249},{"type":10,"tag":181,"props":1827,"children":1829},{"className":1828},[1245,1290],[1830],{"type":16,"value":44},{"type":10,"tag":181,"props":1832,"children":1834},{"className":1833,"style":1296},[1245],[1835],{"type":16,"value":255},{"type":10,"tag":181,"props":1837,"children":1839},{"className":1838,"style":1366},[1245,1290],[1840],{"type":16,"value":311},{"type":10,"tag":181,"props":1842,"children":1844},{"className":1843},[1171],[1845],{"type":16,"value":219},{"type":10,"tag":181,"props":1847,"children":1849},{"className":1848},[1245],[1850],{"type":16,"value":383},{"type":10,"tag":181,"props":1852,"children":1854},{"className":1853,"style":1643},[1323],[],{"type":10,"tag":181,"props":1856,"children":1858},{"className":1857},[1648],[1859],{"type":16,"value":388},{"type":10,"tag":181,"props":1861,"children":1863},{"className":1862,"style":1643},[1323],[],{"type":10,"tag":181,"props":1865,"children":1867},{"className":1866},[1245,1290],[1868],{"type":16,"value":393},{"type":10,"tag":181,"props":1870,"children":1872},{"className":1871},[1406],[1873],{"type":16,"value":324},{"type":10,"tag":181,"props":1875,"children":1877},{"className":1876,"style":1643},[1323],[],{"type":10,"tag":181,"props":1879,"children":1881},{"className":1880},[1648],[1882],{"type":16,"value":388},{"type":10,"tag":181,"props":1884,"children":1886},{"className":1885,"style":1643},[1323],[],{"type":10,"tag":181,"props":1888,"children":1890},{"className":1889},[1245,1290],[1891],{"type":16,"value":468},{"type":10,"tag":181,"props":1893,"children":1895},{"className":1894},[1245,1290],[1896],{"type":16,"value":44},{"type":10,"tag":181,"props":1898,"children":1900},{"className":1899,"style":1296},[1245],[1901],{"type":16,"value":255},{"type":10,"tag":181,"props":1903,"children":1905},{"className":1904,"style":1329},[1245,1290],[1906],{"type":16,"value":282},{"type":10,"tag":181,"props":1908,"children":1910},{"className":1909},[1226],[1911],{"type":16,"value":1229},{"type":10,"tag":181,"props":1913,"children":1915},{"className":1914},[1188],[1916],{"type":10,"tag":181,"props":1917,"children":1919},{"className":1918,"style":1237},[1193],[1920],{"type":10,"tag":181,"props":1921,"children":1922},{},[],{"type":10,"tag":181,"props":1924,"children":1926},{"className":1925,"style":1255},[1254],[],{"type":10,"tag":181,"props":1928,"children":1930},{"className":1929,"style":1255},[1254],[],{"type":10,"tag":181,"props":1932,"children":1934},{"className":1933},[1260],[1935],{"type":10,"tag":181,"props":1936,"children":1938},{"className":1937},[1182,1183],[1939,2279],{"type":10,"tag":181,"props":1940,"children":1942},{"className":1941},[1188],[1943,2274],{"type":10,"tag":181,"props":1944,"children":1946},{"className":1945,"style":1194},[1193],[1947,2054,2167],{"type":10,"tag":181,"props":1948,"children":1949},{"style":1276},[1950,1954],{"type":10,"tag":181,"props":1951,"children":1953},{"className":1952,"style":1281},[1203],[],{"type":10,"tag":181,"props":1955,"children":1957},{"className":1956},[1245],[1958,1963,1968,1973,1978,1983,1988,1993,1998,2002,2007,2011,2016,2021,2025,2030,2034,2039,2044,2049],{"type":10,"tag":181,"props":1959,"children":1961},{"className":1960},[1245,1290],[1962],{"type":16,"value":44},{"type":10,"tag":181,"props":1964,"children":1966},{"className":1965,"style":1296},[1245],[1967],{"type":16,"value":255},{"type":10,"tag":181,"props":1969,"children":1971},{"className":1970},[1245,1290],[1972],{"type":16,"value":249},{"type":10,"tag":181,"props":1974,"children":1976},{"className":1975},[1245,1290],[1977],{"type":16,"value":44},{"type":10,"tag":181,"props":1979,"children":1981},{"className":1980,"style":1296},[1245],[1982],{"type":16,"value":255},{"type":10,"tag":181,"props":1984,"children":1986},{"className":1985,"style":1329},[1245,1290],[1987],{"type":16,"value":282},{"type":10,"tag":181,"props":1989,"children":1991},{"className":1990},[1171],[1992],{"type":16,"value":219},{"type":10,"tag":181,"props":1994,"children":1996},{"className":1995},[1245],[1997],{"type":16,"value":383},{"type":10,"tag":181,"props":1999,"children":2001},{"className":2000,"style":1643},[1323],[],{"type":10,"tag":181,"props":2003,"children":2005},{"className":2004},[1648],[2006],{"type":16,"value":388},{"type":10,"tag":181,"props":2008,"children":2010},{"className":2009,"style":1643},[1323],[],{"type":10,"tag":181,"props":2012,"children":2014},{"className":2013},[1245,1290],[2015],{"type":16,"value":393},{"type":10,"tag":181,"props":2017,"children":2019},{"className":2018},[1406],[2020],{"type":16,"value":324},{"type":10,"tag":181,"props":2022,"children":2024},{"className":2023,"style":1643},[1323],[],{"type":10,"tag":181,"props":2026,"children":2028},{"className":2027},[1648],[2029],{"type":16,"value":388},{"type":10,"tag":181,"props":2031,"children":2033},{"className":2032,"style":1643},[1323],[],{"type":10,"tag":181,"props":2035,"children":2037},{"className":2036},[1245,1290],[2038],{"type":16,"value":468},{"type":10,"tag":181,"props":2040,"children":2042},{"className":2041},[1245,1290],[2043],{"type":16,"value":44},{"type":10,"tag":181,"props":2045,"children":2047},{"className":2046,"style":1296},[1245],[2048],{"type":16,"value":255},{"type":10,"tag":181,"props":2050,"children":2052},{"className":2051,"style":1366},[1245,1290],[2053],{"type":16,"value":311},{"type":10,"tag":181,"props":2055,"children":2056},{"style":1310},[2057,2061],{"type":10,"tag":181,"props":2058,"children":2060},{"className":2059,"style":1281},[1203],[],{"type":10,"tag":181,"props":2062,"children":2064},{"className":2063},[1245],[2065,2070,2075,2116,2121,2126,2130,2135,2139,2144,2149,2153,2158,2162],{"type":10,"tag":181,"props":2066,"children":2068},{"className":2067},[1245,1290],[2069],{"type":16,"value":44},{"type":10,"tag":181,"props":2071,"children":2073},{"className":2072,"style":1296},[1245],[2074],{"type":16,"value":255},{"type":10,"tag":181,"props":2076,"children":2078},{"className":2077},[1245],[2079,2084],{"type":10,"tag":181,"props":2080,"children":2082},{"className":2081,"style":1329},[1245,1290],[2083],{"type":16,"value":282},{"type":10,"tag":181,"props":2085,"children":2087},{"className":2086},[1593],[2088],{"type":10,"tag":181,"props":2089,"children":2091},{"className":2090},[1182],[2092],{"type":10,"tag":181,"props":2093,"children":2095},{"className":2094},[1188],[2096],{"type":10,"tag":181,"props":2097,"children":2099},{"className":2098,"style":1606},[1193],[2100],{"type":10,"tag":181,"props":2101,"children":2102},{"style":1610},[2103,2107],{"type":10,"tag":181,"props":2104,"children":2106},{"className":2105,"style":1615},[1203],[],{"type":10,"tag":181,"props":2108,"children":2110},{"className":2109},[1620,1621,1622,1623],[2111],{"type":10,"tag":181,"props":2112,"children":2114},{"className":2113},[1245,1623],[2115],{"type":16,"value":374},{"type":10,"tag":181,"props":2117,"children":2119},{"className":2118},[1171],[2120],{"type":16,"value":219},{"type":10,"tag":181,"props":2122,"children":2124},{"className":2123},[1245],[2125],{"type":16,"value":383},{"type":10,"tag":181,"props":2127,"children":2129},{"className":2128,"style":1643},[1323],[],{"type":10,"tag":181,"props":2131,"children":2133},{"className":2132},[1648],[2134],{"type":16,"value":388},{"type":10,"tag":181,"props":2136,"children":2138},{"className":2137,"style":1643},[1323],[],{"type":10,"tag":181,"props":2140,"children":2142},{"className":2141},[1245,1290],[2143],{"type":16,"value":393},{"type":10,"tag":181,"props":2145,"children":2147},{"className":2146},[1406],[2148],{"type":16,"value":324},{"type":10,"tag":181,"props":2150,"children":2152},{"className":2151,"style":1643},[1323],[],{"type":10,"tag":181,"props":2154,"children":2156},{"className":2155},[1648],[2157],{"type":16,"value":402},{"type":10,"tag":181,"props":2159,"children":2161},{"className":2160,"style":1643},[1323],[],{"type":10,"tag":181,"props":2163,"children":2165},{"className":2164},[1245,1290],[2166],{"type":16,"value":393},{"type":10,"tag":181,"props":2168,"children":2169},{"style":1348},[2170,2174],{"type":10,"tag":181,"props":2171,"children":2173},{"className":2172,"style":1281},[1203],[],{"type":10,"tag":181,"props":2175,"children":2177},{"className":2176},[1245],[2178,2183,2188,2193,2198,2203,2208,2213,2218,2222,2227,2231,2236,2241,2245,2250,2254,2259,2264,2269],{"type":10,"tag":181,"props":2179,"children":2181},{"className":2180},[1245,1290],[2182],{"type":16,"value":44},{"type":10,"tag":181,"props":2184,"children":2186},{"className":2185,"style":1296},[1245],[2187],{"type":16,"value":255},{"type":10,"tag":181,"props":2189,"children":2191},{"className":2190,"style":1329},[1245,1290],[2192],{"type":16,"value":282},{"type":10,"tag":181,"props":2194,"children":2196},{"className":2195},[1245,1290],[2197],{"type":16,"value":44},{"type":10,"tag":181,"props":2199,"children":2201},{"className":2200,"style":1296},[1245],[2202],{"type":16,"value":255},{"type":10,"tag":181,"props":2204,"children":2206},{"className":2205,"style":1366},[1245,1290],[2207],{"type":16,"value":311},{"type":10,"tag":181,"props":2209,"children":2211},{"className":2210},[1171],[2212],{"type":16,"value":219},{"type":10,"tag":181,"props":2214,"children":2216},{"className":2215},[1245],[2217],{"type":16,"value":383},{"type":10,"tag":181,"props":2219,"children":2221},{"className":2220,"style":1643},[1323],[],{"type":10,"tag":181,"props":2223,"children":2225},{"className":2224},[1648],[2226],{"type":16,"value":388},{"type":10,"tag":181,"props":2228,"children":2230},{"className":2229,"style":1643},[1323],[],{"type":10,"tag":181,"props":2232,"children":2234},{"className":2233},[1245,1290],[2235],{"type":16,"value":393},{"type":10,"tag":181,"props":2237,"children":2239},{"className":2238},[1406],[2240],{"type":16,"value":324},{"type":10,"tag":181,"props":2242,"children":2244},{"className":2243,"style":1643},[1323],[],{"type":10,"tag":181,"props":2246,"children":2248},{"className":2247},[1648],[2249],{"type":16,"value":402},{"type":10,"tag":181,"props":2251,"children":2253},{"className":2252,"style":1643},[1323],[],{"type":10,"tag":181,"props":2255,"children":2257},{"className":2256},[1245,1290],[2258],{"type":16,"value":468},{"type":10,"tag":181,"props":2260,"children":2262},{"className":2261},[1245,1290],[2263],{"type":16,"value":44},{"type":10,"tag":181,"props":2265,"children":2267},{"className":2266,"style":1296},[1245],[2268],{"type":16,"value":255},{"type":10,"tag":181,"props":2270,"children":2272},{"className":2271},[1245,1290],[2273],{"type":16,"value":249},{"type":10,"tag":181,"props":2275,"children":2277},{"className":2276},[1226],[2278],{"type":16,"value":1229},{"type":10,"tag":181,"props":2280,"children":2282},{"className":2281},[1188],[2283],{"type":10,"tag":181,"props":2284,"children":2286},{"className":2285,"style":1237},[1193],[2287],{"type":10,"tag":181,"props":2288,"children":2289},{},[],{"type":10,"tag":181,"props":2291,"children":2293},{"className":2292,"style":1255},[1254],[],{"type":10,"tag":181,"props":2295,"children":2297},{"className":2296,"style":1255},[1254],[],{"type":10,"tag":181,"props":2299,"children":2301},{"className":2300},[1260],[2302],{"type":10,"tag":181,"props":2303,"children":2305},{"className":2304},[1182,1183],[2306,2646],{"type":10,"tag":181,"props":2307,"children":2309},{"className":2308},[1188],[2310,2641],{"type":10,"tag":181,"props":2311,"children":2313},{"className":2312,"style":1194},[1193],[2314,2421,2528],{"type":10,"tag":181,"props":2315,"children":2316},{"style":1276},[2317,2321],{"type":10,"tag":181,"props":2318,"children":2320},{"className":2319,"style":1281},[1203],[],{"type":10,"tag":181,"props":2322,"children":2324},{"className":2323},[1245],[2325,2330,2335,2340,2345,2350,2355,2360,2365,2369,2374,2378,2383,2388,2392,2397,2401,2406,2411,2416],{"type":10,"tag":181,"props":2326,"children":2328},{"className":2327},[1245,1290],[2329],{"type":16,"value":44},{"type":10,"tag":181,"props":2331,"children":2333},{"className":2332,"style":1296},[1245],[2334],{"type":16,"value":255},{"type":10,"tag":181,"props":2336,"children":2338},{"className":2337},[1245,1290],[2339],{"type":16,"value":249},{"type":10,"tag":181,"props":2341,"children":2343},{"className":2342},[1245,1290],[2344],{"type":16,"value":44},{"type":10,"tag":181,"props":2346,"children":2348},{"className":2347,"style":1296},[1245],[2349],{"type":16,"value":255},{"type":10,"tag":181,"props":2351,"children":2353},{"className":2352,"style":1366},[1245,1290],[2354],{"type":16,"value":311},{"type":10,"tag":181,"props":2356,"children":2358},{"className":2357},[1171],[2359],{"type":16,"value":219},{"type":10,"tag":181,"props":2361,"children":2363},{"className":2362},[1245],[2364],{"type":16,"value":383},{"type":10,"tag":181,"props":2366,"children":2368},{"className":2367,"style":1643},[1323],[],{"type":10,"tag":181,"props":2370,"children":2372},{"className":2371},[1648],[2373],{"type":16,"value":388},{"type":10,"tag":181,"props":2375,"children":2377},{"className":2376,"style":1643},[1323],[],{"type":10,"tag":181,"props":2379,"children":2381},{"className":2380},[1245,1290],[2382],{"type":16,"value":393},{"type":10,"tag":181,"props":2384,"children":2386},{"className":2385},[1406],[2387],{"type":16,"value":324},{"type":10,"tag":181,"props":2389,"children":2391},{"className":2390,"style":1643},[1323],[],{"type":10,"tag":181,"props":2393,"children":2395},{"className":2394},[1648],[2396],{"type":16,"value":402},{"type":10,"tag":181,"props":2398,"children":2400},{"className":2399,"style":1643},[1323],[],{"type":10,"tag":181,"props":2402,"children":2404},{"className":2403},[1245,1290],[2405],{"type":16,"value":468},{"type":10,"tag":181,"props":2407,"children":2409},{"className":2408},[1245,1290],[2410],{"type":16,"value":44},{"type":10,"tag":181,"props":2412,"children":2414},{"className":2413,"style":1296},[1245],[2415],{"type":16,"value":255},{"type":10,"tag":181,"props":2417,"children":2419},{"className":2418,"style":1329},[1245,1290],[2420],{"type":16,"value":282},{"type":10,"tag":181,"props":2422,"children":2423},{"style":1310},[2424,2428],{"type":10,"tag":181,"props":2425,"children":2427},{"className":2426,"style":1281},[1203],[],{"type":10,"tag":181,"props":2429,"children":2431},{"className":2430},[1245],[2432,2437,2442,2447,2452,2457,2462,2467,2472,2476,2481,2485,2490,2495,2499,2504,2508,2513,2518,2523],{"type":10,"tag":181,"props":2433,"children":2435},{"className":2434},[1245,1290],[2436],{"type":16,"value":44},{"type":10,"tag":181,"props":2438,"children":2440},{"className":2439,"style":1296},[1245],[2441],{"type":16,"value":255},{"type":10,"tag":181,"props":2443,"children":2445},{"className":2444,"style":1329},[1245,1290],[2446],{"type":16,"value":282},{"type":10,"tag":181,"props":2448,"children":2450},{"className":2449},[1245,1290],[2451],{"type":16,"value":44},{"type":10,"tag":181,"props":2453,"children":2455},{"className":2454,"style":1296},[1245],[2456],{"type":16,"value":255},{"type":10,"tag":181,"props":2458,"children":2460},{"className":2459,"style":1366},[1245,1290],[2461],{"type":16,"value":311},{"type":10,"tag":181,"props":2463,"children":2465},{"className":2464},[1171],[2466],{"type":16,"value":219},{"type":10,"tag":181,"props":2468,"children":2470},{"className":2469},[1245],[2471],{"type":16,"value":383},{"type":10,"tag":181,"props":2473,"children":2475},{"className":2474,"style":1643},[1323],[],{"type":10,"tag":181,"props":2477,"children":2479},{"className":2478},[1648],[2480],{"type":16,"value":388},{"type":10,"tag":181,"props":2482,"children":2484},{"className":2483,"style":1643},[1323],[],{"type":10,"tag":181,"props":2486,"children":2488},{"className":2487},[1245,1290],[2489],{"type":16,"value":393},{"type":10,"tag":181,"props":2491,"children":2493},{"className":2492},[1406],[2494],{"type":16,"value":324},{"type":10,"tag":181,"props":2496,"children":2498},{"className":2497,"style":1643},[1323],[],{"type":10,"tag":181,"props":2500,"children":2502},{"className":2501},[1648],[2503],{"type":16,"value":388},{"type":10,"tag":181,"props":2505,"children":2507},{"className":2506,"style":1643},[1323],[],{"type":10,"tag":181,"props":2509,"children":2511},{"className":2510},[1245,1290],[2512],{"type":16,"value":468},{"type":10,"tag":181,"props":2514,"children":2516},{"className":2515},[1245,1290],[2517],{"type":16,"value":44},{"type":10,"tag":181,"props":2519,"children":2521},{"className":2520,"style":1296},[1245],[2522],{"type":16,"value":255},{"type":10,"tag":181,"props":2524,"children":2526},{"className":2525},[1245,1290],[2527],{"type":16,"value":249},{"type":10,"tag":181,"props":2529,"children":2530},{"style":1348},[2531,2535],{"type":10,"tag":181,"props":2532,"children":2534},{"className":2533,"style":1281},[1203],[],{"type":10,"tag":181,"props":2536,"children":2538},{"className":2537},[1245],[2539,2544,2549,2590,2595,2600,2604,2609,2613,2618,2623,2627,2632,2636],{"type":10,"tag":181,"props":2540,"children":2542},{"className":2541},[1245,1290],[2543],{"type":16,"value":44},{"type":10,"tag":181,"props":2545,"children":2547},{"className":2546,"style":1296},[1245],[2548],{"type":16,"value":255},{"type":10,"tag":181,"props":2550,"children":2552},{"className":2551},[1245],[2553,2558],{"type":10,"tag":181,"props":2554,"children":2556},{"className":2555,"style":1366},[1245,1290],[2557],{"type":16,"value":311},{"type":10,"tag":181,"props":2559,"children":2561},{"className":2560},[1593],[2562],{"type":10,"tag":181,"props":2563,"children":2565},{"className":2564},[1182],[2566],{"type":10,"tag":181,"props":2567,"children":2569},{"className":2568},[1188],[2570],{"type":10,"tag":181,"props":2571,"children":2573},{"className":2572,"style":1606},[1193],[2574],{"type":10,"tag":181,"props":2575,"children":2576},{"style":1610},[2577,2581],{"type":10,"tag":181,"props":2578,"children":2580},{"className":2579,"style":1615},[1203],[],{"type":10,"tag":181,"props":2582,"children":2584},{"className":2583},[1620,1621,1622,1623],[2585],{"type":10,"tag":181,"props":2586,"children":2588},{"className":2587},[1245,1623],[2589],{"type":16,"value":374},{"type":10,"tag":181,"props":2591,"children":2593},{"className":2592},[1171],[2594],{"type":16,"value":219},{"type":10,"tag":181,"props":2596,"children":2598},{"className":2597},[1245],[2599],{"type":16,"value":383},{"type":10,"tag":181,"props":2601,"children":2603},{"className":2602,"style":1643},[1323],[],{"type":10,"tag":181,"props":2605,"children":2607},{"className":2606},[1648],[2608],{"type":16,"value":388},{"type":10,"tag":181,"props":2610,"children":2612},{"className":2611,"style":1643},[1323],[],{"type":10,"tag":181,"props":2614,"children":2616},{"className":2615},[1245,1290],[2617],{"type":16,"value":393},{"type":10,"tag":181,"props":2619,"children":2621},{"className":2620},[1406],[2622],{"type":16,"value":324},{"type":10,"tag":181,"props":2624,"children":2626},{"className":2625,"style":1643},[1323],[],{"type":10,"tag":181,"props":2628,"children":2630},{"className":2629},[1648],[2631],{"type":16,"value":402},{"type":10,"tag":181,"props":2633,"children":2635},{"className":2634,"style":1643},[1323],[],{"type":10,"tag":181,"props":2637,"children":2639},{"className":2638},[1245,1290],[2640],{"type":16,"value":393},{"type":10,"tag":181,"props":2642,"children":2644},{"className":2643},[1226],[2645],{"type":16,"value":1229},{"type":10,"tag":181,"props":2647,"children":2649},{"className":2648},[1188],[2650],{"type":10,"tag":181,"props":2651,"children":2653},{"className":2652,"style":1237},[1193],[2654],{"type":10,"tag":181,"props":2655,"children":2656},{},[],{"type":10,"tag":181,"props":2658,"children":2660},{"className":2659},[1406],[2661],{"type":10,"tag":181,"props":2662,"children":2664},{"className":2663},[1176,1177],[2665],{"type":10,"tag":181,"props":2666,"children":2668},{"className":2667},[1182,1183],[2669,2698],{"type":10,"tag":181,"props":2670,"children":2672},{"className":2671},[1188],[2673,2693],{"type":10,"tag":181,"props":2674,"children":2676},{"className":2675,"style":1194},[1193],[2677],{"type":10,"tag":181,"props":2678,"children":2679},{"style":1198},[2680,2684],{"type":10,"tag":181,"props":2681,"children":2683},{"className":2682,"style":1204},[1203],[],{"type":10,"tag":181,"props":2685,"children":2686},{"style":1208},[2687],{"type":10,"tag":1211,"props":2688,"children":2689},{"xmlns":1213,"width":1214,"height":1215,"viewBox":1216},[2690],{"type":10,"tag":1219,"props":2691,"children":2692},{"d":1439},[],{"type":10,"tag":181,"props":2694,"children":2696},{"className":2695},[1226],[2697],{"type":16,"value":1229},{"type":10,"tag":181,"props":2699,"children":2701},{"className":2700},[1188],[2702],{"type":10,"tag":181,"props":2703,"children":2705},{"className":2704,"style":1237},[1193],[2706],{"type":10,"tag":181,"props":2707,"children":2708},{},[],{"type":10,"tag":181,"props":2710,"children":2713},{"className":2711,"style":2712},[1323],"margin-right:0.1667em;",[],{"type":10,"tag":181,"props":2715,"children":2717},{"className":2716},[1166],[2718,2770,3017],{"type":10,"tag":181,"props":2719,"children":2721},{"className":2720},[1171],[2722],{"type":10,"tag":181,"props":2723,"children":2725},{"className":2724},[1176,1177],[2726],{"type":10,"tag":181,"props":2727,"children":2729},{"className":2728},[1182,1183],[2730,2759],{"type":10,"tag":181,"props":2731,"children":2733},{"className":2732},[1188],[2734,2754],{"type":10,"tag":181,"props":2735,"children":2737},{"className":2736,"style":1194},[1193],[2738],{"type":10,"tag":181,"props":2739,"children":2740},{"style":1198},[2741,2745],{"type":10,"tag":181,"props":2742,"children":2744},{"className":2743,"style":1204},[1203],[],{"type":10,"tag":181,"props":2746,"children":2747},{"style":1208},[2748],{"type":10,"tag":1211,"props":2749,"children":2750},{"xmlns":1213,"width":1214,"height":1215,"viewBox":1216},[2751],{"type":10,"tag":1219,"props":2752,"children":2753},{"d":1221},[],{"type":10,"tag":181,"props":2755,"children":2757},{"className":2756},[1226],[2758],{"type":16,"value":1229},{"type":10,"tag":181,"props":2760,"children":2762},{"className":2761},[1188],[2763],{"type":10,"tag":181,"props":2764,"children":2766},{"className":2765,"style":1237},[1193],[2767],{"type":10,"tag":181,"props":2768,"children":2769},{},[],{"type":10,"tag":181,"props":2771,"children":2773},{"className":2772},[1245],[2774],{"type":10,"tag":181,"props":2775,"children":2777},{"className":2776},[221],[2778,2782,3013],{"type":10,"tag":181,"props":2779,"children":2781},{"className":2780,"style":1255},[1254],[],{"type":10,"tag":181,"props":2783,"children":2785},{"className":2784},[1260],[2786],{"type":10,"tag":181,"props":2787,"children":2789},{"className":2788},[1182,1183],[2790,3002],{"type":10,"tag":181,"props":2791,"children":2793},{"className":2792},[1188],[2794,2997],{"type":10,"tag":181,"props":2795,"children":2797},{"className":2796,"style":1194},[1193],[2798,2861,2929],{"type":10,"tag":181,"props":2799,"children":2800},{"style":1276},[2801,2805],{"type":10,"tag":181,"props":2802,"children":2804},{"className":2803,"style":1281},[1203],[],{"type":10,"tag":181,"props":2806,"children":2808},{"className":2807},[1245],[2809,2814,2819,2833,2837,2842,2846,2851,2856],{"type":10,"tag":181,"props":2810,"children":2812},{"className":2811},[1245,1290],[2813],{"type":16,"value":249},{"type":10,"tag":181,"props":2815,"children":2817},{"className":2816,"style":1296},[1245],[2818],{"type":16,"value":255},{"type":10,"tag":181,"props":2820,"children":2822},{"className":2821},[1245],[2823,2828],{"type":10,"tag":181,"props":2824,"children":2826},{"className":2825},[1245,1290],[2827],{"type":16,"value":44},{"type":10,"tag":181,"props":2829,"children":2831},{"className":2830},[1245,1290],[2832],{"type":16,"value":468},{"type":10,"tag":181,"props":2834,"children":2836},{"className":2835,"style":1643},[1323],[],{"type":10,"tag":181,"props":2838,"children":2840},{"className":2839},[1648],[2841],{"type":16,"value":388},{"type":10,"tag":181,"props":2843,"children":2845},{"className":2844,"style":1643},[1323],[],{"type":10,"tag":181,"props":2847,"children":2849},{"className":2848},[1245,1290],[2850],{"type":16,"value":1025},{"type":10,"tag":181,"props":2852,"children":2854},{"className":2853,"style":1296},[1245],[2855],{"type":16,"value":255},{"type":10,"tag":181,"props":2857,"children":2859},{"className":2858},[1245,1290],[2860],{"type":16,"value":249},{"type":10,"tag":181,"props":2862,"children":2863},{"style":1310},[2864,2868],{"type":10,"tag":181,"props":2865,"children":2867},{"className":2866,"style":1281},[1203],[],{"type":10,"tag":181,"props":2869,"children":2871},{"className":2870},[1245],[2872,2877,2882,2887,2901,2905,2910,2914,2919,2924],{"type":10,"tag":181,"props":2873,"children":2875},{"className":2874},[1323],[2876],{"type":16,"value":277},{"type":10,"tag":181,"props":2878,"children":2880},{"className":2879,"style":1329},[1245,1290],[2881],{"type":16,"value":282},{"type":10,"tag":181,"props":2883,"children":2885},{"className":2884,"style":1296},[1245],[2886],{"type":16,"value":255},{"type":10,"tag":181,"props":2888,"children":2890},{"className":2889},[1245],[2891,2896],{"type":10,"tag":181,"props":2892,"children":2894},{"className":2893},[1245,1290],[2895],{"type":16,"value":44},{"type":10,"tag":181,"props":2897,"children":2899},{"className":2898},[1245,1290],[2900],{"type":16,"value":468},{"type":10,"tag":181,"props":2902,"children":2904},{"className":2903,"style":1643},[1323],[],{"type":10,"tag":181,"props":2906,"children":2908},{"className":2907},[1648],[2909],{"type":16,"value":388},{"type":10,"tag":181,"props":2911,"children":2913},{"className":2912,"style":1643},[1323],[],{"type":10,"tag":181,"props":2915,"children":2917},{"className":2916},[1245,1290],[2918],{"type":16,"value":1025},{"type":10,"tag":181,"props":2920,"children":2922},{"className":2921,"style":1296},[1245],[2923],{"type":16,"value":255},{"type":10,"tag":181,"props":2925,"children":2927},{"className":2926,"style":1329},[1245,1290],[2928],{"type":16,"value":282},{"type":10,"tag":181,"props":2930,"children":2931},{"style":1348},[2932,2936],{"type":10,"tag":181,"props":2933,"children":2935},{"className":2934,"style":1281},[1203],[],{"type":10,"tag":181,"props":2937,"children":2939},{"className":2938},[1245],[2940,2945,2950,2955,2969,2973,2978,2982,2987,2992],{"type":10,"tag":181,"props":2941,"children":2943},{"className":2942},[1323],[2944],{"type":16,"value":277},{"type":10,"tag":181,"props":2946,"children":2948},{"className":2947,"style":1366},[1245,1290],[2949],{"type":16,"value":311},{"type":10,"tag":181,"props":2951,"children":2953},{"className":2952,"style":1296},[1245],[2954],{"type":16,"value":255},{"type":10,"tag":181,"props":2956,"children":2958},{"className":2957},[1245],[2959,2964],{"type":10,"tag":181,"props":2960,"children":2962},{"className":2961},[1245,1290],[2963],{"type":16,"value":44},{"type":10,"tag":181,"props":2965,"children":2967},{"className":2966},[1245,1290],[2968],{"type":16,"value":468},{"type":10,"tag":181,"props":2970,"children":2972},{"className":2971,"style":1643},[1323],[],{"type":10,"tag":181,"props":2974,"children":2976},{"className":2975},[1648],[2977],{"type":16,"value":388},{"type":10,"tag":181,"props":2979,"children":2981},{"className":2980,"style":1643},[1323],[],{"type":10,"tag":181,"props":2983,"children":2985},{"className":2984},[1245,1290],[2986],{"type":16,"value":1025},{"type":10,"tag":181,"props":2988,"children":2990},{"className":2989,"style":1296},[1245],[2991],{"type":16,"value":255},{"type":10,"tag":181,"props":2993,"children":2995},{"className":2994,"style":1366},[1245,1290],[2996],{"type":16,"value":311},{"type":10,"tag":181,"props":2998,"children":3000},{"className":2999},[1226],[3001],{"type":16,"value":1229},{"type":10,"tag":181,"props":3003,"children":3005},{"className":3004},[1188],[3006],{"type":10,"tag":181,"props":3007,"children":3009},{"className":3008,"style":1237},[1193],[3010],{"type":10,"tag":181,"props":3011,"children":3012},{},[],{"type":10,"tag":181,"props":3014,"children":3016},{"className":3015,"style":1255},[1254],[],{"type":10,"tag":181,"props":3018,"children":3020},{"className":3019},[1406],[3021],{"type":10,"tag":181,"props":3022,"children":3024},{"className":3023},[1176,1177],[3025],{"type":10,"tag":181,"props":3026,"children":3028},{"className":3027},[1182,1183],[3029,3058],{"type":10,"tag":181,"props":3030,"children":3032},{"className":3031},[1188],[3033,3053],{"type":10,"tag":181,"props":3034,"children":3036},{"className":3035,"style":1194},[1193],[3037],{"type":10,"tag":181,"props":3038,"children":3039},{"style":1198},[3040,3044],{"type":10,"tag":181,"props":3041,"children":3043},{"className":3042,"style":1204},[1203],[],{"type":10,"tag":181,"props":3045,"children":3046},{"style":1208},[3047],{"type":10,"tag":1211,"props":3048,"children":3049},{"xmlns":1213,"width":1214,"height":1215,"viewBox":1216},[3050],{"type":10,"tag":1219,"props":3051,"children":3052},{"d":1439},[],{"type":10,"tag":181,"props":3054,"children":3056},{"className":3055},[1226],[3057],{"type":16,"value":1229},{"type":10,"tag":181,"props":3059,"children":3061},{"className":3060},[1188],[3062],{"type":10,"tag":181,"props":3063,"children":3065},{"className":3064,"style":1237},[1193],[3066],{"type":10,"tag":181,"props":3067,"children":3068},{},[],{"type":10,"tag":18,"props":3070,"children":3071},{},[3072,3118,3120,3165,3167,3211],{"type":10,"tag":181,"props":3073,"children":3075},{"className":3074},[189],[3076,3099],{"type":10,"tag":181,"props":3077,"children":3079},{"className":3078},[194],[3080],{"type":10,"tag":197,"props":3081,"children":3082},{"xmlns":199},[3083],{"type":10,"tag":203,"props":3084,"children":3085},{},[3086,3094],{"type":10,"tag":207,"props":3087,"children":3088},{},[3089],{"type":10,"tag":245,"props":3090,"children":3092},{"mathvariant":3091},"bold",[3093],{"type":16,"value":44},{"type":10,"tag":1141,"props":3095,"children":3096},{"encoding":1143},[3097],{"type":16,"value":3098},"\\mathbf{a}",{"type":10,"tag":181,"props":3100,"children":3102},{"className":3101,"ariaHidden":216},[1150],[3103],{"type":10,"tag":181,"props":3104,"children":3106},{"className":3105},[1155],[3107,3112],{"type":10,"tag":181,"props":3108,"children":3111},{"className":3109,"style":3110},[1160],"height:0.4444em;",[],{"type":10,"tag":181,"props":3113,"children":3116},{"className":3114},[1245,3115],"mathbf",[3117],{"type":16,"value":44},{"type":16,"value":3119}," is the axis of rotation from the unnormalized ray\ndirection vector ",{"type":10,"tag":181,"props":3121,"children":3123},{"className":3122},[189],[3124,3147],{"type":10,"tag":181,"props":3125,"children":3127},{"className":3126},[194],[3128],{"type":10,"tag":197,"props":3129,"children":3130},{"xmlns":199},[3131],{"type":10,"tag":203,"props":3132,"children":3133},{},[3134,3142],{"type":10,"tag":207,"props":3135,"children":3136},{},[3137],{"type":10,"tag":245,"props":3138,"children":3139},{"mathvariant":3091},[3140],{"type":16,"value":3141},"d",{"type":10,"tag":1141,"props":3143,"children":3144},{"encoding":1143},[3145],{"type":16,"value":3146},"\\mathbf{d}",{"type":10,"tag":181,"props":3148,"children":3150},{"className":3149,"ariaHidden":216},[1150],[3151],{"type":10,"tag":181,"props":3152,"children":3154},{"className":3153},[1155],[3155,3160],{"type":10,"tag":181,"props":3156,"children":3159},{"className":3157,"style":3158},[1160],"height:0.6944em;",[],{"type":10,"tag":181,"props":3161,"children":3163},{"className":3162},[1245,3115],[3164],{"type":16,"value":3141},{"type":16,"value":3166}," to the axis vector\n",{"type":10,"tag":181,"props":3168,"children":3170},{"className":3169},[189],[3171,3194],{"type":10,"tag":181,"props":3172,"children":3174},{"className":3173},[194],[3175],{"type":10,"tag":197,"props":3176,"children":3177},{"xmlns":199},[3178],{"type":10,"tag":203,"props":3179,"children":3180},{},[3181,3189],{"type":10,"tag":207,"props":3182,"children":3183},{},[3184],{"type":10,"tag":245,"props":3185,"children":3186},{"mathvariant":3091},[3187],{"type":16,"value":3188},"k",{"type":10,"tag":1141,"props":3190,"children":3191},{"encoding":1143},[3192],{"type":16,"value":3193},"\\mathbf{k}",{"type":10,"tag":181,"props":3195,"children":3197},{"className":3196,"ariaHidden":216},[1150],[3198],{"type":10,"tag":181,"props":3199,"children":3201},{"className":3200},[1155],[3202,3206],{"type":10,"tag":181,"props":3203,"children":3205},{"className":3204,"style":3158},[1160],[],{"type":10,"tag":181,"props":3207,"children":3209},{"className":3208},[1245,3115],[3210],{"type":16,"value":3188},{"type":16,"value":3212},":",{"type":10,"tag":181,"props":3214,"children":3216},{"className":3215},[184],[3217],{"type":10,"tag":181,"props":3218,"children":3220},{"className":3219},[189],[3221,3559],{"type":10,"tag":181,"props":3222,"children":3224},{"className":3223},[194],[3225],{"type":10,"tag":197,"props":3226,"children":3227},{"xmlns":199,"display":200},[3228],{"type":10,"tag":203,"props":3229,"children":3230},{},[3231,3554],{"type":10,"tag":207,"props":3232,"children":3233},{},[3234,3238,3242],{"type":10,"tag":245,"props":3235,"children":3236},{"mathvariant":3091},[3237],{"type":16,"value":44},{"type":10,"tag":214,"props":3239,"children":3240},{},[3241],{"type":16,"value":329},{"type":10,"tag":207,"props":3243,"children":3244},{},[3245,3250],{"type":10,"tag":214,"props":3246,"children":3247},{"fence":216},[3248],{"type":16,"value":3249},"{",{"type":10,"tag":221,"props":3251,"children":3254},{"rowspacing":3252,"columnalign":3253,"columnspacing":225},"0.36em","left left",[3255,3335,3389,3489,3541],{"type":10,"tag":228,"props":3256,"children":3257},{},[3258,3316],{"type":10,"tag":232,"props":3259,"children":3260},{},[3261],{"type":10,"tag":236,"props":3262,"children":3263},{"scriptlevel":238,"displaystyle":239},[3264],{"type":10,"tag":3265,"props":3266,"children":3267},"mfrac",{},[3268,3284],{"type":10,"tag":207,"props":3269,"children":3270},{},[3271,3275,3280],{"type":10,"tag":245,"props":3272,"children":3273},{"mathvariant":3091},[3274],{"type":16,"value":3141},{"type":10,"tag":214,"props":3276,"children":3277},{},[3278],{"type":16,"value":3279},"×",{"type":10,"tag":245,"props":3281,"children":3282},{"mathvariant":3091},[3283],{"type":16,"value":3188},{"type":10,"tag":207,"props":3285,"children":3286},{},[3287,3292,3296,3300,3304,3308,3312],{"type":10,"tag":245,"props":3288,"children":3289},{"mathvariant":252},[3290],{"type":16,"value":3291},"∣",{"type":10,"tag":245,"props":3293,"children":3294},{"mathvariant":252},[3295],{"type":16,"value":3291},{"type":10,"tag":245,"props":3297,"children":3298},{"mathvariant":3091},[3299],{"type":16,"value":3141},{"type":10,"tag":214,"props":3301,"children":3302},{},[3303],{"type":16,"value":3279},{"type":10,"tag":245,"props":3305,"children":3306},{"mathvariant":3091},[3307],{"type":16,"value":3188},{"type":10,"tag":245,"props":3309,"children":3310},{"mathvariant":252},[3311],{"type":16,"value":3291},{"type":10,"tag":245,"props":3313,"children":3314},{"mathvariant":252},[3315],{"type":16,"value":3291},{"type":10,"tag":232,"props":3317,"children":3318},{},[3319],{"type":10,"tag":236,"props":3320,"children":3321},{"scriptlevel":238,"displaystyle":239},[3322],{"type":10,"tag":207,"props":3323,"children":3324},{},[3325,3330],{"type":10,"tag":245,"props":3326,"children":3327},{"mathvariant":252},[3328],{"type":16,"value":3329},"i",{"type":10,"tag":245,"props":3331,"children":3332},{"mathvariant":252},[3333],{"type":16,"value":3334},"f",{"type":10,"tag":228,"props":3336,"children":3337},{},[3338],{"type":10,"tag":232,"props":3339,"children":3340},{},[3341],{"type":10,"tag":236,"props":3342,"children":3343},{"scriptlevel":238,"displaystyle":239},[3344],{"type":10,"tag":207,"props":3345,"children":3346},{},[3347,3352,3356,3360,3364,3368,3372,3376,3380,3385],{"type":10,"tag":214,"props":3348,"children":3349},{"separator":216},[3350],{"type":16,"value":3351},";",{"type":10,"tag":245,"props":3353,"children":3354},{"mathvariant":252},[3355],{"type":16,"value":3291},{"type":10,"tag":245,"props":3357,"children":3358},{"mathvariant":252},[3359],{"type":16,"value":3291},{"type":10,"tag":245,"props":3361,"children":3362},{"mathvariant":3091},[3363],{"type":16,"value":3141},{"type":10,"tag":214,"props":3365,"children":3366},{},[3367],{"type":16,"value":3279},{"type":10,"tag":245,"props":3369,"children":3370},{"mathvariant":3091},[3371],{"type":16,"value":3188},{"type":10,"tag":245,"props":3373,"children":3374},{"mathvariant":252},[3375],{"type":16,"value":3291},{"type":10,"tag":245,"props":3377,"children":3378},{"mathvariant":252},[3379],{"type":16,"value":3291},{"type":10,"tag":214,"props":3381,"children":3382},{"mathvariant":252},[3383],{"type":16,"value":3384},"≠",{"type":10,"tag":370,"props":3386,"children":3387},{},[3388],{"type":16,"value":238},{"type":10,"tag":228,"props":3390,"children":3391},{},[3392,3472],{"type":10,"tag":232,"props":3393,"children":3394},{},[3395],{"type":10,"tag":236,"props":3396,"children":3397},{"scriptlevel":238,"displaystyle":239},[3398],{"type":10,"tag":207,"props":3399,"children":3400},{},[3401,3405],{"type":10,"tag":273,"props":3402,"children":3403},{},[3404],{"type":16,"value":277},{"type":10,"tag":207,"props":3406,"children":3407},{},[3408,3412,3468],{"type":10,"tag":214,"props":3409,"children":3410},{"fence":216},[3411],{"type":16,"value":219},{"type":10,"tag":221,"props":3413,"children":3414},{"rowspacing":223,"columnalign":224,"columnspacing":225},[3415,3428,3448],{"type":10,"tag":228,"props":3416,"children":3417},{},[3418],{"type":10,"tag":232,"props":3419,"children":3420},{},[3421],{"type":10,"tag":236,"props":3422,"children":3423},{"scriptlevel":238,"displaystyle":239},[3424],{"type":10,"tag":370,"props":3425,"children":3426},{},[3427],{"type":16,"value":238},{"type":10,"tag":228,"props":3429,"children":3430},{},[3431],{"type":10,"tag":232,"props":3432,"children":3433},{},[3434],{"type":10,"tag":236,"props":3435,"children":3436},{"scriptlevel":238,"displaystyle":239},[3437],{"type":10,"tag":207,"props":3438,"children":3439},{},[3440,3444],{"type":10,"tag":273,"props":3441,"children":3442},{},[3443],{"type":16,"value":277},{"type":10,"tag":370,"props":3445,"children":3446},{},[3447],{"type":16,"value":383},{"type":10,"tag":228,"props":3449,"children":3450},{},[3451],{"type":10,"tag":232,"props":3452,"children":3453},{},[3454],{"type":10,"tag":236,"props":3455,"children":3456},{"scriptlevel":238,"displaystyle":239},[3457],{"type":10,"tag":207,"props":3458,"children":3459},{},[3460,3464],{"type":10,"tag":273,"props":3461,"children":3462},{},[3463],{"type":16,"value":277},{"type":10,"tag":370,"props":3465,"children":3466},{},[3467],{"type":16,"value":238},{"type":10,"tag":214,"props":3469,"children":3470},{"fence":216},[3471],{"type":16,"value":324},{"type":10,"tag":232,"props":3473,"children":3474},{},[3475],{"type":10,"tag":236,"props":3476,"children":3477},{"scriptlevel":238,"displaystyle":239},[3478],{"type":10,"tag":207,"props":3479,"children":3480},{},[3481,3485],{"type":10,"tag":245,"props":3482,"children":3483},{"mathvariant":252},[3484],{"type":16,"value":3329},{"type":10,"tag":245,"props":3486,"children":3487},{"mathvariant":252},[3488],{"type":16,"value":3334},{"type":10,"tag":228,"props":3490,"children":3491},{},[3492],{"type":10,"tag":232,"props":3493,"children":3494},{},[3495],{"type":10,"tag":236,"props":3496,"children":3497},{"scriptlevel":238,"displaystyle":239},[3498],{"type":10,"tag":207,"props":3499,"children":3500},{},[3501,3505,3509,3513,3517,3521,3525,3529,3533,3537],{"type":10,"tag":214,"props":3502,"children":3503},{"separator":216},[3504],{"type":16,"value":3351},{"type":10,"tag":245,"props":3506,"children":3507},{"mathvariant":252},[3508],{"type":16,"value":3291},{"type":10,"tag":245,"props":3510,"children":3511},{"mathvariant":252},[3512],{"type":16,"value":3291},{"type":10,"tag":245,"props":3514,"children":3515},{"mathvariant":3091},[3516],{"type":16,"value":3141},{"type":10,"tag":214,"props":3518,"children":3519},{},[3520],{"type":16,"value":3279},{"type":10,"tag":245,"props":3522,"children":3523},{"mathvariant":3091},[3524],{"type":16,"value":3188},{"type":10,"tag":245,"props":3526,"children":3527},{"mathvariant":252},[3528],{"type":16,"value":3291},{"type":10,"tag":245,"props":3530,"children":3531},{"mathvariant":252},[3532],{"type":16,"value":3291},{"type":10,"tag":214,"props":3534,"children":3535},{},[3536],{"type":16,"value":329},{"type":10,"tag":370,"props":3538,"children":3539},{},[3540],{"type":16,"value":238},{"type":10,"tag":228,"props":3542,"children":3543},{},[3544],{"type":10,"tag":232,"props":3545,"children":3546},{},[3547],{"type":10,"tag":236,"props":3548,"children":3549},{"scriptlevel":238,"displaystyle":239},[3550],{"type":10,"tag":273,"props":3551,"children":3552},{},[3553],{"type":16,"value":277},{"type":10,"tag":1141,"props":3555,"children":3556},{"encoding":1143},[3557],{"type":16,"value":3558},"\\mathbf{a} = \\begin{cases}\n\\frac{\\mathbf{d} \\times \\mathbf{k}}{|| \\mathbf{d} \\times \\mathbf{k} ||} & \\mathrm{if}\\\\; || \\mathbf{d} \\times \\mathbf{k} || \\ne 0 \\\\\\\n\\left(\\begin{array}{c}\n0 \\\\\\\n1 \\\\\\\n0\n\\end{array}\n\\right) & \\mathrm{if}\\\\; || \\mathbf{d} \\times \\mathbf{k} || = 0 \\\\\\\n\\end{cases}",{"type":10,"tag":181,"props":3560,"children":3562},{"className":3561,"ariaHidden":216},[1150],[3563,3589],{"type":10,"tag":181,"props":3564,"children":3566},{"className":3565},[1155],[3567,3571,3576,3580,3585],{"type":10,"tag":181,"props":3568,"children":3570},{"className":3569,"style":3110},[1160],[],{"type":10,"tag":181,"props":3572,"children":3574},{"className":3573},[1245,3115],[3575],{"type":16,"value":44},{"type":10,"tag":181,"props":3577,"children":3579},{"className":3578,"style":1460},[1323],[],{"type":10,"tag":181,"props":3581,"children":3583},{"className":3582},[1465],[3584],{"type":16,"value":329},{"type":10,"tag":181,"props":3586,"children":3588},{"className":3587,"style":1460},[1323],[],{"type":10,"tag":181,"props":3590,"children":3592},{"className":3591},[1155],[3593,3598],{"type":10,"tag":181,"props":3594,"children":3597},{"className":3595,"style":3596},[1160],"height:9.448em;vertical-align:-4.474em;",[],{"type":10,"tag":181,"props":3599,"children":3601},{"className":3600},[1166],[3602,3735,4447],{"type":10,"tag":181,"props":3603,"children":3605},{"className":3604},[1171],[3606],{"type":10,"tag":181,"props":3607,"children":3609},{"className":3608},[1176,1177],[3610],{"type":10,"tag":181,"props":3611,"children":3613},{"className":3612},[1182,1183],[3614,3723],{"type":10,"tag":181,"props":3615,"children":3617},{"className":3616},[1188],[3618,3718],{"type":10,"tag":181,"props":3619,"children":3622},{"className":3620,"style":3621},[1193],"height:4.75em;",[3623,3643,3667,3684,3701],{"type":10,"tag":181,"props":3624,"children":3626},{"style":3625},"top:-1.366em;",[3627,3632],{"type":10,"tag":181,"props":3628,"children":3631},{"className":3629,"style":3630},[1203],"height:4.716em;",[],{"type":10,"tag":181,"props":3633,"children":3637},{"className":3634},[3635,3636],"delimsizinginner","delim-size4",[3638],{"type":10,"tag":181,"props":3639,"children":3640},{},[3641],{"type":16,"value":3642},"⎩",{"type":10,"tag":181,"props":3644,"children":3646},{"style":3645},"top:-1.358em;",[3647,3651],{"type":10,"tag":181,"props":3648,"children":3650},{"className":3649,"style":3630},[1203],[],{"type":10,"tag":181,"props":3652,"children":3654},{"style":3653},"height:2.716em;width:0.8889em;",[3655],{"type":10,"tag":1211,"props":3656,"children":3662},{"xmlns":1213,"width":3657,"height":3658,"style":3659,"viewBox":3660,"preserveAspectRatio":3661},"0.8889em","2.716em","width:0.8889em","0 0 888.89 2716","xMinYMin",[3663],{"type":10,"tag":1219,"props":3664,"children":3666},{"d":3665},"M384 0 H504 V2716 H384z M384 0 H504 V2716 H384z",[],{"type":10,"tag":181,"props":3668,"children":3670},{"style":3669},"top:-4.716em;",[3671,3675],{"type":10,"tag":181,"props":3672,"children":3674},{"className":3673,"style":3630},[1203],[],{"type":10,"tag":181,"props":3676,"children":3678},{"className":3677},[3635,3636],[3679],{"type":10,"tag":181,"props":3680,"children":3681},{},[3682],{"type":16,"value":3683},"⎨",{"type":10,"tag":181,"props":3685,"children":3687},{"style":3686},"top:-5.858em;",[3688,3692],{"type":10,"tag":181,"props":3689,"children":3691},{"className":3690,"style":3630},[1203],[],{"type":10,"tag":181,"props":3693,"children":3694},{"style":3653},[3695],{"type":10,"tag":1211,"props":3696,"children":3697},{"xmlns":1213,"width":3657,"height":3658,"style":3659,"viewBox":3660,"preserveAspectRatio":3661},[3698],{"type":10,"tag":1219,"props":3699,"children":3700},{"d":3665},[],{"type":10,"tag":181,"props":3702,"children":3704},{"style":3703},"top:-8.566em;",[3705,3709],{"type":10,"tag":181,"props":3706,"children":3708},{"className":3707,"style":3630},[1203],[],{"type":10,"tag":181,"props":3710,"children":3712},{"className":3711},[3635,3636],[3713],{"type":10,"tag":181,"props":3714,"children":3715},{},[3716],{"type":16,"value":3717},"⎧",{"type":10,"tag":181,"props":3719,"children":3721},{"className":3720},[1226],[3722],{"type":16,"value":1229},{"type":10,"tag":181,"props":3724,"children":3726},{"className":3725},[1188],[3727],{"type":10,"tag":181,"props":3728,"children":3731},{"className":3729,"style":3730},[1193],"height:4.25em;",[3732],{"type":10,"tag":181,"props":3733,"children":3734},{},[],{"type":10,"tag":181,"props":3736,"children":3738},{"className":3737},[1245],[3739],{"type":10,"tag":181,"props":3740,"children":3742},{"className":3741},[221],[3743,4366,4371],{"type":10,"tag":181,"props":3744,"children":3747},{"className":3745},[3746],"col-align-l",[3748],{"type":10,"tag":181,"props":3749,"children":3751},{"className":3750},[1182,1183],[3752,4354],{"type":10,"tag":181,"props":3753,"children":3755},{"className":3754},[1188],[3756,4349],{"type":10,"tag":181,"props":3757,"children":3760},{"className":3758,"style":3759},[1193],"height:4.974em;",[3761,3908,4029,4260,4332],{"type":10,"tag":181,"props":3762,"children":3764},{"style":3763},"top:-8.016em;",[3765,3770],{"type":10,"tag":181,"props":3766,"children":3769},{"className":3767,"style":3768},[1203],"height:4.05em;",[],{"type":10,"tag":181,"props":3771,"children":3773},{"className":3772},[1245],[3774],{"type":10,"tag":181,"props":3775,"children":3777},{"className":3776},[1245],[3778,3783,3904],{"type":10,"tag":181,"props":3779,"children":3782},{"className":3780},[1171,3781],"nulldelimiter",[],{"type":10,"tag":181,"props":3784,"children":3786},{"className":3785},[3265],[3787],{"type":10,"tag":181,"props":3788,"children":3790},{"className":3789},[1182,1183],[3791,3892],{"type":10,"tag":181,"props":3792,"children":3794},{"className":3793},[1188],[3795,3887],{"type":10,"tag":181,"props":3796,"children":3799},{"className":3797,"style":3798},[1193],"height:0.8801em;",[3800,3842,3856],{"type":10,"tag":181,"props":3801,"children":3803},{"style":3802},"top:-2.655em;",[3804,3808],{"type":10,"tag":181,"props":3805,"children":3807},{"className":3806,"style":1281},[1203],[],{"type":10,"tag":181,"props":3809,"children":3811},{"className":3810},[1620,1621,1622,1623],[3812],{"type":10,"tag":181,"props":3813,"children":3815},{"className":3814},[1245,1623],[3816,3822,3827,3832,3837],{"type":10,"tag":181,"props":3817,"children":3819},{"className":3818},[1245,1623],[3820],{"type":16,"value":3821},"∣∣",{"type":10,"tag":181,"props":3823,"children":3825},{"className":3824},[1245,3115,1623],[3826],{"type":16,"value":3141},{"type":10,"tag":181,"props":3828,"children":3830},{"className":3829},[1648,1623],[3831],{"type":16,"value":3279},{"type":10,"tag":181,"props":3833,"children":3835},{"className":3834},[1245,3115,1623],[3836],{"type":16,"value":3188},{"type":10,"tag":181,"props":3838,"children":3840},{"className":3839},[1245,1623],[3841],{"type":16,"value":3821},{"type":10,"tag":181,"props":3843,"children":3845},{"style":3844},"top:-3.23em;",[3846,3850],{"type":10,"tag":181,"props":3847,"children":3849},{"className":3848,"style":1281},[1203],[],{"type":10,"tag":181,"props":3851,"children":3855},{"className":3852,"style":3854},[3853],"frac-line","border-bottom-width:0.04em;",[],{"type":10,"tag":181,"props":3857,"children":3859},{"style":3858},"top:-3.394em;",[3860,3864],{"type":10,"tag":181,"props":3861,"children":3863},{"className":3862,"style":1281},[1203],[],{"type":10,"tag":181,"props":3865,"children":3867},{"className":3866},[1620,1621,1622,1623],[3868],{"type":10,"tag":181,"props":3869,"children":3871},{"className":3870},[1245,1623],[3872,3877,3882],{"type":10,"tag":181,"props":3873,"children":3875},{"className":3874},[1245,3115,1623],[3876],{"type":16,"value":3141},{"type":10,"tag":181,"props":3878,"children":3880},{"className":3879},[1648,1623],[3881],{"type":16,"value":3279},{"type":10,"tag":181,"props":3883,"children":3885},{"className":3884},[1245,3115,1623],[3886],{"type":16,"value":3188},{"type":10,"tag":181,"props":3888,"children":3890},{"className":3889},[1226],[3891],{"type":16,"value":1229},{"type":10,"tag":181,"props":3893,"children":3895},{"className":3894},[1188],[3896],{"type":10,"tag":181,"props":3897,"children":3900},{"className":3898,"style":3899},[1193],"height:0.52em;",[3901],{"type":10,"tag":181,"props":3902,"children":3903},{},[],{"type":10,"tag":181,"props":3905,"children":3907},{"className":3906},[1406,3781],[],{"type":10,"tag":181,"props":3909,"children":3911},{"style":3910},"top:-6.488em;",[3912,3916],{"type":10,"tag":181,"props":3913,"children":3915},{"className":3914,"style":3768},[1203],[],{"type":10,"tag":181,"props":3917,"children":3919},{"className":3918},[1245],[3920,3926,3930,3935,3940,3944,3949,3953,3958,3963,3967,4020,4024],{"type":10,"tag":181,"props":3921,"children":3924},{"className":3922},[3923],"mpunct",[3925],{"type":16,"value":3351},{"type":10,"tag":181,"props":3927,"children":3929},{"className":3928,"style":2712},[1323],[],{"type":10,"tag":181,"props":3931,"children":3933},{"className":3932},[1245],[3934],{"type":16,"value":3821},{"type":10,"tag":181,"props":3936,"children":3938},{"className":3937},[1245,3115],[3939],{"type":16,"value":3141},{"type":10,"tag":181,"props":3941,"children":3943},{"className":3942,"style":1643},[1323],[],{"type":10,"tag":181,"props":3945,"children":3947},{"className":3946},[1648],[3948],{"type":16,"value":3279},{"type":10,"tag":181,"props":3950,"children":3952},{"className":3951,"style":1643},[1323],[],{"type":10,"tag":181,"props":3954,"children":3956},{"className":3955},[1245,3115],[3957],{"type":16,"value":3188},{"type":10,"tag":181,"props":3959,"children":3961},{"className":3960},[1245],[3962],{"type":16,"value":3821},{"type":10,"tag":181,"props":3964,"children":3966},{"className":3965,"style":1460},[1323],[],{"type":10,"tag":181,"props":3968,"children":3970},{"className":3969},[1465],[3971,4015],{"type":10,"tag":181,"props":3972,"children":3974},{"className":3973},[1465],[3975],{"type":10,"tag":181,"props":3976,"children":3979},{"className":3977},[1245,3978],"vbox",[3980],{"type":10,"tag":181,"props":3981,"children":3984},{"className":3982},[3983],"thinbox",[3985],{"type":10,"tag":181,"props":3986,"children":3989},{"className":3987},[3988],"rlap",[3990,3995,4010],{"type":10,"tag":181,"props":3991,"children":3994},{"className":3992,"style":3993},[1160],"height:0.8889em;vertical-align:-0.1944em;",[],{"type":10,"tag":181,"props":3996,"children":3999},{"className":3997},[3998],"inner",[4000],{"type":10,"tag":181,"props":4001,"children":4003},{"className":4002},[1245],[4004],{"type":10,"tag":181,"props":4005,"children":4007},{"className":4006},[1465],[4008],{"type":16,"value":4009},"",{"type":10,"tag":181,"props":4011,"children":4014},{"className":4012},[4013],"fix",[],{"type":10,"tag":181,"props":4016,"children":4018},{"className":4017},[1465],[4019],{"type":16,"value":329},{"type":10,"tag":181,"props":4021,"children":4023},{"className":4022,"style":1460},[1323],[],{"type":10,"tag":181,"props":4025,"children":4027},{"className":4026},[1245],[4028],{"type":16,"value":238},{"type":10,"tag":181,"props":4030,"children":4032},{"style":4031},"top:-4.006em;",[4033,4037],{"type":10,"tag":181,"props":4034,"children":4036},{"className":4035,"style":3768},[1203],[],{"type":10,"tag":181,"props":4038,"children":4040},{"className":4039},[1245],[4041,4046],{"type":10,"tag":181,"props":4042,"children":4044},{"className":4043},[1323],[4045],{"type":16,"value":277},{"type":10,"tag":181,"props":4047,"children":4049},{"className":4048},[1166],[4050,4102,4208],{"type":10,"tag":181,"props":4051,"children":4053},{"className":4052},[1171],[4054],{"type":10,"tag":181,"props":4055,"children":4057},{"className":4056},[1176,1177],[4058],{"type":10,"tag":181,"props":4059,"children":4061},{"className":4060},[1182,1183],[4062,4091],{"type":10,"tag":181,"props":4063,"children":4065},{"className":4064},[1188],[4066,4086],{"type":10,"tag":181,"props":4067,"children":4069},{"className":4068,"style":1194},[1193],[4070],{"type":10,"tag":181,"props":4071,"children":4072},{"style":1198},[4073,4077],{"type":10,"tag":181,"props":4074,"children":4076},{"className":4075,"style":1204},[1203],[],{"type":10,"tag":181,"props":4078,"children":4079},{"style":1208},[4080],{"type":10,"tag":1211,"props":4081,"children":4082},{"xmlns":1213,"width":1214,"height":1215,"viewBox":1216},[4083],{"type":10,"tag":1219,"props":4084,"children":4085},{"d":1221},[],{"type":10,"tag":181,"props":4087,"children":4089},{"className":4088},[1226],[4090],{"type":16,"value":1229},{"type":10,"tag":181,"props":4092,"children":4094},{"className":4093},[1188],[4095],{"type":10,"tag":181,"props":4096,"children":4098},{"className":4097,"style":1237},[1193],[4099],{"type":10,"tag":181,"props":4100,"children":4101},{},[],{"type":10,"tag":181,"props":4103,"children":4105},{"className":4104},[1245],[4106],{"type":10,"tag":181,"props":4107,"children":4109},{"className":4108},[221],[4110,4114,4204],{"type":10,"tag":181,"props":4111,"children":4113},{"className":4112,"style":1255},[1254],[],{"type":10,"tag":181,"props":4115,"children":4117},{"className":4116},[1260],[4118],{"type":10,"tag":181,"props":4119,"children":4121},{"className":4120},[1182,1183],[4122,4193],{"type":10,"tag":181,"props":4123,"children":4125},{"className":4124},[1188],[4126,4188],{"type":10,"tag":181,"props":4127,"children":4129},{"className":4128,"style":1194},[1193],[4130,4146,4167],{"type":10,"tag":181,"props":4131,"children":4132},{"style":1276},[4133,4137],{"type":10,"tag":181,"props":4134,"children":4136},{"className":4135,"style":1281},[1203],[],{"type":10,"tag":181,"props":4138,"children":4140},{"className":4139},[1245],[4141],{"type":10,"tag":181,"props":4142,"children":4144},{"className":4143},[1245],[4145],{"type":16,"value":238},{"type":10,"tag":181,"props":4147,"children":4148},{"style":1310},[4149,4153],{"type":10,"tag":181,"props":4150,"children":4152},{"className":4151,"style":1281},[1203],[],{"type":10,"tag":181,"props":4154,"children":4156},{"className":4155},[1245],[4157,4162],{"type":10,"tag":181,"props":4158,"children":4160},{"className":4159},[1323],[4161],{"type":16,"value":277},{"type":10,"tag":181,"props":4163,"children":4165},{"className":4164},[1245],[4166],{"type":16,"value":383},{"type":10,"tag":181,"props":4168,"children":4169},{"style":1348},[4170,4174],{"type":10,"tag":181,"props":4171,"children":4173},{"className":4172,"style":1281},[1203],[],{"type":10,"tag":181,"props":4175,"children":4177},{"className":4176},[1245],[4178,4183],{"type":10,"tag":181,"props":4179,"children":4181},{"className":4180},[1323],[4182],{"type":16,"value":277},{"type":10,"tag":181,"props":4184,"children":4186},{"className":4185},[1245],[4187],{"type":16,"value":238},{"type":10,"tag":181,"props":4189,"children":4191},{"className":4190},[1226],[4192],{"type":16,"value":1229},{"type":10,"tag":181,"props":4194,"children":4196},{"className":4195},[1188],[4197],{"type":10,"tag":181,"props":4198,"children":4200},{"className":4199,"style":1237},[1193],[4201],{"type":10,"tag":181,"props":4202,"children":4203},{},[],{"type":10,"tag":181,"props":4205,"children":4207},{"className":4206,"style":1255},[1254],[],{"type":10,"tag":181,"props":4209,"children":4211},{"className":4210},[1406],[4212],{"type":10,"tag":181,"props":4213,"children":4215},{"className":4214},[1176,1177],[4216],{"type":10,"tag":181,"props":4217,"children":4219},{"className":4218},[1182,1183],[4220,4249],{"type":10,"tag":181,"props":4221,"children":4223},{"className":4222},[1188],[4224,4244],{"type":10,"tag":181,"props":4225,"children":4227},{"className":4226,"style":1194},[1193],[4228],{"type":10,"tag":181,"props":4229,"children":4230},{"style":1198},[4231,4235],{"type":10,"tag":181,"props":4232,"children":4234},{"className":4233,"style":1204},[1203],[],{"type":10,"tag":181,"props":4236,"children":4237},{"style":1208},[4238],{"type":10,"tag":1211,"props":4239,"children":4240},{"xmlns":1213,"width":1214,"height":1215,"viewBox":1216},[4241],{"type":10,"tag":1219,"props":4242,"children":4243},{"d":1439},[],{"type":10,"tag":181,"props":4245,"children":4247},{"className":4246},[1226],[4248],{"type":16,"value":1229},{"type":10,"tag":181,"props":4250,"children":4252},{"className":4251},[1188],[4253],{"type":10,"tag":181,"props":4254,"children":4256},{"className":4255,"style":1237},[1193],[4257],{"type":10,"tag":181,"props":4258,"children":4259},{},[],{"type":10,"tag":181,"props":4261,"children":4263},{"style":4262},"top:-1.448em;",[4264,4268],{"type":10,"tag":181,"props":4265,"children":4267},{"className":4266,"style":3768},[1203],[],{"type":10,"tag":181,"props":4269,"children":4271},{"className":4270},[1245],[4272,4277,4281,4286,4291,4295,4300,4304,4309,4314,4318,4323,4327],{"type":10,"tag":181,"props":4273,"children":4275},{"className":4274},[3923],[4276],{"type":16,"value":3351},{"type":10,"tag":181,"props":4278,"children":4280},{"className":4279,"style":2712},[1323],[],{"type":10,"tag":181,"props":4282,"children":4284},{"className":4283},[1245],[4285],{"type":16,"value":3821},{"type":10,"tag":181,"props":4287,"children":4289},{"className":4288},[1245,3115],[4290],{"type":16,"value":3141},{"type":10,"tag":181,"props":4292,"children":4294},{"className":4293,"style":1643},[1323],[],{"type":10,"tag":181,"props":4296,"children":4298},{"className":4297},[1648],[4299],{"type":16,"value":3279},{"type":10,"tag":181,"props":4301,"children":4303},{"className":4302,"style":1643},[1323],[],{"type":10,"tag":181,"props":4305,"children":4307},{"className":4306},[1245,3115],[4308],{"type":16,"value":3188},{"type":10,"tag":181,"props":4310,"children":4312},{"className":4311},[1245],[4313],{"type":16,"value":3821},{"type":10,"tag":181,"props":4315,"children":4317},{"className":4316,"style":1460},[1323],[],{"type":10,"tag":181,"props":4319,"children":4321},{"className":4320},[1465],[4322],{"type":16,"value":329},{"type":10,"tag":181,"props":4324,"children":4326},{"className":4325,"style":1460},[1323],[],{"type":10,"tag":181,"props":4328,"children":4330},{"className":4329},[1245],[4331],{"type":16,"value":238},{"type":10,"tag":181,"props":4333,"children":4335},{"style":4334},"top:-0.008em;",[4336,4340],{"type":10,"tag":181,"props":4337,"children":4339},{"className":4338,"style":3768},[1203],[],{"type":10,"tag":181,"props":4341,"children":4343},{"className":4342},[1245],[4344],{"type":10,"tag":181,"props":4345,"children":4347},{"className":4346},[1323],[4348],{"type":16,"value":277},{"type":10,"tag":181,"props":4350,"children":4352},{"className":4351},[1226],[4353],{"type":16,"value":1229},{"type":10,"tag":181,"props":4355,"children":4357},{"className":4356},[1188],[4358],{"type":10,"tag":181,"props":4359,"children":4362},{"className":4360,"style":4361},[1193],"height:4.474em;",[4363],{"type":10,"tag":181,"props":4364,"children":4365},{},[],{"type":10,"tag":181,"props":4367,"children":4370},{"className":4368,"style":4369},[1254],"width:1em;",[],{"type":10,"tag":181,"props":4372,"children":4374},{"className":4373},[3746],[4375],{"type":10,"tag":181,"props":4376,"children":4378},{"className":4377},[1182,1183],[4379,4435],{"type":10,"tag":181,"props":4380,"children":4382},{"className":4381},[1188],[4383,4430],{"type":10,"tag":181,"props":4384,"children":4386},{"className":4385,"style":3759},[1193],[4387,4410],{"type":10,"tag":181,"props":4388,"children":4389},{"style":3763},[4390,4394],{"type":10,"tag":181,"props":4391,"children":4393},{"className":4392,"style":3768},[1203],[],{"type":10,"tag":181,"props":4395,"children":4397},{"className":4396},[1245],[4398],{"type":10,"tag":181,"props":4399,"children":4401},{"className":4400},[1245],[4402],{"type":10,"tag":181,"props":4403,"children":4407},{"className":4404,"style":4406},[1245,4405],"mathrm","margin-right:0.07778em;",[4408],{"type":16,"value":4409},"if",{"type":10,"tag":181,"props":4411,"children":4412},{"style":4031},[4413,4417],{"type":10,"tag":181,"props":4414,"children":4416},{"className":4415,"style":3768},[1203],[],{"type":10,"tag":181,"props":4418,"children":4420},{"className":4419},[1245],[4421],{"type":10,"tag":181,"props":4422,"children":4424},{"className":4423},[1245],[4425],{"type":10,"tag":181,"props":4426,"children":4428},{"className":4427,"style":4406},[1245,4405],[4429],{"type":16,"value":4409},{"type":10,"tag":181,"props":4431,"children":4433},{"className":4432},[1226],[4434],{"type":16,"value":1229},{"type":10,"tag":181,"props":4436,"children":4438},{"className":4437},[1188],[4439],{"type":10,"tag":181,"props":4440,"children":4443},{"className":4441,"style":4442},[1193],"height:1.594em;",[4444],{"type":10,"tag":181,"props":4445,"children":4446},{},[],{"type":10,"tag":181,"props":4448,"children":4450},{"className":4449},[1406,3781],[],{"type":10,"tag":18,"props":4452,"children":4453},{},[4454,4499,4501,4544,4546,4588,4590,4632,4634,4676],{"type":10,"tag":181,"props":4455,"children":4457},{"className":4456},[189],[4458,4480],{"type":10,"tag":181,"props":4459,"children":4461},{"className":4460},[194],[4462],{"type":10,"tag":197,"props":4463,"children":4464},{"xmlns":199},[4465],{"type":10,"tag":203,"props":4466,"children":4467},{},[4468,4475],{"type":10,"tag":207,"props":4469,"children":4470},{},[4471],{"type":10,"tag":245,"props":4472,"children":4473},{},[4474],{"type":16,"value":468},{"type":10,"tag":1141,"props":4476,"children":4477},{"encoding":1143},[4478],{"type":16,"value":4479},"\\mathit{s}",{"type":10,"tag":181,"props":4481,"children":4483},{"className":4482,"ariaHidden":216},[1150],[4484],{"type":10,"tag":181,"props":4485,"children":4487},{"className":4486},[1155],[4488,4493],{"type":10,"tag":181,"props":4489,"children":4492},{"className":4490,"style":4491},[1160],"height:0.4306em;",[],{"type":10,"tag":181,"props":4494,"children":4497},{"className":4495},[1245,4496],"mathit",[4498],{"type":16,"value":468},{"type":16,"value":4500}," and ",{"type":10,"tag":181,"props":4502,"children":4504},{"className":4503},[189],[4505,4527],{"type":10,"tag":181,"props":4506,"children":4508},{"className":4507},[194],[4509],{"type":10,"tag":197,"props":4510,"children":4511},{"xmlns":199},[4512],{"type":10,"tag":203,"props":4513,"children":4514},{},[4515,4522],{"type":10,"tag":207,"props":4516,"children":4517},{},[4518],{"type":10,"tag":245,"props":4519,"children":4520},{},[4521],{"type":16,"value":393},{"type":10,"tag":1141,"props":4523,"children":4524},{"encoding":1143},[4525],{"type":16,"value":4526},"\\mathit{c}",{"type":10,"tag":181,"props":4528,"children":4530},{"className":4529,"ariaHidden":216},[1150],[4531],{"type":10,"tag":181,"props":4532,"children":4534},{"className":4533},[1155],[4535,4539],{"type":10,"tag":181,"props":4536,"children":4538},{"className":4537,"style":4491},[1160],[],{"type":10,"tag":181,"props":4540,"children":4542},{"className":4541},[1245,4496],[4543],{"type":16,"value":393},{"type":16,"value":4545}," are the sine and cosine of\nthe angle of rotation about ",{"type":10,"tag":181,"props":4547,"children":4549},{"className":4548},[189],[4550,4571],{"type":10,"tag":181,"props":4551,"children":4553},{"className":4552},[194],[4554],{"type":10,"tag":197,"props":4555,"children":4556},{"xmlns":199},[4557],{"type":10,"tag":203,"props":4558,"children":4559},{},[4560,4567],{"type":10,"tag":207,"props":4561,"children":4562},{},[4563],{"type":10,"tag":245,"props":4564,"children":4565},{"mathvariant":3091},[4566],{"type":16,"value":44},{"type":10,"tag":1141,"props":4568,"children":4569},{"encoding":1143},[4570],{"type":16,"value":3098},{"type":10,"tag":181,"props":4572,"children":4574},{"className":4573,"ariaHidden":216},[1150],[4575],{"type":10,"tag":181,"props":4576,"children":4578},{"className":4577},[1155],[4579,4583],{"type":10,"tag":181,"props":4580,"children":4582},{"className":4581,"style":3110},[1160],[],{"type":10,"tag":181,"props":4584,"children":4586},{"className":4585},[1245,3115],[4587],{"type":16,"value":44},{"type":16,"value":4589}," from\n",{"type":10,"tag":181,"props":4591,"children":4593},{"className":4592},[189],[4594,4615],{"type":10,"tag":181,"props":4595,"children":4597},{"className":4596},[194],[4598],{"type":10,"tag":197,"props":4599,"children":4600},{"xmlns":199},[4601],{"type":10,"tag":203,"props":4602,"children":4603},{},[4604,4611],{"type":10,"tag":207,"props":4605,"children":4606},{},[4607],{"type":10,"tag":245,"props":4608,"children":4609},{"mathvariant":3091},[4610],{"type":16,"value":3141},{"type":10,"tag":1141,"props":4612,"children":4613},{"encoding":1143},[4614],{"type":16,"value":3146},{"type":10,"tag":181,"props":4616,"children":4618},{"className":4617,"ariaHidden":216},[1150],[4619],{"type":10,"tag":181,"props":4620,"children":4622},{"className":4621},[1155],[4623,4627],{"type":10,"tag":181,"props":4624,"children":4626},{"className":4625,"style":3158},[1160],[],{"type":10,"tag":181,"props":4628,"children":4630},{"className":4629},[1245,3115],[4631],{"type":16,"value":3141},{"type":16,"value":4633}," to ",{"type":10,"tag":181,"props":4635,"children":4637},{"className":4636},[189],[4638,4659],{"type":10,"tag":181,"props":4639,"children":4641},{"className":4640},[194],[4642],{"type":10,"tag":197,"props":4643,"children":4644},{"xmlns":199},[4645],{"type":10,"tag":203,"props":4646,"children":4647},{},[4648,4655],{"type":10,"tag":207,"props":4649,"children":4650},{},[4651],{"type":10,"tag":245,"props":4652,"children":4653},{"mathvariant":3091},[4654],{"type":16,"value":3188},{"type":10,"tag":1141,"props":4656,"children":4657},{"encoding":1143},[4658],{"type":16,"value":3193},{"type":10,"tag":181,"props":4660,"children":4662},{"className":4661,"ariaHidden":216},[1150],[4663],{"type":10,"tag":181,"props":4664,"children":4666},{"className":4665},[1155],[4667,4671],{"type":10,"tag":181,"props":4668,"children":4670},{"className":4669,"style":3158},[1160],[],{"type":10,"tag":181,"props":4672,"children":4674},{"className":4673},[1245,3115],[4675],{"type":16,"value":3188},{"type":16,"value":3212},{"type":10,"tag":181,"props":4678,"children":4680},{"className":4679},[184],[4681],{"type":10,"tag":181,"props":4682,"children":4684},{"className":4683},[189],[4685,4839],{"type":10,"tag":181,"props":4686,"children":4688},{"className":4687},[194],[4689],{"type":10,"tag":197,"props":4690,"children":4691},{"xmlns":199,"display":200},[4692],{"type":10,"tag":203,"props":4693,"children":4694},{},[4695,4834],{"type":10,"tag":221,"props":4696,"children":4700},{"rowspacing":4697,"columnalign":4698,"columnspacing":4699},"0.25em","right left","0em",[4701,4772],{"type":10,"tag":228,"props":4702,"children":4703},{},[4704,4714],{"type":10,"tag":232,"props":4705,"children":4706},{},[4707],{"type":10,"tag":236,"props":4708,"children":4709},{"scriptlevel":238,"displaystyle":216},[4710],{"type":10,"tag":245,"props":4711,"children":4712},{},[4713],{"type":16,"value":393},{"type":10,"tag":232,"props":4715,"children":4716},{},[4717],{"type":10,"tag":236,"props":4718,"children":4719},{"scriptlevel":238,"displaystyle":216},[4720],{"type":10,"tag":207,"props":4721,"children":4722},{},[4723,4726,4730],{"type":10,"tag":207,"props":4724,"children":4725},{},[],{"type":10,"tag":214,"props":4727,"children":4728},{},[4729],{"type":16,"value":329},{"type":10,"tag":3265,"props":4731,"children":4732},{},[4733,4749],{"type":10,"tag":207,"props":4734,"children":4735},{},[4736,4740,4745],{"type":10,"tag":245,"props":4737,"children":4738},{"mathvariant":3091},[4739],{"type":16,"value":3141},{"type":10,"tag":214,"props":4741,"children":4742},{},[4743],{"type":16,"value":4744},"⋅",{"type":10,"tag":245,"props":4746,"children":4747},{"mathvariant":3091},[4748],{"type":16,"value":3188},{"type":10,"tag":207,"props":4750,"children":4751},{},[4752,4756,4760,4764,4768],{"type":10,"tag":245,"props":4753,"children":4754},{"mathvariant":252},[4755],{"type":16,"value":3291},{"type":10,"tag":245,"props":4757,"children":4758},{"mathvariant":252},[4759],{"type":16,"value":3291},{"type":10,"tag":245,"props":4761,"children":4762},{"mathvariant":3091},[4763],{"type":16,"value":3141},{"type":10,"tag":245,"props":4765,"children":4766},{"mathvariant":252},[4767],{"type":16,"value":3291},{"type":10,"tag":245,"props":4769,"children":4770},{"mathvariant":252},[4771],{"type":16,"value":3291},{"type":10,"tag":228,"props":4773,"children":4774},{},[4775,4792],{"type":10,"tag":232,"props":4776,"children":4777},{},[4778],{"type":10,"tag":236,"props":4779,"children":4780},{"scriptlevel":238,"displaystyle":216},[4781],{"type":10,"tag":207,"props":4782,"children":4783},{},[4784,4788],{"type":10,"tag":273,"props":4785,"children":4786},{},[4787],{"type":16,"value":277},{"type":10,"tag":245,"props":4789,"children":4790},{},[4791],{"type":16,"value":468},{"type":10,"tag":232,"props":4793,"children":4794},{},[4795],{"type":10,"tag":236,"props":4796,"children":4797},{"scriptlevel":238,"displaystyle":216},[4798],{"type":10,"tag":207,"props":4799,"children":4800},{},[4801,4804,4808],{"type":10,"tag":207,"props":4802,"children":4803},{},[],{"type":10,"tag":214,"props":4805,"children":4806},{},[4807],{"type":16,"value":329},{"type":10,"tag":4809,"props":4810,"children":4811},"msqrt",{},[4812],{"type":10,"tag":207,"props":4813,"children":4814},{},[4815,4819,4823],{"type":10,"tag":370,"props":4816,"children":4817},{},[4818],{"type":16,"value":383},{"type":10,"tag":214,"props":4820,"children":4821},{},[4822],{"type":16,"value":388},{"type":10,"tag":362,"props":4824,"children":4825},{},[4826,4830],{"type":10,"tag":245,"props":4827,"children":4828},{},[4829],{"type":16,"value":393},{"type":10,"tag":370,"props":4831,"children":4832},{},[4833],{"type":16,"value":374},{"type":10,"tag":1141,"props":4835,"children":4836},{"encoding":1143},[4837],{"type":16,"value":4838},"\\begin{aligned}\nc &= {{\\mathbf{d} \\cdot \\mathbf{k}}\\over{||\\mathbf{d}||}} \\\\\\\ns &= \\sqrt{1 - c^2}\n\\end{aligned}",{"type":10,"tag":181,"props":4840,"children":4842},{"className":4841,"ariaHidden":216},[1150],[4843],{"type":10,"tag":181,"props":4844,"children":4846},{"className":4845},[1155],[4847,4852],{"type":10,"tag":181,"props":4848,"children":4851},{"className":4849,"style":4850},[1160],"height:4.3297em;vertical-align:-1.9149em;",[],{"type":10,"tag":181,"props":4853,"children":4855},{"className":4854},[1245],[4856],{"type":10,"tag":181,"props":4857,"children":4859},{"className":4858},[221],[4860,4935],{"type":10,"tag":181,"props":4861,"children":4864},{"className":4862},[4863],"col-align-r",[4865],{"type":10,"tag":181,"props":4866,"children":4868},{"className":4867},[1182,1183],[4869,4923],{"type":10,"tag":181,"props":4870,"children":4872},{"className":4871},[1188],[4873,4918],{"type":10,"tag":181,"props":4874,"children":4877},{"className":4875,"style":4876},[1193],"height:2.4149em;",[4878,4896],{"type":10,"tag":181,"props":4879,"children":4881},{"style":4880},"top:-4.4149em;",[4882,4887],{"type":10,"tag":181,"props":4883,"children":4886},{"className":4884,"style":4885},[1203],"height:3.3714em;",[],{"type":10,"tag":181,"props":4888,"children":4890},{"className":4889},[1245],[4891],{"type":10,"tag":181,"props":4892,"children":4894},{"className":4893},[1245,1290],[4895],{"type":16,"value":393},{"type":10,"tag":181,"props":4897,"children":4899},{"style":4898},"top:-2.1166em;",[4900,4904],{"type":10,"tag":181,"props":4901,"children":4903},{"className":4902,"style":4885},[1203],[],{"type":10,"tag":181,"props":4905,"children":4907},{"className":4906},[1245],[4908,4913],{"type":10,"tag":181,"props":4909,"children":4911},{"className":4910},[1323],[4912],{"type":16,"value":277},{"type":10,"tag":181,"props":4914,"children":4916},{"className":4915},[1245,1290],[4917],{"type":16,"value":468},{"type":10,"tag":181,"props":4919,"children":4921},{"className":4920},[1226],[4922],{"type":16,"value":1229},{"type":10,"tag":181,"props":4924,"children":4926},{"className":4925},[1188],[4927],{"type":10,"tag":181,"props":4928,"children":4931},{"className":4929,"style":4930},[1193],"height:1.9149em;",[4932],{"type":10,"tag":181,"props":4933,"children":4934},{},[],{"type":10,"tag":181,"props":4936,"children":4938},{"className":4937},[3746],[4939],{"type":10,"tag":181,"props":4940,"children":4942},{"className":4941},[1182,1183],[4943,5272],{"type":10,"tag":181,"props":4944,"children":4946},{"className":4945},[1188],[4947,5267],{"type":10,"tag":181,"props":4948,"children":4950},{"className":4949,"style":4876},[1193],[4951,5102],{"type":10,"tag":181,"props":4952,"children":4953},{"style":4880},[4954,4958],{"type":10,"tag":181,"props":4955,"children":4957},{"className":4956,"style":4885},[1203],[],{"type":10,"tag":181,"props":4959,"children":4961},{"className":4960},[1245],[4962,4966,4970,4975,4979],{"type":10,"tag":181,"props":4963,"children":4965},{"className":4964},[1245],[],{"type":10,"tag":181,"props":4967,"children":4969},{"className":4968,"style":1460},[1323],[],{"type":10,"tag":181,"props":4971,"children":4973},{"className":4972},[1465],[4974],{"type":16,"value":329},{"type":10,"tag":181,"props":4976,"children":4978},{"className":4977,"style":1460},[1323],[],{"type":10,"tag":181,"props":4980,"children":4982},{"className":4981},[1245],[4983],{"type":10,"tag":181,"props":4984,"children":4986},{"className":4985},[1245],[4987,4991,5098],{"type":10,"tag":181,"props":4988,"children":4990},{"className":4989},[1171,3781],[],{"type":10,"tag":181,"props":4992,"children":4994},{"className":4993},[3265],[4995],{"type":10,"tag":181,"props":4996,"children":4998},{"className":4997},[1182,1183],[4999,5086],{"type":10,"tag":181,"props":5000,"children":5002},{"className":5001},[1188],[5003,5081],{"type":10,"tag":181,"props":5004,"children":5007},{"className":5005,"style":5006},[1193],"height:1.3714em;",[5008,5035,5046],{"type":10,"tag":181,"props":5009,"children":5011},{"style":5010},"top:-2.314em;",[5012,5016],{"type":10,"tag":181,"props":5013,"children":5015},{"className":5014,"style":1281},[1203],[],{"type":10,"tag":181,"props":5017,"children":5019},{"className":5018},[1245],[5020,5025,5030],{"type":10,"tag":181,"props":5021,"children":5023},{"className":5022},[1245],[5024],{"type":16,"value":3821},{"type":10,"tag":181,"props":5026,"children":5028},{"className":5027},[1245,3115],[5029],{"type":16,"value":3141},{"type":10,"tag":181,"props":5031,"children":5033},{"className":5032},[1245],[5034],{"type":16,"value":3821},{"type":10,"tag":181,"props":5036,"children":5037},{"style":3844},[5038,5042],{"type":10,"tag":181,"props":5039,"children":5041},{"className":5040,"style":1281},[1203],[],{"type":10,"tag":181,"props":5043,"children":5045},{"className":5044,"style":3854},[3853],[],{"type":10,"tag":181,"props":5047,"children":5049},{"style":5048},"top:-3.677em;",[5050,5054],{"type":10,"tag":181,"props":5051,"children":5053},{"className":5052,"style":1281},[1203],[],{"type":10,"tag":181,"props":5055,"children":5057},{"className":5056},[1245],[5058,5063,5067,5072,5076],{"type":10,"tag":181,"props":5059,"children":5061},{"className":5060},[1245,3115],[5062],{"type":16,"value":3141},{"type":10,"tag":181,"props":5064,"children":5066},{"className":5065,"style":1643},[1323],[],{"type":10,"tag":181,"props":5068,"children":5070},{"className":5069},[1648],[5071],{"type":16,"value":4744},{"type":10,"tag":181,"props":5073,"children":5075},{"className":5074,"style":1643},[1323],[],{"type":10,"tag":181,"props":5077,"children":5079},{"className":5078},[1245,3115],[5080],{"type":16,"value":3188},{"type":10,"tag":181,"props":5082,"children":5084},{"className":5083},[1226],[5085],{"type":16,"value":1229},{"type":10,"tag":181,"props":5087,"children":5089},{"className":5088},[1188],[5090],{"type":10,"tag":181,"props":5091,"children":5094},{"className":5092,"style":5093},[1193],"height:0.936em;",[5095],{"type":10,"tag":181,"props":5096,"children":5097},{},[],{"type":10,"tag":181,"props":5099,"children":5101},{"className":5100},[1406,3781],[],{"type":10,"tag":181,"props":5103,"children":5104},{"style":4898},[5105,5109],{"type":10,"tag":181,"props":5106,"children":5108},{"className":5107,"style":4885},[1203],[],{"type":10,"tag":181,"props":5110,"children":5112},{"className":5111},[1245],[5113,5117,5121,5126,5130],{"type":10,"tag":181,"props":5114,"children":5116},{"className":5115},[1245],[],{"type":10,"tag":181,"props":5118,"children":5120},{"className":5119,"style":1460},[1323],[],{"type":10,"tag":181,"props":5122,"children":5124},{"className":5123},[1465],[5125],{"type":16,"value":329},{"type":10,"tag":181,"props":5127,"children":5129},{"className":5128,"style":1460},[1323],[],{"type":10,"tag":181,"props":5131,"children":5134},{"className":5132},[1245,5133],"sqrt",[5135],{"type":10,"tag":181,"props":5136,"children":5138},{"className":5137},[1182,1183],[5139,5255],{"type":10,"tag":181,"props":5140,"children":5142},{"className":5141},[1188],[5143,5250],{"type":10,"tag":181,"props":5144,"children":5147},{"className":5145,"style":5146},[1193],"height:1.0623em;",[5148,5225],{"type":10,"tag":181,"props":5149,"children":5153},{"className":5150,"style":5152},[5151],"svg-align","top:-3.2em;",[5154,5159],{"type":10,"tag":181,"props":5155,"children":5158},{"className":5156,"style":5157},[1203],"height:3.2em;",[],{"type":10,"tag":181,"props":5160,"children":5163},{"className":5161,"style":5162},[1245],"padding-left:1em;",[5164,5169,5173,5178,5182],{"type":10,"tag":181,"props":5165,"children":5167},{"className":5166},[1245],[5168],{"type":16,"value":383},{"type":10,"tag":181,"props":5170,"children":5172},{"className":5171,"style":1643},[1323],[],{"type":10,"tag":181,"props":5174,"children":5176},{"className":5175},[1648],[5177],{"type":16,"value":388},{"type":10,"tag":181,"props":5179,"children":5181},{"className":5180,"style":1643},[1323],[],{"type":10,"tag":181,"props":5183,"children":5185},{"className":5184},[1245],[5186,5191],{"type":10,"tag":181,"props":5187,"children":5189},{"className":5188},[1245,1290],[5190],{"type":16,"value":393},{"type":10,"tag":181,"props":5192,"children":5194},{"className":5193},[1593],[5195],{"type":10,"tag":181,"props":5196,"children":5198},{"className":5197},[1182],[5199],{"type":10,"tag":181,"props":5200,"children":5202},{"className":5201},[1188],[5203],{"type":10,"tag":181,"props":5204,"children":5207},{"className":5205,"style":5206},[1193],"height:0.7401em;",[5208],{"type":10,"tag":181,"props":5209,"children":5211},{"style":5210},"top:-2.989em;margin-right:0.05em;",[5212,5216],{"type":10,"tag":181,"props":5213,"children":5215},{"className":5214,"style":1615},[1203],[],{"type":10,"tag":181,"props":5217,"children":5219},{"className":5218},[1620,1621,1622,1623],[5220],{"type":10,"tag":181,"props":5221,"children":5223},{"className":5222},[1245,1623],[5224],{"type":16,"value":374},{"type":10,"tag":181,"props":5226,"children":5228},{"style":5227},"top:-3.0223em;",[5229,5233],{"type":10,"tag":181,"props":5230,"children":5232},{"className":5231,"style":5157},[1203],[],{"type":10,"tag":181,"props":5234,"children":5238},{"className":5235,"style":5237},[5236],"hide-tail","min-width:1.02em;height:1.28em;",[5239],{"type":10,"tag":1211,"props":5240,"children":5245},{"xmlns":1213,"width":5241,"height":5242,"viewBox":5243,"preserveAspectRatio":5244},"400em","1.28em","0 0 400000 1296","xMinYMin slice",[5246],{"type":10,"tag":1219,"props":5247,"children":5249},{"d":5248},"M263,681c0.7,0,18,39.7,52,119\nc34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120\nc340,-704.7,510.7,-1060.3,512,-1067\nl0 -0\nc4.7,-7.3,11,-11,19,-11\nH40000v40H1012.3\ns-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232\nc-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1\ns-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26\nc-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z\nM1001 80h400000v40h-400000z",[],{"type":10,"tag":181,"props":5251,"children":5253},{"className":5252},[1226],[5254],{"type":16,"value":1229},{"type":10,"tag":181,"props":5256,"children":5258},{"className":5257},[1188],[5259],{"type":10,"tag":181,"props":5260,"children":5263},{"className":5261,"style":5262},[1193],"height:0.1777em;",[5264],{"type":10,"tag":181,"props":5265,"children":5266},{},[],{"type":10,"tag":181,"props":5268,"children":5270},{"className":5269},[1226],[5271],{"type":16,"value":1229},{"type":10,"tag":181,"props":5273,"children":5275},{"className":5274},[1188],[5276],{"type":10,"tag":181,"props":5277,"children":5279},{"className":5278,"style":4930},[1193],[5280],{"type":10,"tag":181,"props":5281,"children":5282},{},[],{"type":10,"tag":18,"props":5284,"children":5285},{},[5286,5328],{"type":10,"tag":181,"props":5287,"children":5289},{"className":5288},[189],[5290,5311],{"type":10,"tag":181,"props":5291,"children":5293},{"className":5292},[194],[5294],{"type":10,"tag":197,"props":5295,"children":5296},{"xmlns":199},[5297],{"type":10,"tag":203,"props":5298,"children":5299},{},[5300,5307],{"type":10,"tag":207,"props":5301,"children":5302},{},[5303],{"type":10,"tag":245,"props":5304,"children":5305},{"mathvariant":3091},[5306],{"type":16,"value":3188},{"type":10,"tag":1141,"props":5308,"children":5309},{"encoding":1143},[5310],{"type":16,"value":3193},{"type":10,"tag":181,"props":5312,"children":5314},{"className":5313,"ariaHidden":216},[1150],[5315],{"type":10,"tag":181,"props":5316,"children":5318},{"className":5317},[1155],[5319,5323],{"type":10,"tag":181,"props":5320,"children":5322},{"className":5321,"style":3158},[1160],[],{"type":10,"tag":181,"props":5324,"children":5326},{"className":5325},[1245,3115],[5327],{"type":16,"value":3188},{"type":16,"value":5329}," is the unit vector:",{"type":10,"tag":181,"props":5331,"children":5333},{"className":5332},[184],[5334],{"type":10,"tag":181,"props":5335,"children":5337},{"className":5336},[189],[5338,5435],{"type":10,"tag":181,"props":5339,"children":5341},{"className":5340},[194],[5342],{"type":10,"tag":197,"props":5343,"children":5344},{"xmlns":199,"display":200},[5345],{"type":10,"tag":203,"props":5346,"children":5347},{},[5348,5430],{"type":10,"tag":207,"props":5349,"children":5350},{},[5351,5355,5359],{"type":10,"tag":245,"props":5352,"children":5353},{"mathvariant":3091},[5354],{"type":16,"value":3188},{"type":10,"tag":214,"props":5356,"children":5357},{},[5358],{"type":16,"value":329},{"type":10,"tag":207,"props":5360,"children":5361},{},[5362,5366,5426],{"type":10,"tag":214,"props":5363,"children":5364},{"fence":216},[5365],{"type":16,"value":219},{"type":10,"tag":221,"props":5367,"children":5368},{"rowspacing":223,"columnalign":224,"columnspacing":225},[5369,5382,5402],{"type":10,"tag":228,"props":5370,"children":5371},{},[5372],{"type":10,"tag":232,"props":5373,"children":5374},{},[5375],{"type":10,"tag":236,"props":5376,"children":5377},{"scriptlevel":238,"displaystyle":239},[5378],{"type":10,"tag":370,"props":5379,"children":5380},{},[5381],{"type":16,"value":238},{"type":10,"tag":228,"props":5383,"children":5384},{},[5385],{"type":10,"tag":232,"props":5386,"children":5387},{},[5388],{"type":10,"tag":236,"props":5389,"children":5390},{"scriptlevel":238,"displaystyle":239},[5391],{"type":10,"tag":207,"props":5392,"children":5393},{},[5394,5398],{"type":10,"tag":273,"props":5395,"children":5396},{},[5397],{"type":16,"value":277},{"type":10,"tag":370,"props":5399,"children":5400},{},[5401],{"type":16,"value":238},{"type":10,"tag":228,"props":5403,"children":5404},{},[5405],{"type":10,"tag":232,"props":5406,"children":5407},{},[5408],{"type":10,"tag":236,"props":5409,"children":5410},{"scriptlevel":238,"displaystyle":239},[5411],{"type":10,"tag":207,"props":5412,"children":5413},{},[5414,5418,5422],{"type":10,"tag":273,"props":5415,"children":5416},{},[5417],{"type":16,"value":277},{"type":10,"tag":214,"props":5419,"children":5420},{},[5421],{"type":16,"value":388},{"type":10,"tag":370,"props":5423,"children":5424},{},[5425],{"type":16,"value":383},{"type":10,"tag":214,"props":5427,"children":5428},{"fence":216},[5429],{"type":16,"value":324},{"type":10,"tag":1141,"props":5431,"children":5432},{"encoding":1143},[5433],{"type":16,"value":5434},"\\mathbf{k} = \\left(\n\\begin{array}{c}\n0 \\\\\\\n0 \\\\\\\n-1\n\\end{array}\n\\right)",{"type":10,"tag":181,"props":5436,"children":5438},{"className":5437,"ariaHidden":216},[1150],[5439,5465],{"type":10,"tag":181,"props":5440,"children":5442},{"className":5441},[1155],[5443,5447,5452,5456,5461],{"type":10,"tag":181,"props":5444,"children":5446},{"className":5445,"style":3158},[1160],[],{"type":10,"tag":181,"props":5448,"children":5450},{"className":5449},[1245,3115],[5451],{"type":16,"value":3188},{"type":10,"tag":181,"props":5453,"children":5455},{"className":5454,"style":1460},[1323],[],{"type":10,"tag":181,"props":5457,"children":5459},{"className":5458},[1465],[5460],{"type":16,"value":329},{"type":10,"tag":181,"props":5462,"children":5464},{"className":5463,"style":1460},[1323],[],{"type":10,"tag":181,"props":5466,"children":5468},{"className":5467},[1155],[5469,5473],{"type":10,"tag":181,"props":5470,"children":5472},{"className":5471,"style":1161},[1160],[],{"type":10,"tag":181,"props":5474,"children":5476},{"className":5475},[1166],[5477,5529,5640],{"type":10,"tag":181,"props":5478,"children":5480},{"className":5479},[1171],[5481],{"type":10,"tag":181,"props":5482,"children":5484},{"className":5483},[1176,1177],[5485],{"type":10,"tag":181,"props":5486,"children":5488},{"className":5487},[1182,1183],[5489,5518],{"type":10,"tag":181,"props":5490,"children":5492},{"className":5491},[1188],[5493,5513],{"type":10,"tag":181,"props":5494,"children":5496},{"className":5495,"style":1194},[1193],[5497],{"type":10,"tag":181,"props":5498,"children":5499},{"style":1198},[5500,5504],{"type":10,"tag":181,"props":5501,"children":5503},{"className":5502,"style":1204},[1203],[],{"type":10,"tag":181,"props":5505,"children":5506},{"style":1208},[5507],{"type":10,"tag":1211,"props":5508,"children":5509},{"xmlns":1213,"width":1214,"height":1215,"viewBox":1216},[5510],{"type":10,"tag":1219,"props":5511,"children":5512},{"d":1221},[],{"type":10,"tag":181,"props":5514,"children":5516},{"className":5515},[1226],[5517],{"type":16,"value":1229},{"type":10,"tag":181,"props":5519,"children":5521},{"className":5520},[1188],[5522],{"type":10,"tag":181,"props":5523,"children":5525},{"className":5524,"style":1237},[1193],[5526],{"type":10,"tag":181,"props":5527,"children":5528},{},[],{"type":10,"tag":181,"props":5530,"children":5532},{"className":5531},[1245],[5533],{"type":10,"tag":181,"props":5534,"children":5536},{"className":5535},[221],[5537,5541,5636],{"type":10,"tag":181,"props":5538,"children":5540},{"className":5539,"style":1255},[1254],[],{"type":10,"tag":181,"props":5542,"children":5544},{"className":5543},[1260],[5545],{"type":10,"tag":181,"props":5546,"children":5548},{"className":5547},[1182,1183],[5549,5625],{"type":10,"tag":181,"props":5550,"children":5552},{"className":5551},[1188],[5553,5620],{"type":10,"tag":181,"props":5554,"children":5556},{"className":5555,"style":1194},[1193],[5557,5573,5594],{"type":10,"tag":181,"props":5558,"children":5559},{"style":1276},[5560,5564],{"type":10,"tag":181,"props":5561,"children":5563},{"className":5562,"style":1281},[1203],[],{"type":10,"tag":181,"props":5565,"children":5567},{"className":5566},[1245],[5568],{"type":10,"tag":181,"props":5569,"children":5571},{"className":5570},[1245],[5572],{"type":16,"value":238},{"type":10,"tag":181,"props":5574,"children":5575},{"style":1310},[5576,5580],{"type":10,"tag":181,"props":5577,"children":5579},{"className":5578,"style":1281},[1203],[],{"type":10,"tag":181,"props":5581,"children":5583},{"className":5582},[1245],[5584,5589],{"type":10,"tag":181,"props":5585,"children":5587},{"className":5586},[1323],[5588],{"type":16,"value":277},{"type":10,"tag":181,"props":5590,"children":5592},{"className":5591},[1245],[5593],{"type":16,"value":238},{"type":10,"tag":181,"props":5595,"children":5596},{"style":1348},[5597,5601],{"type":10,"tag":181,"props":5598,"children":5600},{"className":5599,"style":1281},[1203],[],{"type":10,"tag":181,"props":5602,"children":5604},{"className":5603},[1245],[5605,5610,5615],{"type":10,"tag":181,"props":5606,"children":5608},{"className":5607},[1323],[5609],{"type":16,"value":277},{"type":10,"tag":181,"props":5611,"children":5613},{"className":5612},[1245],[5614],{"type":16,"value":388},{"type":10,"tag":181,"props":5616,"children":5618},{"className":5617},[1245],[5619],{"type":16,"value":383},{"type":10,"tag":181,"props":5621,"children":5623},{"className":5622},[1226],[5624],{"type":16,"value":1229},{"type":10,"tag":181,"props":5626,"children":5628},{"className":5627},[1188],[5629],{"type":10,"tag":181,"props":5630,"children":5632},{"className":5631,"style":1237},[1193],[5633],{"type":10,"tag":181,"props":5634,"children":5635},{},[],{"type":10,"tag":181,"props":5637,"children":5639},{"className":5638,"style":1255},[1254],[],{"type":10,"tag":181,"props":5641,"children":5643},{"className":5642},[1406],[5644],{"type":10,"tag":181,"props":5645,"children":5647},{"className":5646},[1176,1177],[5648],{"type":10,"tag":181,"props":5649,"children":5651},{"className":5650},[1182,1183],[5652,5681],{"type":10,"tag":181,"props":5653,"children":5655},{"className":5654},[1188],[5656,5676],{"type":10,"tag":181,"props":5657,"children":5659},{"className":5658,"style":1194},[1193],[5660],{"type":10,"tag":181,"props":5661,"children":5662},{"style":1198},[5663,5667],{"type":10,"tag":181,"props":5664,"children":5666},{"className":5665,"style":1204},[1203],[],{"type":10,"tag":181,"props":5668,"children":5669},{"style":1208},[5670],{"type":10,"tag":1211,"props":5671,"children":5672},{"xmlns":1213,"width":1214,"height":1215,"viewBox":1216},[5673],{"type":10,"tag":1219,"props":5674,"children":5675},{"d":1439},[],{"type":10,"tag":181,"props":5677,"children":5679},{"className":5678},[1226],[5680],{"type":16,"value":1229},{"type":10,"tag":181,"props":5682,"children":5684},{"className":5683},[1188],[5685],{"type":10,"tag":181,"props":5686,"children":5688},{"className":5687,"style":1237},[1193],[5689],{"type":10,"tag":181,"props":5690,"children":5691},{},[],{"type":10,"tag":18,"props":5693,"children":5694},{},[5695,5738,5739,5781,5783,5787,5789,5793,5795,5799,5801,5805,5807,5811,5812,5816],{"type":10,"tag":181,"props":5696,"children":5698},{"className":5697},[189],[5699,5721],{"type":10,"tag":181,"props":5700,"children":5702},{"className":5701},[194],[5703],{"type":10,"tag":197,"props":5704,"children":5705},{"xmlns":199},[5706],{"type":10,"tag":203,"props":5707,"children":5708},{},[5709,5716],{"type":10,"tag":207,"props":5710,"children":5711},{},[5712],{"type":10,"tag":245,"props":5713,"children":5714},{"mathvariant":3091},[5715],{"type":16,"value":1025},{"type":10,"tag":1141,"props":5717,"children":5718},{"encoding":1143},[5719],{"type":16,"value":5720},"\\mathbf{o}",{"type":10,"tag":181,"props":5722,"children":5724},{"className":5723,"ariaHidden":216},[1150],[5725],{"type":10,"tag":181,"props":5726,"children":5728},{"className":5727},[1155],[5729,5733],{"type":10,"tag":181,"props":5730,"children":5732},{"className":5731,"style":3110},[1160],[],{"type":10,"tag":181,"props":5734,"children":5736},{"className":5735},[1245,3115],[5737],{"type":16,"value":1025},{"type":16,"value":4500},{"type":10,"tag":181,"props":5740,"children":5742},{"className":5741},[189],[5743,5764],{"type":10,"tag":181,"props":5744,"children":5746},{"className":5745},[194],[5747],{"type":10,"tag":197,"props":5748,"children":5749},{"xmlns":199},[5750],{"type":10,"tag":203,"props":5751,"children":5752},{},[5753,5760],{"type":10,"tag":207,"props":5754,"children":5755},{},[5756],{"type":10,"tag":245,"props":5757,"children":5758},{"mathvariant":3091},[5759],{"type":16,"value":3141},{"type":10,"tag":1141,"props":5761,"children":5762},{"encoding":1143},[5763],{"type":16,"value":3146},{"type":10,"tag":181,"props":5765,"children":5767},{"className":5766,"ariaHidden":216},[1150],[5768],{"type":10,"tag":181,"props":5769,"children":5771},{"className":5770},[1155],[5772,5776],{"type":10,"tag":181,"props":5773,"children":5775},{"className":5774,"style":3158},[1160],[],{"type":10,"tag":181,"props":5777,"children":5779},{"className":5778},[1245,3115],[5780],{"type":16,"value":3141},{"type":16,"value":5782}," are the ray origin and\nunnormalized direction, respectively; the vector described by x",{"type":10,"tag":163,"props":5784,"children":5785},{},[5786],{"type":16,"value":167},{"type":16,"value":5788},",\ny",{"type":10,"tag":163,"props":5790,"children":5791},{},[5792],{"type":16,"value":167},{"type":16,"value":5794},", and z",{"type":10,"tag":163,"props":5796,"children":5797},{},[5798],{"type":16,"value":167},{"type":16,"value":5800}," is any position in acceleration structure\nspace; and the vector described by x",{"type":10,"tag":163,"props":5802,"children":5803},{},[5804],{"type":16,"value":177},{"type":16,"value":5806},", y",{"type":10,"tag":163,"props":5808,"children":5809},{},[5810],{"type":16,"value":177},{"type":16,"value":5794},{"type":10,"tag":163,"props":5813,"children":5814},{},[5815],{"type":16,"value":177},{"type":16,"value":5817}," is\nthe same position in ray space.",{"type":10,"tag":18,"props":5819,"children":5820},{},[5821,5823,5828,5830,5912],{"type":16,"value":5822},"An ",{"type":10,"tag":159,"props":5824,"children":5825},{},[5826],{"type":16,"value":5827},"intersection candidate",{"type":16,"value":5829}," is a unique point of intersection between a ray\nand a geometric primitive.\nFor any primitive that has within its bounds a position\n",{"type":10,"tag":181,"props":5831,"children":5833},{"className":5832},[189],[5834,5879],{"type":10,"tag":181,"props":5835,"children":5837},{"className":5836},[194],[5838],{"type":10,"tag":197,"props":5839,"children":5840},{"xmlns":199},[5841],{"type":10,"tag":203,"props":5842,"children":5843},{},[5844,5874],{"type":10,"tag":207,"props":5845,"children":5846},{},[5847,5851,5855,5859,5863],{"type":10,"tag":245,"props":5848,"children":5849},{"mathvariant":3091},[5850],{"type":16,"value":249},{"type":10,"tag":245,"props":5852,"children":5853},{"mathvariant":3091},[5854],{"type":16,"value":282},{"type":10,"tag":245,"props":5856,"children":5857},{"mathvariant":3091},[5858],{"type":16,"value":311},{"type":10,"tag":245,"props":5860,"children":5861},{"mathvariant":3091},[5862],{"type":16,"value":255},{"type":10,"tag":207,"props":5864,"children":5865},{},[5866,5870],{"type":10,"tag":245,"props":5867,"children":5868},{"mathvariant":3091},[5869],{"type":16,"value":44},{"type":10,"tag":245,"props":5871,"children":5872},{"mathvariant":3091},[5873],{"type":16,"value":468},{"type":10,"tag":1141,"props":5875,"children":5876},{"encoding":1143},[5877],{"type":16,"value":5878},"\\mathbf{xyz\\_{as}}",{"type":10,"tag":181,"props":5880,"children":5882},{"className":5881,"ariaHidden":216},[1150],[5883],{"type":10,"tag":181,"props":5884,"children":5886},{"className":5885},[1155],[5887,5892],{"type":10,"tag":181,"props":5888,"children":5891},{"className":5889,"style":5890},[1160],"height:0.7544em;vertical-align:-0.31em;",[],{"type":10,"tag":181,"props":5893,"children":5895},{"className":5894},[1245],[5896,5903],{"type":10,"tag":181,"props":5897,"children":5900},{"className":5898,"style":5899},[1245,3115],"margin-right:0.03194em;",[5901],{"type":16,"value":5902},"xyz_",{"type":10,"tag":181,"props":5904,"children":5906},{"className":5905},[1245],[5907],{"type":10,"tag":181,"props":5908,"children":5910},{"className":5909},[1245,3115],[5911],{"type":16,"value":167},{"type":16,"value":5913}," such that",{"type":10,"tag":181,"props":5915,"children":5917},{"className":5916},[184],[5918],{"type":10,"tag":181,"props":5919,"children":5921},{"className":5920},[189],[5922,6334],{"type":10,"tag":181,"props":5923,"children":5925},{"className":5924},[194],[5926],{"type":10,"tag":197,"props":5927,"children":5928},{"xmlns":199,"display":200},[5929],{"type":10,"tag":203,"props":5930,"children":5931},{},[5932,6329],{"type":10,"tag":221,"props":5933,"children":5936},{"rowspacing":4697,"columnalign":5934,"columnspacing":5935},"right left right","0em 1em",[5937,5981,6029,6174,6316],{"type":10,"tag":228,"props":5938,"children":5939},{},[5940,5961],{"type":10,"tag":232,"props":5941,"children":5942},{},[5943],{"type":10,"tag":236,"props":5944,"children":5945},{"scriptlevel":238,"displaystyle":216},[5946],{"type":10,"tag":207,"props":5947,"children":5948},{},[5949,5953,5957],{"type":10,"tag":245,"props":5950,"children":5951},{},[5952],{"type":16,"value":249},{"type":10,"tag":245,"props":5954,"children":5955},{"mathvariant":252},[5956],{"type":16,"value":255},{"type":10,"tag":245,"props":5958,"children":5959},{},[5960],{"type":16,"value":177},{"type":10,"tag":232,"props":5962,"children":5963},{},[5964],{"type":10,"tag":236,"props":5965,"children":5966},{"scriptlevel":238,"displaystyle":216},[5967],{"type":10,"tag":207,"props":5968,"children":5969},{},[5970,5973,5977],{"type":10,"tag":207,"props":5971,"children":5972},{},[],{"type":10,"tag":214,"props":5974,"children":5975},{},[5976],{"type":16,"value":329},{"type":10,"tag":370,"props":5978,"children":5979},{},[5980],{"type":16,"value":238},{"type":10,"tag":228,"props":5982,"children":5983},{},[5984,6009],{"type":10,"tag":232,"props":5985,"children":5986},{},[5987],{"type":10,"tag":236,"props":5988,"children":5989},{"scriptlevel":238,"displaystyle":216},[5990],{"type":10,"tag":207,"props":5991,"children":5992},{},[5993,5997,6001,6005],{"type":10,"tag":273,"props":5994,"children":5995},{},[5996],{"type":16,"value":277},{"type":10,"tag":245,"props":5998,"children":5999},{},[6000],{"type":16,"value":282},{"type":10,"tag":245,"props":6002,"children":6003},{"mathvariant":252},[6004],{"type":16,"value":255},{"type":10,"tag":245,"props":6006,"children":6007},{},[6008],{"type":16,"value":177},{"type":10,"tag":232,"props":6010,"children":6011},{},[6012],{"type":10,"tag":236,"props":6013,"children":6014},{"scriptlevel":238,"displaystyle":216},[6015],{"type":10,"tag":207,"props":6016,"children":6017},{},[6018,6021,6025],{"type":10,"tag":207,"props":6019,"children":6020},{},[],{"type":10,"tag":214,"props":6022,"children":6023},{},[6024],{"type":16,"value":329},{"type":10,"tag":370,"props":6026,"children":6027},{},[6028],{"type":16,"value":238},{"type":10,"tag":228,"props":6030,"children":6031},{},[6032,6124,6163],{"type":10,"tag":232,"props":6033,"children":6034},{},[6035],{"type":10,"tag":236,"props":6036,"children":6037},{"scriptlevel":238,"displaystyle":216},[6038],{"type":10,"tag":207,"props":6039,"children":6040},{},[6041,6045,6050,6054,6071,6076],{"type":10,"tag":273,"props":6042,"children":6043},{},[6044],{"type":16,"value":277},{"type":10,"tag":245,"props":6046,"children":6047},{},[6048],{"type":16,"value":6049},"t",{"type":10,"tag":245,"props":6051,"children":6052},{"mathvariant":252},[6053],{"type":16,"value":255},{"type":10,"tag":207,"props":6055,"children":6056},{},[6057,6062,6066],{"type":10,"tag":245,"props":6058,"children":6059},{},[6060],{"type":16,"value":6061},"m",{"type":10,"tag":245,"props":6063,"children":6064},{},[6065],{"type":16,"value":3329},{"type":10,"tag":245,"props":6067,"children":6068},{},[6069],{"type":16,"value":6070},"n",{"type":10,"tag":214,"props":6072,"children":6073},{},[6074],{"type":16,"value":6075},"\u003C",{"type":10,"tag":3265,"props":6077,"children":6078},{},[6079,6101],{"type":10,"tag":207,"props":6080,"children":6081},{},[6082,6086],{"type":10,"tag":214,"props":6083,"children":6084},{},[6085],{"type":16,"value":388},{"type":10,"tag":207,"props":6087,"children":6088},{},[6089,6093,6097],{"type":10,"tag":245,"props":6090,"children":6091},{},[6092],{"type":16,"value":311},{"type":10,"tag":245,"props":6094,"children":6095},{"mathvariant":252},[6096],{"type":16,"value":255},{"type":10,"tag":245,"props":6098,"children":6099},{},[6100],{"type":16,"value":177},{"type":10,"tag":207,"props":6102,"children":6103},{},[6104,6108,6112,6116,6120],{"type":10,"tag":245,"props":6105,"children":6106},{"mathvariant":252},[6107],{"type":16,"value":3291},{"type":10,"tag":245,"props":6109,"children":6110},{"mathvariant":252},[6111],{"type":16,"value":3291},{"type":10,"tag":245,"props":6113,"children":6114},{"mathvariant":3091},[6115],{"type":16,"value":3141},{"type":10,"tag":245,"props":6117,"children":6118},{"mathvariant":252},[6119],{"type":16,"value":3291},{"type":10,"tag":245,"props":6121,"children":6122},{"mathvariant":252},[6123],{"type":16,"value":3291},{"type":10,"tag":232,"props":6125,"children":6126},{},[6127],{"type":10,"tag":236,"props":6128,"children":6129},{"scriptlevel":238,"displaystyle":216},[6130],{"type":10,"tag":207,"props":6131,"children":6132},{},[6133,6136,6140,6144,6148],{"type":10,"tag":207,"props":6134,"children":6135},{},[],{"type":10,"tag":214,"props":6137,"children":6138},{},[6139],{"type":16,"value":6075},{"type":10,"tag":245,"props":6141,"children":6142},{},[6143],{"type":16,"value":6049},{"type":10,"tag":245,"props":6145,"children":6146},{"mathvariant":252},[6147],{"type":16,"value":255},{"type":10,"tag":207,"props":6149,"children":6150},{},[6151,6155,6159],{"type":10,"tag":245,"props":6152,"children":6153},{},[6154],{"type":16,"value":6061},{"type":10,"tag":245,"props":6156,"children":6157},{},[6158],{"type":16,"value":44},{"type":10,"tag":245,"props":6160,"children":6161},{},[6162],{"type":16,"value":249},{"type":10,"tag":232,"props":6164,"children":6165},{},[6166],{"type":10,"tag":236,"props":6167,"children":6168},{"scriptlevel":238,"displaystyle":216},[6169],{"type":10,"tag":273,"props":6170,"children":6171},{},[6172],{"type":16,"value":6173},"if the primitive is a triangle,",{"type":10,"tag":228,"props":6175,"children":6176},{},[6177,6266,6305],{"type":10,"tag":232,"props":6178,"children":6179},{},[6180],{"type":10,"tag":236,"props":6181,"children":6182},{"scriptlevel":238,"displaystyle":216},[6183],{"type":10,"tag":207,"props":6184,"children":6185},{},[6186,6190,6194,6198,6213,6218],{"type":10,"tag":273,"props":6187,"children":6188},{},[6189],{"type":16,"value":277},{"type":10,"tag":245,"props":6191,"children":6192},{},[6193],{"type":16,"value":6049},{"type":10,"tag":245,"props":6195,"children":6196},{"mathvariant":252},[6197],{"type":16,"value":255},{"type":10,"tag":207,"props":6199,"children":6200},{},[6201,6205,6209],{"type":10,"tag":245,"props":6202,"children":6203},{},[6204],{"type":16,"value":6061},{"type":10,"tag":245,"props":6206,"children":6207},{},[6208],{"type":16,"value":3329},{"type":10,"tag":245,"props":6210,"children":6211},{},[6212],{"type":16,"value":6070},{"type":10,"tag":214,"props":6214,"children":6215},{},[6216],{"type":16,"value":6217},"≤",{"type":10,"tag":3265,"props":6219,"children":6220},{},[6221,6243],{"type":10,"tag":207,"props":6222,"children":6223},{},[6224,6228],{"type":10,"tag":214,"props":6225,"children":6226},{},[6227],{"type":16,"value":388},{"type":10,"tag":207,"props":6229,"children":6230},{},[6231,6235,6239],{"type":10,"tag":245,"props":6232,"children":6233},{},[6234],{"type":16,"value":311},{"type":10,"tag":245,"props":6236,"children":6237},{"mathvariant":252},[6238],{"type":16,"value":255},{"type":10,"tag":245,"props":6240,"children":6241},{},[6242],{"type":16,"value":177},{"type":10,"tag":207,"props":6244,"children":6245},{},[6246,6250,6254,6258,6262],{"type":10,"tag":245,"props":6247,"children":6248},{"mathvariant":252},[6249],{"type":16,"value":3291},{"type":10,"tag":245,"props":6251,"children":6252},{"mathvariant":252},[6253],{"type":16,"value":3291},{"type":10,"tag":245,"props":6255,"children":6256},{"mathvariant":3091},[6257],{"type":16,"value":3141},{"type":10,"tag":245,"props":6259,"children":6260},{"mathvariant":252},[6261],{"type":16,"value":3291},{"type":10,"tag":245,"props":6263,"children":6264},{"mathvariant":252},[6265],{"type":16,"value":3291},{"type":10,"tag":232,"props":6267,"children":6268},{},[6269],{"type":10,"tag":236,"props":6270,"children":6271},{"scriptlevel":238,"displaystyle":216},[6272],{"type":10,"tag":207,"props":6273,"children":6274},{},[6275,6278,6282,6286,6290],{"type":10,"tag":207,"props":6276,"children":6277},{},[],{"type":10,"tag":214,"props":6279,"children":6280},{},[6281],{"type":16,"value":6217},{"type":10,"tag":245,"props":6283,"children":6284},{},[6285],{"type":16,"value":6049},{"type":10,"tag":245,"props":6287,"children":6288},{"mathvariant":252},[6289],{"type":16,"value":255},{"type":10,"tag":207,"props":6291,"children":6292},{},[6293,6297,6301],{"type":10,"tag":245,"props":6294,"children":6295},{},[6296],{"type":16,"value":6061},{"type":10,"tag":245,"props":6298,"children":6299},{},[6300],{"type":16,"value":44},{"type":10,"tag":245,"props":6302,"children":6303},{},[6304],{"type":16,"value":249},{"type":10,"tag":232,"props":6306,"children":6307},{},[6308],{"type":10,"tag":236,"props":6309,"children":6310},{"scriptlevel":238,"displaystyle":216},[6311],{"type":10,"tag":273,"props":6312,"children":6313},{},[6314],{"type":16,"value":6315},"otherwise",{"type":10,"tag":228,"props":6317,"children":6318},{},[6319],{"type":10,"tag":232,"props":6320,"children":6321},{},[6322],{"type":10,"tag":236,"props":6323,"children":6324},{"scriptlevel":238,"displaystyle":216},[6325],{"type":10,"tag":273,"props":6326,"children":6327},{},[6328],{"type":16,"value":277},{"type":10,"tag":1141,"props":6330,"children":6331},{"encoding":1143},[6332],{"type":16,"value":6333},"\\begin{aligned}\nx\\_r &= 0 \\\\\\\ny\\_r &= 0 \\\\\\\nt\\_\\mathit{min} \\lt {-{z\\_r}\\over{||\\mathbf{d}||}} &\\lt t\\_\\mathit{max} & \\text{if the primitive is a triangle,} \\\\\\\nt\\_\\mathit{min} \\leq {-{z\\_r}\\over{||\\mathbf{d}||}} &\\leq t\\_\\mathit{max} & \\text{otherwise} \\\\\\\n\\end{aligned}",{"type":10,"tag":181,"props":6335,"children":6337},{"className":6336,"ariaHidden":216},[1150],[6338],{"type":10,"tag":181,"props":6339,"children":6341},{"className":6340},[1155],[6342,6347],{"type":10,"tag":181,"props":6343,"children":6346},{"className":6344,"style":6345},[1160],"height:9.5387em;vertical-align:-4.5193em;",[],{"type":10,"tag":181,"props":6348,"children":6350},{"className":6349},[1245],[6351],{"type":10,"tag":181,"props":6352,"children":6354},{"className":6353},[221],[6355,6807,7001,7005],{"type":10,"tag":181,"props":6356,"children":6358},{"className":6357},[4863],[6359],{"type":10,"tag":181,"props":6360,"children":6362},{"className":6361},[1182,1183],[6363,6795],{"type":10,"tag":181,"props":6364,"children":6366},{"className":6365},[1188],[6367,6790],{"type":10,"tag":181,"props":6368,"children":6371},{"className":6369,"style":6370},[1193],"height:5.0193em;",[6372,6400,6432,6604,6773],{"type":10,"tag":181,"props":6373,"children":6375},{"style":6374},"top:-7.4627em;",[6376,6381],{"type":10,"tag":181,"props":6377,"children":6380},{"className":6378,"style":6379},[1203],"height:3.2833em;",[],{"type":10,"tag":181,"props":6382,"children":6384},{"className":6383},[1245],[6385,6390,6395],{"type":10,"tag":181,"props":6386,"children":6388},{"className":6387},[1245,1290],[6389],{"type":16,"value":249},{"type":10,"tag":181,"props":6391,"children":6393},{"className":6392,"style":1296},[1245],[6394],{"type":16,"value":255},{"type":10,"tag":181,"props":6396,"children":6398},{"className":6397,"style":1296},[1245,1290],[6399],{"type":16,"value":177},{"type":10,"tag":181,"props":6401,"children":6403},{"style":6402},"top:-5.9627em;",[6404,6408],{"type":10,"tag":181,"props":6405,"children":6407},{"className":6406,"style":6379},[1203],[],{"type":10,"tag":181,"props":6409,"children":6411},{"className":6410},[1245],[6412,6417,6422,6427],{"type":10,"tag":181,"props":6413,"children":6415},{"className":6414},[1323],[6416],{"type":16,"value":277},{"type":10,"tag":181,"props":6418,"children":6420},{"className":6419,"style":1329},[1245,1290],[6421],{"type":16,"value":282},{"type":10,"tag":181,"props":6423,"children":6425},{"className":6424,"style":1296},[1245],[6426],{"type":16,"value":255},{"type":10,"tag":181,"props":6428,"children":6430},{"className":6429,"style":1296},[1245,1290],[6431],{"type":16,"value":177},{"type":10,"tag":181,"props":6433,"children":6435},{"style":6434},"top:-4.0193em;",[6436,6440],{"type":10,"tag":181,"props":6437,"children":6439},{"className":6438,"style":6379},[1203],[],{"type":10,"tag":181,"props":6441,"children":6443},{"className":6442},[1245],[6444,6449,6454,6459,6469,6473,6478,6482],{"type":10,"tag":181,"props":6445,"children":6447},{"className":6446},[1323],[6448],{"type":16,"value":277},{"type":10,"tag":181,"props":6450,"children":6452},{"className":6451},[1245,1290],[6453],{"type":16,"value":6049},{"type":10,"tag":181,"props":6455,"children":6457},{"className":6456,"style":1296},[1245],[6458],{"type":16,"value":255},{"type":10,"tag":181,"props":6460,"children":6462},{"className":6461},[1245],[6463],{"type":10,"tag":181,"props":6464,"children":6466},{"className":6465},[1245,4496],[6467],{"type":16,"value":6468},"min",{"type":10,"tag":181,"props":6470,"children":6472},{"className":6471,"style":1460},[1323],[],{"type":10,"tag":181,"props":6474,"children":6476},{"className":6475},[1465],[6477],{"type":16,"value":6075},{"type":10,"tag":181,"props":6479,"children":6481},{"className":6480,"style":1460},[1323],[],{"type":10,"tag":181,"props":6483,"children":6485},{"className":6484},[1245],[6486],{"type":10,"tag":181,"props":6487,"children":6489},{"className":6488},[1245],[6490,6494,6600],{"type":10,"tag":181,"props":6491,"children":6493},{"className":6492},[1171,3781],[],{"type":10,"tag":181,"props":6495,"children":6497},{"className":6496},[3265],[6498],{"type":10,"tag":181,"props":6499,"children":6501},{"className":6500},[1182,1183],[6502,6589],{"type":10,"tag":181,"props":6503,"children":6505},{"className":6504},[1188],[6506,6584],{"type":10,"tag":181,"props":6507,"children":6510},{"className":6508,"style":6509},[1193],"height:1.2833em;",[6511,6537,6548],{"type":10,"tag":181,"props":6512,"children":6513},{"style":5010},[6514,6518],{"type":10,"tag":181,"props":6515,"children":6517},{"className":6516,"style":1281},[1203],[],{"type":10,"tag":181,"props":6519,"children":6521},{"className":6520},[1245],[6522,6527,6532],{"type":10,"tag":181,"props":6523,"children":6525},{"className":6524},[1245],[6526],{"type":16,"value":3821},{"type":10,"tag":181,"props":6528,"children":6530},{"className":6529},[1245,3115],[6531],{"type":16,"value":3141},{"type":10,"tag":181,"props":6533,"children":6535},{"className":6534},[1245],[6536],{"type":16,"value":3821},{"type":10,"tag":181,"props":6538,"children":6539},{"style":3844},[6540,6544],{"type":10,"tag":181,"props":6541,"children":6543},{"className":6542,"style":1281},[1203],[],{"type":10,"tag":181,"props":6545,"children":6547},{"className":6546,"style":3854},[3853],[],{"type":10,"tag":181,"props":6549,"children":6551},{"style":6550},"top:-3.7em;",[6552,6556],{"type":10,"tag":181,"props":6553,"children":6555},{"className":6554,"style":1281},[1203],[],{"type":10,"tag":181,"props":6557,"children":6559},{"className":6558},[1245],[6560,6565],{"type":10,"tag":181,"props":6561,"children":6563},{"className":6562},[1245],[6564],{"type":16,"value":388},{"type":10,"tag":181,"props":6566,"children":6568},{"className":6567},[1245],[6569,6574,6579],{"type":10,"tag":181,"props":6570,"children":6572},{"className":6571,"style":1366},[1245,1290],[6573],{"type":16,"value":311},{"type":10,"tag":181,"props":6575,"children":6577},{"className":6576,"style":1296},[1245],[6578],{"type":16,"value":255},{"type":10,"tag":181,"props":6580,"children":6582},{"className":6581,"style":1296},[1245,1290],[6583],{"type":16,"value":177},{"type":10,"tag":181,"props":6585,"children":6587},{"className":6586},[1226],[6588],{"type":16,"value":1229},{"type":10,"tag":181,"props":6590,"children":6592},{"className":6591},[1188],[6593],{"type":10,"tag":181,"props":6594,"children":6596},{"className":6595,"style":5093},[1193],[6597],{"type":10,"tag":181,"props":6598,"children":6599},{},[],{"type":10,"tag":181,"props":6601,"children":6603},{"className":6602},[1406,3781],[],{"type":10,"tag":181,"props":6605,"children":6607},{"style":6606},"top:-1.5em;",[6608,6612],{"type":10,"tag":181,"props":6609,"children":6611},{"className":6610,"style":6379},[1203],[],{"type":10,"tag":181,"props":6613,"children":6615},{"className":6614},[1245],[6616,6621,6626,6631,6640,6644,6649,6653],{"type":10,"tag":181,"props":6617,"children":6619},{"className":6618},[1323],[6620],{"type":16,"value":277},{"type":10,"tag":181,"props":6622,"children":6624},{"className":6623},[1245,1290],[6625],{"type":16,"value":6049},{"type":10,"tag":181,"props":6627,"children":6629},{"className":6628,"style":1296},[1245],[6630],{"type":16,"value":255},{"type":10,"tag":181,"props":6632,"children":6634},{"className":6633},[1245],[6635],{"type":10,"tag":181,"props":6636,"children":6638},{"className":6637},[1245,4496],[6639],{"type":16,"value":6468},{"type":10,"tag":181,"props":6641,"children":6643},{"className":6642,"style":1460},[1323],[],{"type":10,"tag":181,"props":6645,"children":6647},{"className":6646},[1465],[6648],{"type":16,"value":6217},{"type":10,"tag":181,"props":6650,"children":6652},{"className":6651,"style":1460},[1323],[],{"type":10,"tag":181,"props":6654,"children":6656},{"className":6655},[1245],[6657],{"type":10,"tag":181,"props":6658,"children":6660},{"className":6659},[1245],[6661,6665,6769],{"type":10,"tag":181,"props":6662,"children":6664},{"className":6663},[1171,3781],[],{"type":10,"tag":181,"props":6666,"children":6668},{"className":6667},[3265],[6669],{"type":10,"tag":181,"props":6670,"children":6672},{"className":6671},[1182,1183],[6673,6758],{"type":10,"tag":181,"props":6674,"children":6676},{"className":6675},[1188],[6677,6753],{"type":10,"tag":181,"props":6678,"children":6680},{"className":6679,"style":6509},[1193],[6681,6707,6718],{"type":10,"tag":181,"props":6682,"children":6683},{"style":5010},[6684,6688],{"type":10,"tag":181,"props":6685,"children":6687},{"className":6686,"style":1281},[1203],[],{"type":10,"tag":181,"props":6689,"children":6691},{"className":6690},[1245],[6692,6697,6702],{"type":10,"tag":181,"props":6693,"children":6695},{"className":6694},[1245],[6696],{"type":16,"value":3821},{"type":10,"tag":181,"props":6698,"children":6700},{"className":6699},[1245,3115],[6701],{"type":16,"value":3141},{"type":10,"tag":181,"props":6703,"children":6705},{"className":6704},[1245],[6706],{"type":16,"value":3821},{"type":10,"tag":181,"props":6708,"children":6709},{"style":3844},[6710,6714],{"type":10,"tag":181,"props":6711,"children":6713},{"className":6712,"style":1281},[1203],[],{"type":10,"tag":181,"props":6715,"children":6717},{"className":6716,"style":3854},[3853],[],{"type":10,"tag":181,"props":6719,"children":6720},{"style":6550},[6721,6725],{"type":10,"tag":181,"props":6722,"children":6724},{"className":6723,"style":1281},[1203],[],{"type":10,"tag":181,"props":6726,"children":6728},{"className":6727},[1245],[6729,6734],{"type":10,"tag":181,"props":6730,"children":6732},{"className":6731},[1245],[6733],{"type":16,"value":388},{"type":10,"tag":181,"props":6735,"children":6737},{"className":6736},[1245],[6738,6743,6748],{"type":10,"tag":181,"props":6739,"children":6741},{"className":6740,"style":1366},[1245,1290],[6742],{"type":16,"value":311},{"type":10,"tag":181,"props":6744,"children":6746},{"className":6745,"style":1296},[1245],[6747],{"type":16,"value":255},{"type":10,"tag":181,"props":6749,"children":6751},{"className":6750,"style":1296},[1245,1290],[6752],{"type":16,"value":177},{"type":10,"tag":181,"props":6754,"children":6756},{"className":6755},[1226],[6757],{"type":16,"value":1229},{"type":10,"tag":181,"props":6759,"children":6761},{"className":6760},[1188],[6762],{"type":10,"tag":181,"props":6763,"children":6765},{"className":6764,"style":5093},[1193],[6766],{"type":10,"tag":181,"props":6767,"children":6768},{},[],{"type":10,"tag":181,"props":6770,"children":6772},{"className":6771},[1406,3781],[],{"type":10,"tag":181,"props":6774,"children":6776},{"style":6775},"top:0.576em;",[6777,6781],{"type":10,"tag":181,"props":6778,"children":6780},{"className":6779,"style":6379},[1203],[],{"type":10,"tag":181,"props":6782,"children":6784},{"className":6783},[1245],[6785],{"type":10,"tag":181,"props":6786,"children":6788},{"className":6787},[1323],[6789],{"type":16,"value":277},{"type":10,"tag":181,"props":6791,"children":6793},{"className":6792},[1226],[6794],{"type":16,"value":1229},{"type":10,"tag":181,"props":6796,"children":6798},{"className":6797},[1188],[6799],{"type":10,"tag":181,"props":6800,"children":6803},{"className":6801,"style":6802},[1193],"height:4.5193em;",[6804],{"type":10,"tag":181,"props":6805,"children":6806},{},[],{"type":10,"tag":181,"props":6808,"children":6810},{"className":6809},[3746],[6811],{"type":10,"tag":181,"props":6812,"children":6814},{"className":6813},[1182,1183],[6815,6989],{"type":10,"tag":181,"props":6816,"children":6818},{"className":6817},[1188],[6819,6984],{"type":10,"tag":181,"props":6820,"children":6822},{"className":6821,"style":6370},[1193],[6823,6856,6889,6937],{"type":10,"tag":181,"props":6824,"children":6825},{"style":6374},[6826,6830],{"type":10,"tag":181,"props":6827,"children":6829},{"className":6828,"style":6379},[1203],[],{"type":10,"tag":181,"props":6831,"children":6833},{"className":6832},[1245],[6834,6838,6842,6847,6851],{"type":10,"tag":181,"props":6835,"children":6837},{"className":6836},[1245],[],{"type":10,"tag":181,"props":6839,"children":6841},{"className":6840,"style":1460},[1323],[],{"type":10,"tag":181,"props":6843,"children":6845},{"className":6844},[1465],[6846],{"type":16,"value":329},{"type":10,"tag":181,"props":6848,"children":6850},{"className":6849,"style":1460},[1323],[],{"type":10,"tag":181,"props":6852,"children":6854},{"className":6853},[1245],[6855],{"type":16,"value":238},{"type":10,"tag":181,"props":6857,"children":6858},{"style":6402},[6859,6863],{"type":10,"tag":181,"props":6860,"children":6862},{"className":6861,"style":6379},[1203],[],{"type":10,"tag":181,"props":6864,"children":6866},{"className":6865},[1245],[6867,6871,6875,6880,6884],{"type":10,"tag":181,"props":6868,"children":6870},{"className":6869},[1245],[],{"type":10,"tag":181,"props":6872,"children":6874},{"className":6873,"style":1460},[1323],[],{"type":10,"tag":181,"props":6876,"children":6878},{"className":6877},[1465],[6879],{"type":16,"value":329},{"type":10,"tag":181,"props":6881,"children":6883},{"className":6882,"style":1460},[1323],[],{"type":10,"tag":181,"props":6885,"children":6887},{"className":6886},[1245],[6888],{"type":16,"value":238},{"type":10,"tag":181,"props":6890,"children":6891},{"style":6434},[6892,6896],{"type":10,"tag":181,"props":6893,"children":6895},{"className":6894,"style":6379},[1203],[],{"type":10,"tag":181,"props":6897,"children":6899},{"className":6898},[1245],[6900,6904,6908,6913,6917,6922,6927],{"type":10,"tag":181,"props":6901,"children":6903},{"className":6902},[1245],[],{"type":10,"tag":181,"props":6905,"children":6907},{"className":6906,"style":1460},[1323],[],{"type":10,"tag":181,"props":6909,"children":6911},{"className":6910},[1465],[6912],{"type":16,"value":6075},{"type":10,"tag":181,"props":6914,"children":6916},{"className":6915,"style":1460},[1323],[],{"type":10,"tag":181,"props":6918,"children":6920},{"className":6919},[1245,1290],[6921],{"type":16,"value":6049},{"type":10,"tag":181,"props":6923,"children":6925},{"className":6924,"style":1296},[1245],[6926],{"type":16,"value":255},{"type":10,"tag":181,"props":6928,"children":6930},{"className":6929},[1245],[6931],{"type":10,"tag":181,"props":6932,"children":6934},{"className":6933},[1245,4496],[6935],{"type":16,"value":6936},"max",{"type":10,"tag":181,"props":6938,"children":6939},{"style":6606},[6940,6944],{"type":10,"tag":181,"props":6941,"children":6943},{"className":6942,"style":6379},[1203],[],{"type":10,"tag":181,"props":6945,"children":6947},{"className":6946},[1245],[6948,6952,6956,6961,6965,6970,6975],{"type":10,"tag":181,"props":6949,"children":6951},{"className":6950},[1245],[],{"type":10,"tag":181,"props":6953,"children":6955},{"className":6954,"style":1460},[1323],[],{"type":10,"tag":181,"props":6957,"children":6959},{"className":6958},[1465],[6960],{"type":16,"value":6217},{"type":10,"tag":181,"props":6962,"children":6964},{"className":6963,"style":1460},[1323],[],{"type":10,"tag":181,"props":6966,"children":6968},{"className":6967},[1245,1290],[6969],{"type":16,"value":6049},{"type":10,"tag":181,"props":6971,"children":6973},{"className":6972,"style":1296},[1245],[6974],{"type":16,"value":255},{"type":10,"tag":181,"props":6976,"children":6978},{"className":6977},[1245],[6979],{"type":10,"tag":181,"props":6980,"children":6982},{"className":6981},[1245,4496],[6983],{"type":16,"value":6936},{"type":10,"tag":181,"props":6985,"children":6987},{"className":6986},[1226],[6988],{"type":16,"value":1229},{"type":10,"tag":181,"props":6990,"children":6992},{"className":6991},[1188],[6993],{"type":10,"tag":181,"props":6994,"children":6997},{"className":6995,"style":6996},[1193],"height:3.0193em;",[6998],{"type":10,"tag":181,"props":6999,"children":7000},{},[],{"type":10,"tag":181,"props":7002,"children":7004},{"className":7003,"style":4369},[1254],[],{"type":10,"tag":181,"props":7006,"children":7008},{"className":7007},[4863],[7009],{"type":10,"tag":181,"props":7010,"children":7012},{"className":7011},[1182,1183],[7013,7067],{"type":10,"tag":181,"props":7014,"children":7016},{"className":7015},[1188],[7017,7062],{"type":10,"tag":181,"props":7018,"children":7021},{"className":7019,"style":7020},[1193],"height:2.0193em;",[7022,7042],{"type":10,"tag":181,"props":7023,"children":7024},{"style":6434},[7025,7029],{"type":10,"tag":181,"props":7026,"children":7028},{"className":7027,"style":6379},[1203],[],{"type":10,"tag":181,"props":7030,"children":7032},{"className":7031},[1245],[7033],{"type":10,"tag":181,"props":7034,"children":7036},{"className":7035},[1245,16],[7037],{"type":10,"tag":181,"props":7038,"children":7040},{"className":7039},[1245],[7041],{"type":16,"value":6173},{"type":10,"tag":181,"props":7043,"children":7044},{"style":6606},[7045,7049],{"type":10,"tag":181,"props":7046,"children":7048},{"className":7047,"style":6379},[1203],[],{"type":10,"tag":181,"props":7050,"children":7052},{"className":7051},[1245],[7053],{"type":10,"tag":181,"props":7054,"children":7056},{"className":7055},[1245,16],[7057],{"type":10,"tag":181,"props":7058,"children":7060},{"className":7059},[1245],[7061],{"type":16,"value":6315},{"type":10,"tag":181,"props":7063,"children":7065},{"className":7064},[1226],[7066],{"type":16,"value":1229},{"type":10,"tag":181,"props":7068,"children":7070},{"className":7069},[1188],[7071],{"type":10,"tag":181,"props":7072,"children":7074},{"className":7073,"style":6996},[1193],[7075],{"type":10,"tag":181,"props":7076,"children":7077},{},[],{"type":10,"tag":18,"props":7079,"children":7080},{},[7081,7083,7331],{"type":16,"value":7082},"(where ",{"type":10,"tag":181,"props":7084,"children":7086},{"className":7085},[189],[7087,7161],{"type":10,"tag":181,"props":7088,"children":7090},{"className":7089},[194],[7091],{"type":10,"tag":197,"props":7092,"children":7093},{"xmlns":199},[7094],{"type":10,"tag":203,"props":7095,"children":7096},{},[7097,7156],{"type":10,"tag":207,"props":7098,"children":7099},{},[7100,7104,7108],{"type":10,"tag":245,"props":7101,"children":7102},{},[7103],{"type":16,"value":6049},{"type":10,"tag":214,"props":7105,"children":7106},{},[7107],{"type":16,"value":329},{"type":10,"tag":3265,"props":7109,"children":7110},{},[7111,7133],{"type":10,"tag":207,"props":7112,"children":7113},{},[7114,7118],{"type":10,"tag":214,"props":7115,"children":7116},{},[7117],{"type":16,"value":388},{"type":10,"tag":207,"props":7119,"children":7120},{},[7121,7125,7129],{"type":10,"tag":245,"props":7122,"children":7123},{},[7124],{"type":16,"value":311},{"type":10,"tag":245,"props":7126,"children":7127},{"mathvariant":252},[7128],{"type":16,"value":255},{"type":10,"tag":245,"props":7130,"children":7131},{},[7132],{"type":16,"value":177},{"type":10,"tag":207,"props":7134,"children":7135},{},[7136,7140,7144,7148,7152],{"type":10,"tag":245,"props":7137,"children":7138},{"mathvariant":252},[7139],{"type":16,"value":3291},{"type":10,"tag":245,"props":7141,"children":7142},{"mathvariant":252},[7143],{"type":16,"value":3291},{"type":10,"tag":245,"props":7145,"children":7146},{"mathvariant":3091},[7147],{"type":16,"value":3141},{"type":10,"tag":245,"props":7149,"children":7150},{"mathvariant":252},[7151],{"type":16,"value":3291},{"type":10,"tag":245,"props":7153,"children":7154},{"mathvariant":252},[7155],{"type":16,"value":3291},{"type":10,"tag":1141,"props":7157,"children":7158},{"encoding":1143},[7159],{"type":16,"value":7160},"t = {-{z\\_r}\\over{||\\mathbf{d}||}}",{"type":10,"tag":181,"props":7162,"children":7164},{"className":7163,"ariaHidden":216},[1150],[7165,7192],{"type":10,"tag":181,"props":7166,"children":7168},{"className":7167},[1155],[7169,7174,7179,7183,7188],{"type":10,"tag":181,"props":7170,"children":7173},{"className":7171,"style":7172},[1160],"height:0.6151em;",[],{"type":10,"tag":181,"props":7175,"children":7177},{"className":7176},[1245,1290],[7178],{"type":16,"value":6049},{"type":10,"tag":181,"props":7180,"children":7182},{"className":7181,"style":1460},[1323],[],{"type":10,"tag":181,"props":7184,"children":7186},{"className":7185},[1465],[7187],{"type":16,"value":329},{"type":10,"tag":181,"props":7189,"children":7191},{"className":7190,"style":1460},[1323],[],{"type":10,"tag":181,"props":7193,"children":7195},{"className":7194},[1155],[7196,7201],{"type":10,"tag":181,"props":7197,"children":7200},{"className":7198,"style":7199},[1160],"height:1.4553em;vertical-align:-0.52em;",[],{"type":10,"tag":181,"props":7202,"children":7204},{"className":7203},[1245],[7205],{"type":10,"tag":181,"props":7206,"children":7208},{"className":7207},[1245],[7209,7213,7327],{"type":10,"tag":181,"props":7210,"children":7212},{"className":7211},[1171,3781],[],{"type":10,"tag":181,"props":7214,"children":7216},{"className":7215},[3265],[7217],{"type":10,"tag":181,"props":7218,"children":7220},{"className":7219},[1182,1183],[7221,7316],{"type":10,"tag":181,"props":7222,"children":7224},{"className":7223},[1188],[7225,7311],{"type":10,"tag":181,"props":7226,"children":7229},{"className":7227,"style":7228},[1193],"height:0.9353em;",[7230,7260,7271],{"type":10,"tag":181,"props":7231,"children":7232},{"style":3802},[7233,7237],{"type":10,"tag":181,"props":7234,"children":7236},{"className":7235,"style":1281},[1203],[],{"type":10,"tag":181,"props":7238,"children":7240},{"className":7239},[1620,1621,1622,1623],[7241],{"type":10,"tag":181,"props":7242,"children":7244},{"className":7243},[1245,1623],[7245,7250,7255],{"type":10,"tag":181,"props":7246,"children":7248},{"className":7247},[1245,1623],[7249],{"type":16,"value":3821},{"type":10,"tag":181,"props":7251,"children":7253},{"className":7252},[1245,3115,1623],[7254],{"type":16,"value":3141},{"type":10,"tag":181,"props":7256,"children":7258},{"className":7257},[1245,1623],[7259],{"type":16,"value":3821},{"type":10,"tag":181,"props":7261,"children":7262},{"style":3844},[7263,7267],{"type":10,"tag":181,"props":7264,"children":7266},{"className":7265,"style":1281},[1203],[],{"type":10,"tag":181,"props":7268,"children":7270},{"className":7269,"style":3854},[3853],[],{"type":10,"tag":181,"props":7272,"children":7274},{"style":7273},"top:-3.527em;",[7275,7279],{"type":10,"tag":181,"props":7276,"children":7278},{"className":7277,"style":1281},[1203],[],{"type":10,"tag":181,"props":7280,"children":7282},{"className":7281},[1620,1621,1622,1623],[7283],{"type":10,"tag":181,"props":7284,"children":7286},{"className":7285},[1245,1623],[7287,7292],{"type":10,"tag":181,"props":7288,"children":7290},{"className":7289},[1245,1623],[7291],{"type":16,"value":388},{"type":10,"tag":181,"props":7293,"children":7295},{"className":7294},[1245,1623],[7296,7301,7306],{"type":10,"tag":181,"props":7297,"children":7299},{"className":7298,"style":1366},[1245,1290,1623],[7300],{"type":16,"value":311},{"type":10,"tag":181,"props":7302,"children":7304},{"className":7303,"style":1296},[1245,1623],[7305],{"type":16,"value":255},{"type":10,"tag":181,"props":7307,"children":7309},{"className":7308,"style":1296},[1245,1290,1623],[7310],{"type":16,"value":177},{"type":10,"tag":181,"props":7312,"children":7314},{"className":7313},[1226],[7315],{"type":16,"value":1229},{"type":10,"tag":181,"props":7317,"children":7319},{"className":7318},[1188],[7320],{"type":10,"tag":181,"props":7321,"children":7323},{"className":7322,"style":3899},[1193],[7324],{"type":10,"tag":181,"props":7325,"children":7326},{},[],{"type":10,"tag":181,"props":7328,"children":7330},{"className":7329},[1406,3781],[],{"type":16,"value":7332},"), an intersection\ncandidate exists.",{"type":10,"tag":18,"props":7334,"children":7335},{},[7336],{"type":16,"value":7337},"Triangle primitive bounds consist of all points on the plane formed by the\nthree vertices and within the bounds of the edges between the vertices,\nsubject to the watertightness constraints below.\nAABB primitive bounds consist of all points within an implementation-defined\nbound which includes the specified box.",{"type":10,"tag":140,"props":7339,"children":7340},{},[7341],{"type":10,"tag":18,"props":7342,"children":7343},{},[7344],{"type":16,"value":7345},"The bounds of the AABB including all points internal to the bound implies\nthat a ray started within the AABB will hit that AABB.",{"type":10,"tag":18,"props":7347,"children":7348},{},[7349],{"type":10,"tag":7350,"props":7351,"children":7355},"img",{"alt":7352,"src":7353,"title":7354},"ray intersection candidate","https://data.vkdoc.net/images/ray_intersection_candidate.svg","Ray intersection candidate",[],{"type":10,"tag":18,"props":7357,"children":7358},{},[7359,7361,7365,7367,7371],{"type":16,"value":7360},"The determination of this condition is performed in an implementation\nspecific manner, and ",{"type":10,"tag":28,"props":7362,"children":7364},{"type":7363},"may",[],{"type":16,"value":7366}," be performed with floating-point operations.\nDue to the complexity and number of operations involved, inaccuracies are\nexpected, particularly as the scale of values involved begins to diverge.\nImplementations ",{"type":10,"tag":28,"props":7368,"children":7370},{"type":7369},"should",[],{"type":16,"value":7372}," take efforts to maintain as much precision as\npossible.",{"type":10,"tag":140,"props":7374,"children":7375},{},[7376,7389],{"type":10,"tag":18,"props":7377,"children":7378},{},[7379,7381,7387],{"type":16,"value":7380},"One very common case is when geometries are close to each other at some\ndistance from the origin in acceleration structure space, where an effect\nsimilar to ",{"type":10,"tag":35,"props":7382,"children":7384},{"className":7383},[],[7385],{"type":16,"value":7386},"z-fighting",{"type":16,"value":7388}," is likely to be observed.\nApplications can mitigate this by ensuring their detailed geometries remain\nclose to the origin.",{"type":10,"tag":18,"props":7390,"children":7391},{},[7392,7394,7398,7400,7404],{"type":16,"value":7393},"Another likely case is when the origin of a ray is set to a position on a\npreviously intersected surface, and its t",{"type":10,"tag":163,"props":7395,"children":7396},{},[7397],{"type":16,"value":6468},{"type":16,"value":7399}," is zero or near zero;\nan intersection may be detected on the emitting surface.\nThis case can usually be mitigated by offsetting t",{"type":10,"tag":163,"props":7401,"children":7402},{},[7403],{"type":16,"value":6468},{"type":16,"value":7405}," slightly.",{"type":10,"tag":18,"props":7407,"children":7408},{},[7409,7411,7417,7419,7425,7427,7432,7434,7439,7441,7446],{"type":16,"value":7410},"For a motion primitive or a motion instance, the positions for intersection\nare evaluated at the time specified in the ",{"type":10,"tag":35,"props":7412,"children":7414},{"className":7413},[],[7415],{"type":16,"value":7416},"time",{"type":16,"value":7418}," parameter to\n",{"type":10,"tag":35,"props":7420,"children":7422},{"className":7421},[],[7423],{"type":16,"value":7424},"OpTraceRayMotionNV",{"type":16,"value":7426}," by interpolating between the two endpoints as\nspecified for the given motion type.\nIf a motion acceleration structure is traced with ",{"type":10,"tag":35,"props":7428,"children":7430},{"className":7429},[],[7431],{"type":16,"value":69},{"type":16,"value":7433},", it\nbehaves as a ",{"type":10,"tag":35,"props":7435,"children":7437},{"className":7436},[],[7438],{"type":16,"value":7424},{"type":16,"value":7440}," with ",{"type":10,"tag":35,"props":7442,"children":7444},{"className":7443},[],[7445],{"type":16,"value":7416},{"type":16,"value":7447}," of 0.0.",{"type":10,"tag":18,"props":7449,"children":7450},{},[7451,7453,7456,7458,7461],{"type":16,"value":7452},"In the case of AABB geometries, implementations ",{"type":10,"tag":28,"props":7454,"children":7455},{"type":7363},[],{"type":16,"value":7457}," increase their size in\nan acceleration structure in order to mitigate precision issues.\nThis ",{"type":10,"tag":28,"props":7459,"children":7460},{"type":7363},[],{"type":16,"value":7462}," result in false positive intersections being reported to the\napplication.",{"type":10,"tag":18,"props":7464,"children":7465},{},[7466],{"type":16,"value":7467},"For triangle intersection candidates, the b and c",{"type":10,"tag":18,"props":7469,"children":7470},{},[7471,7477,7479,7484,7486,7492],{"type":10,"tag":44,"props":7472,"children":7474},{"href":7473},"/chapters/primsrast#primsrast-polygon-barycentrics",[7475],{"type":16,"value":7476},"barycentric coordinates",{"type":16,"value":7478}," on the triangle\nwhere the above condition is met are made available to future shading.\nIf the ray was traced with a ",{"type":10,"tag":44,"props":7480,"children":7481},{"href":46},[7482],{"type":16,"value":7483},"pipeline trace\nray",{"type":16,"value":7485}," instruction, these values are available as a vector of 2 32-bit\nfloating-point values in the ",{"type":10,"tag":35,"props":7487,"children":7489},{"className":7488},[],[7490],{"type":16,"value":7491},"HitAttributeKHR",{"type":16,"value":7493}," storage class.",{"type":10,"tag":18,"props":7495,"children":7496},{},[7497],{"type":16,"value":7498},"Once an intersection candidate is determined, it proceeds through the\nfollowing operations, in order:",{"type":10,"tag":7500,"props":7501,"children":7502},"ol",{},[7503,7513,7522,7531],{"type":10,"tag":7504,"props":7505,"children":7506},"li",{},[7507],{"type":10,"tag":44,"props":7508,"children":7510},{"href":7509},"/chapters/ray-traversal#ray-intersection-culling",[7511],{"type":16,"value":7512},"Ray Intersection Culling",{"type":10,"tag":7504,"props":7514,"children":7515},{},[7516],{"type":10,"tag":44,"props":7517,"children":7519},{"href":7518},"/chapters/ray-traversal#ray-intersection-confirmation",[7520],{"type":16,"value":7521},"Ray Intersection Confirmation",{"type":10,"tag":7504,"props":7523,"children":7524},{},[7525],{"type":10,"tag":44,"props":7526,"children":7528},{"href":7527},"/chapters/ray-traversal#ray-closest-hit-determination",[7529],{"type":16,"value":7530},"Ray Closest Hit Determination",{"type":10,"tag":7504,"props":7532,"children":7533},{},[7534],{"type":10,"tag":44,"props":7535,"children":7537},{"href":7536},"/chapters/ray-traversal#ray-result-determination",[7538],{"type":16,"value":7539},"Ray Result Determination",{"type":10,"tag":18,"props":7541,"children":7542},{},[7543],{"type":16,"value":7544},"The sections below describe the exact details of these tests.\nThere is no ordering guarantee between operations performed on different\nintersection candidates.",{"type":10,"tag":7546,"props":7547,"children":7549},"h3",{"id":7548},"ray-traversal-watertight",[7550],{"type":16,"value":7551},"Watertightness",{"type":10,"tag":18,"props":7553,"children":7554},{},[7555],{"type":16,"value":7556},"For a set of triangles with identical transforms, within a single instance:",{"type":10,"tag":7558,"props":7559,"children":7560},"ul",{},[7561,7573],{"type":10,"tag":7504,"props":7562,"children":7563},{},[7564,7566,7571],{"type":16,"value":7565},"Any set of two or more triangles where all triangles have one vertex\nwith an identical position value, that vertex is a ",{"type":10,"tag":159,"props":7567,"children":7568},{},[7569],{"type":16,"value":7570},"shared vertex",{"type":16,"value":7572},".",{"type":10,"tag":7504,"props":7574,"children":7575},{},[7576,7578,7584,7586,7591],{"type":16,"value":7577},"Any set of two triangles with two shared vertices that were specified in\nthe same ",{"type":10,"tag":44,"props":7579,"children":7581},{"href":7580},"/chapters/drawing#drawing-triangle-lists",[7582],{"type":16,"value":7583},"winding order",{"type":16,"value":7585}," in each triangle have\na ",{"type":10,"tag":159,"props":7587,"children":7588},{},[7589],{"type":16,"value":7590},"shared edge",{"type":16,"value":7592}," defined by those vertices.",{"type":10,"tag":18,"props":7594,"children":7595},{},[7596,7598,7603],{"type":16,"value":7597},"A ",{"type":10,"tag":159,"props":7599,"children":7600},{},[7601],{"type":16,"value":7602},"closed fan",{"type":16,"value":7604}," is a set of three or more triangles where:",{"type":10,"tag":7558,"props":7606,"children":7607},{},[7608,7613,7618,7623,7628],{"type":10,"tag":7504,"props":7609,"children":7610},{},[7611],{"type":16,"value":7612},"All triangles in the set have the same shared vertex as one of their\nvertices.",{"type":10,"tag":7504,"props":7614,"children":7615},{},[7616],{"type":16,"value":7617},"All edges that include the above vertex are shared edges.",{"type":10,"tag":7504,"props":7619,"children":7620},{},[7621],{"type":16,"value":7622},"All above shared edges are shared by exactly two triangles from the set.",{"type":10,"tag":7504,"props":7624,"children":7625},{},[7626],{"type":16,"value":7627},"No two triangles in the set intersect, except at shared edges.",{"type":10,"tag":7504,"props":7629,"children":7630},{},[7631],{"type":16,"value":7632},"Every triangle in the set is joined to every other triangle in the set\nby a series of the above shared edges.",{"type":10,"tag":18,"props":7634,"children":7635},{},[7636,7638,7641],{"type":16,"value":7637},"Implementations ",{"type":10,"tag":28,"props":7639,"children":7640},{"type":7369},[],{"type":16,"value":7642}," not double-hit or miss when a ray intersects a\nshared edge, or a shared vertex of a closed fan.",{"type":10,"tag":118,"props":7644,"children":7646},{"id":7645},"ray-intersection-culling",[7647],{"type":16,"value":7512},{"type":10,"tag":18,"props":7649,"children":7650},{},[7651],{"type":16,"value":7652},"Candidate intersections go through several phases of culling before\nconfirmation as an actual hit.\nThere is no particular ordering dependency between the different culling\noperations.",{"type":10,"tag":7546,"props":7654,"children":7656},{"id":7655},"ray-traversal-culling-primitive",[7657],{"type":16,"value":7658},"Ray Primitive Culling",{"type":10,"tag":18,"props":7660,"children":7661},{},[7662,7664,7674,7676,7684,7686,7692,7694,7700,7702,7705,7707,7712,7713,7718,7720,7725,7727,7733,7734,7740],{"type":16,"value":7663},"If the ",{"type":10,"tag":44,"props":7665,"children":7667},{"href":7666},"/man/VkPhysicalDeviceRayTracingPipelineFeaturesKHR#features-rayTraversalPrimitiveCulling",[7668],{"type":10,"tag":35,"props":7669,"children":7671},{"className":7670},[],[7672],{"type":16,"value":7673},"rayTraversalPrimitiveCulling",{"type":16,"value":7675}," or ",{"type":10,"tag":44,"props":7677,"children":7678},{"href":96},[7679],{"type":10,"tag":35,"props":7680,"children":7682},{"className":7681},[],[7683],{"type":16,"value":103},{"type":16,"value":7685}," features are enabled, the ",{"type":10,"tag":35,"props":7687,"children":7689},{"className":7688},[],[7690],{"type":16,"value":7691},"SkipTrianglesKHR",{"type":16,"value":7693}," and\n",{"type":10,"tag":35,"props":7695,"children":7697},{"className":7696},[],[7698],{"type":16,"value":7699},"SkipAABBsKHR",{"type":16,"value":7701}," ray flags ",{"type":10,"tag":28,"props":7703,"children":7704},{"type":74},[],{"type":16,"value":7706}," be specified when tracing a ray.\n",{"type":10,"tag":35,"props":7708,"children":7710},{"className":7709},[],[7711],{"type":16,"value":7691},{"type":16,"value":4500},{"type":10,"tag":35,"props":7714,"children":7716},{"className":7715},[],[7717],{"type":16,"value":7699},{"type":16,"value":7719}," are mutually exclusive.\n",{"type":10,"tag":35,"props":7721,"children":7723},{"className":7722},[],[7724],{"type":16,"value":7691},{"type":16,"value":7726}," is also mutually exclusive with\n",{"type":10,"tag":35,"props":7728,"children":7730},{"className":7729},[],[7731],{"type":16,"value":7732},"CullBackFacingTrianglesKHR",{"type":16,"value":4500},{"type":10,"tag":35,"props":7735,"children":7737},{"className":7736},[],[7738],{"type":16,"value":7739},"CullFrontFacingTrianglesKHR",{"type":16,"value":7572},{"type":10,"tag":18,"props":7742,"children":7743},{},[7744,7746,7751,7753,7759,7761,7767,7769,7774,7776,7781,7783,7788],{"type":16,"value":7745},"If ",{"type":10,"tag":35,"props":7747,"children":7749},{"className":7748},[],[7750],{"type":16,"value":7691},{"type":16,"value":7752}," was included in the ",{"type":10,"tag":35,"props":7754,"children":7756},{"className":7755},[],[7757],{"type":16,"value":7758},"Ray Flags",{"type":16,"value":7760}," operand of the ray\ntrace instruction, and the intersection is with a triangle primitive, the\nintersection is dropped, and no further processing of this intersection\noccurs.\nIf ",{"type":10,"tag":35,"props":7762,"children":7764},{"className":7763},[],[7765],{"type":16,"value":7766},"VK_PIPELINE_CREATE_RAY_TRACING_SKIP_TRIANGLES_BIT_KHR",{"type":16,"value":7768}," was included\nin the pipeline, traversal with ",{"type":10,"tag":44,"props":7770,"children":7771},{"href":46},[7772],{"type":16,"value":7773},"pipeline\ntrace ray",{"type":16,"value":7775}," instructions will all behave as if ",{"type":10,"tag":35,"props":7777,"children":7779},{"className":7778},[],[7780],{"type":16,"value":7691},{"type":16,"value":7782}," was\nincluded in their ",{"type":10,"tag":35,"props":7784,"children":7786},{"className":7785},[],[7787],{"type":16,"value":7758},{"type":16,"value":7789}," operand.",{"type":10,"tag":18,"props":7791,"children":7792},{},[7793,7794,7799,7800,7805,7807,7813,7815,7819,7820,7825,7827,7832],{"type":16,"value":7745},{"type":10,"tag":35,"props":7795,"children":7797},{"className":7796},[],[7798],{"type":16,"value":7699},{"type":16,"value":7752},{"type":10,"tag":35,"props":7801,"children":7803},{"className":7802},[],[7804],{"type":16,"value":7758},{"type":16,"value":7806}," operand of the ray\ntrace instruction, and the intersection is with an AABB primitive, the\nintersection is dropped, and no further processing of this intersection\noccurs.\nIf ",{"type":10,"tag":35,"props":7808,"children":7810},{"className":7809},[],[7811],{"type":16,"value":7812},"VK_PIPELINE_CREATE_RAY_TRACING_SKIP_AABBS_BIT_KHR",{"type":16,"value":7814}," was included in\nthe pipeline, traversal with ",{"type":10,"tag":44,"props":7816,"children":7817},{"href":46},[7818],{"type":16,"value":7483},{"type":16,"value":7775},{"type":10,"tag":35,"props":7821,"children":7823},{"className":7822},[],[7824],{"type":16,"value":7699},{"type":16,"value":7826}," was included in\ntheir ",{"type":10,"tag":35,"props":7828,"children":7830},{"className":7829},[],[7831],{"type":16,"value":7758},{"type":16,"value":7789},{"type":10,"tag":7546,"props":7834,"children":7836},{"id":7835},"_ray_mask_culling",[7837],{"type":16,"value":7838},"Ray Mask Culling",{"type":10,"tag":18,"props":7840,"children":7841},{},[7842,7844,7847,7849,7855,7857,7863,7865,7871],{"type":16,"value":7843},"Instances ",{"type":10,"tag":28,"props":7845,"children":7846},{"type":74},[],{"type":16,"value":7848}," be made invisible to particular rays based on the value of\n",{"type":10,"tag":44,"props":7850,"children":7852},{"href":7851},"/man/VkAccelerationStructureInstanceKHR",[7853],{"type":16,"value":7854},"VkAccelerationStructureInstanceKHR",{"type":16,"value":7856},"::",{"type":10,"tag":35,"props":7858,"children":7860},{"className":7859},[],[7861],{"type":16,"value":7862},"mask",{"type":16,"value":7864}," used to add that\ninstance to a top-level acceleration structure, and the ",{"type":10,"tag":35,"props":7866,"children":7868},{"className":7867},[],[7869],{"type":16,"value":7870},"Cull Mask",{"type":16,"value":7872},"\nparameter used to trace the ray.",{"type":10,"tag":18,"props":7874,"children":7875},{},[7876,7878,7883,7885,7890],{"type":16,"value":7877},"For the instance which is intersected, if ",{"type":10,"tag":35,"props":7879,"children":7881},{"className":7880},[],[7882],{"type":16,"value":7862},{"type":16,"value":7884}," & ",{"type":10,"tag":35,"props":7886,"children":7888},{"className":7887},[],[7889],{"type":16,"value":7870},{"type":16,"value":7891}," ==\n0, the intersection is dropped, and no further processing occurs.",{"type":10,"tag":7546,"props":7893,"children":7895},{"id":7894},"ray-traversal-culling-face",[7896],{"type":16,"value":7897},"Ray Face Culling",{"type":10,"tag":18,"props":7899,"children":7900},{},[7901,7903,7909,7911,7914],{"type":16,"value":7902},"As in ",{"type":10,"tag":44,"props":7904,"children":7906},{"href":7905},"/chapters/primsrast#primsrast-polygons-basic",[7907],{"type":16,"value":7908},"polygon rasterization",{"type":16,"value":7910},", one of the stages\nof ray traversal is to determine if a triangle primitive is back- or\nfront-facing, and primitives ",{"type":10,"tag":28,"props":7912,"children":7913},{"type":74},[],{"type":16,"value":7915}," be culled based on that facing.",{"type":10,"tag":18,"props":7917,"children":7918},{},[7919],{"type":16,"value":7920},"If the intersection candidate is with an AABB primitive, this operation is\nskipped.",{"type":10,"tag":7546,"props":7922,"children":7924},{"id":7923},"determination",[7925],{"type":16,"value":7926},"Determination",{"type":10,"tag":18,"props":7928,"children":7929},{},[7930,7932,7937],{"type":16,"value":7931},"When a ray intersects a triangle primitive, the order that vertices are\nspecified for the polygon affects whether the ray intersects the front or\nback face.\nFront or back facing is determined in the same way as they are for\n",{"type":10,"tag":44,"props":7933,"children":7934},{"href":7905},[7935],{"type":16,"value":7936},"rasterization",{"type":16,"value":7938},", based on the sign of the\npolygon’s area but using the ray space coordinates instead of framebuffer\ncoordinates.\nOne way to compute this area is:",{"type":10,"tag":181,"props":7940,"children":7942},{"className":7941},[184],[7943],{"type":10,"tag":181,"props":7944,"children":7946},{"className":7945},[189],[7947,8133],{"type":10,"tag":181,"props":7948,"children":7950},{"className":7949},[194],[7951],{"type":10,"tag":197,"props":7952,"children":7953},{"xmlns":199,"display":200},[7954],{"type":10,"tag":203,"props":7955,"children":7956},{},[7957,8128],{"type":10,"tag":207,"props":7958,"children":7959},{},[7960,7964,7968,7972,7983,7988,7992,8025,8029,8033,8044,8048,8052,8075,8079,8083,8087,8109,8113,8117],{"type":10,"tag":245,"props":7961,"children":7962},{},[7963],{"type":16,"value":44},{"type":10,"tag":214,"props":7965,"children":7966},{},[7967],{"type":16,"value":329},{"type":10,"tag":214,"props":7969,"children":7970},{},[7971],{"type":16,"value":388},{"type":10,"tag":3265,"props":7973,"children":7974},{},[7975,7979],{"type":10,"tag":370,"props":7976,"children":7977},{},[7978],{"type":16,"value":383},{"type":10,"tag":370,"props":7980,"children":7981},{},[7982],{"type":16,"value":374},{"type":10,"tag":214,"props":7984,"children":7985},{},[7986],{"type":16,"value":7987},"∑",{"type":10,"tag":245,"props":7989,"children":7990},{"mathvariant":252},[7991],{"type":16,"value":255},{"type":10,"tag":362,"props":7993,"children":7994},{},[7995,8010],{"type":10,"tag":207,"props":7996,"children":7997},{},[7998,8002,8006],{"type":10,"tag":245,"props":7999,"children":8000},{},[8001],{"type":16,"value":3329},{"type":10,"tag":214,"props":8003,"children":8004},{},[8005],{"type":16,"value":329},{"type":10,"tag":370,"props":8007,"children":8008},{},[8009],{"type":16,"value":238},{"type":10,"tag":207,"props":8011,"children":8012},{},[8013,8017,8021],{"type":10,"tag":245,"props":8014,"children":8015},{},[8016],{"type":16,"value":6070},{"type":10,"tag":214,"props":8018,"children":8019},{},[8020],{"type":16,"value":388},{"type":10,"tag":370,"props":8022,"children":8023},{},[8024],{"type":16,"value":383},{"type":10,"tag":245,"props":8026,"children":8027},{},[8028],{"type":16,"value":249},{"type":10,"tag":245,"props":8030,"children":8031},{"mathvariant":252},[8032],{"type":16,"value":255},{"type":10,"tag":362,"props":8034,"children":8035},{},[8036,8040],{"type":10,"tag":245,"props":8037,"children":8038},{},[8039],{"type":16,"value":177},{"type":10,"tag":245,"props":8041,"children":8042},{},[8043],{"type":16,"value":3329},{"type":10,"tag":245,"props":8045,"children":8046},{},[8047],{"type":16,"value":282},{"type":10,"tag":245,"props":8049,"children":8050},{"mathvariant":252},[8051],{"type":16,"value":255},{"type":10,"tag":362,"props":8053,"children":8054},{},[8055,8059],{"type":10,"tag":245,"props":8056,"children":8057},{},[8058],{"type":16,"value":177},{"type":10,"tag":207,"props":8060,"children":8061},{},[8062,8066,8071],{"type":10,"tag":245,"props":8063,"children":8064},{},[8065],{"type":16,"value":3329},{"type":10,"tag":214,"props":8067,"children":8068},{},[8069],{"type":16,"value":8070},"⊕",{"type":10,"tag":370,"props":8072,"children":8073},{},[8074],{"type":16,"value":383},{"type":10,"tag":214,"props":8076,"children":8077},{},[8078],{"type":16,"value":388},{"type":10,"tag":245,"props":8080,"children":8081},{},[8082],{"type":16,"value":249},{"type":10,"tag":245,"props":8084,"children":8085},{"mathvariant":252},[8086],{"type":16,"value":255},{"type":10,"tag":362,"props":8088,"children":8089},{},[8090,8094],{"type":10,"tag":245,"props":8091,"children":8092},{},[8093],{"type":16,"value":177},{"type":10,"tag":207,"props":8095,"children":8096},{},[8097,8101,8105],{"type":10,"tag":245,"props":8098,"children":8099},{},[8100],{"type":16,"value":3329},{"type":10,"tag":214,"props":8102,"children":8103},{},[8104],{"type":16,"value":8070},{"type":10,"tag":370,"props":8106,"children":8107},{},[8108],{"type":16,"value":383},{"type":10,"tag":245,"props":8110,"children":8111},{},[8112],{"type":16,"value":282},{"type":10,"tag":245,"props":8114,"children":8115},{"mathvariant":252},[8116],{"type":16,"value":255},{"type":10,"tag":362,"props":8118,"children":8119},{},[8120,8124],{"type":10,"tag":245,"props":8121,"children":8122},{},[8123],{"type":16,"value":177},{"type":10,"tag":245,"props":8125,"children":8126},{},[8127],{"type":16,"value":3329},{"type":10,"tag":1141,"props":8129,"children":8130},{"encoding":1143},[8131],{"type":16,"value":8132},"a = -{1 \\over 2}\\sum\\_{i=0}^{n-1}\nx\\_r^i y\\_r^{i \\oplus 1} -\nx\\_r^{i \\oplus 1} y\\_r^i",{"type":10,"tag":181,"props":8134,"children":8136},{"className":8135,"ariaHidden":216},[1150],[8137,8163,8501],{"type":10,"tag":181,"props":8138,"children":8140},{"className":8139},[1155],[8141,8145,8150,8154,8159],{"type":10,"tag":181,"props":8142,"children":8144},{"className":8143,"style":4491},[1160],[],{"type":10,"tag":181,"props":8146,"children":8148},{"className":8147},[1245,1290],[8149],{"type":16,"value":44},{"type":10,"tag":181,"props":8151,"children":8153},{"className":8152,"style":1460},[1323],[],{"type":10,"tag":181,"props":8155,"children":8157},{"className":8156},[1465],[8158],{"type":16,"value":329},{"type":10,"tag":181,"props":8160,"children":8162},{"className":8161,"style":1460},[1323],[],{"type":10,"tag":181,"props":8164,"children":8166},{"className":8165},[1155],[8167,8172,8177,8270,8274,8283,8287,8292,8371,8376,8381,8423,8428,8433,8488,8492,8497],{"type":10,"tag":181,"props":8168,"children":8171},{"className":8169,"style":8170},[1160],"height:2.0074em;vertical-align:-0.686em;",[],{"type":10,"tag":181,"props":8173,"children":8175},{"className":8174},[1245],[8176],{"type":16,"value":388},{"type":10,"tag":181,"props":8178,"children":8180},{"className":8179},[1245],[8181],{"type":10,"tag":181,"props":8182,"children":8184},{"className":8183},[1245],[8185,8189,8266],{"type":10,"tag":181,"props":8186,"children":8188},{"className":8187},[1171,3781],[],{"type":10,"tag":181,"props":8190,"children":8192},{"className":8191},[3265],[8193],{"type":10,"tag":181,"props":8194,"children":8196},{"className":8195},[1182,1183],[8197,8254],{"type":10,"tag":181,"props":8198,"children":8200},{"className":8199},[1188],[8201,8249],{"type":10,"tag":181,"props":8202,"children":8205},{"className":8203,"style":8204},[1193],"height:1.3214em;",[8206,8222,8233],{"type":10,"tag":181,"props":8207,"children":8208},{"style":5010},[8209,8213],{"type":10,"tag":181,"props":8210,"children":8212},{"className":8211,"style":1281},[1203],[],{"type":10,"tag":181,"props":8214,"children":8216},{"className":8215},[1245],[8217],{"type":10,"tag":181,"props":8218,"children":8220},{"className":8219},[1245],[8221],{"type":16,"value":374},{"type":10,"tag":181,"props":8223,"children":8224},{"style":3844},[8225,8229],{"type":10,"tag":181,"props":8226,"children":8228},{"className":8227,"style":1281},[1203],[],{"type":10,"tag":181,"props":8230,"children":8232},{"className":8231,"style":3854},[3853],[],{"type":10,"tag":181,"props":8234,"children":8235},{"style":5048},[8236,8240],{"type":10,"tag":181,"props":8237,"children":8239},{"className":8238,"style":1281},[1203],[],{"type":10,"tag":181,"props":8241,"children":8243},{"className":8242},[1245],[8244],{"type":10,"tag":181,"props":8245,"children":8247},{"className":8246},[1245],[8248],{"type":16,"value":383},{"type":10,"tag":181,"props":8250,"children":8252},{"className":8251},[1226],[8253],{"type":16,"value":1229},{"type":10,"tag":181,"props":8255,"children":8257},{"className":8256},[1188],[8258],{"type":10,"tag":181,"props":8259,"children":8262},{"className":8260,"style":8261},[1193],"height:0.686em;",[8263],{"type":10,"tag":181,"props":8264,"children":8265},{},[],{"type":10,"tag":181,"props":8267,"children":8269},{"className":8268},[1406,3781],[],{"type":10,"tag":181,"props":8271,"children":8273},{"className":8272,"style":2712},[1323],[],{"type":10,"tag":181,"props":8275,"children":8281},{"className":8276,"style":8280},[8277,8278,8279],"mop","op-symbol","large-op","position:relative;top:0em;",[8282],{"type":16,"value":7987},{"type":10,"tag":181,"props":8284,"children":8286},{"className":8285,"style":2712},[1323],[],{"type":10,"tag":181,"props":8288,"children":8290},{"className":8289,"style":1296},[1245],[8291],{"type":16,"value":255},{"type":10,"tag":181,"props":8293,"children":8295},{"className":8294},[1245],[8296,8323],{"type":10,"tag":181,"props":8297,"children":8299},{"className":8298},[1245],[8300,8305,8309,8314,8318],{"type":10,"tag":181,"props":8301,"children":8303},{"className":8302},[1245,1290],[8304],{"type":16,"value":3329},{"type":10,"tag":181,"props":8306,"children":8308},{"className":8307,"style":1460},[1323],[],{"type":10,"tag":181,"props":8310,"children":8312},{"className":8311},[1465],[8313],{"type":16,"value":329},{"type":10,"tag":181,"props":8315,"children":8317},{"className":8316,"style":1460},[1323],[],{"type":10,"tag":181,"props":8319,"children":8321},{"className":8320},[1245],[8322],{"type":16,"value":238},{"type":10,"tag":181,"props":8324,"children":8326},{"className":8325},[1593],[8327],{"type":10,"tag":181,"props":8328,"children":8330},{"className":8329},[1182],[8331],{"type":10,"tag":181,"props":8332,"children":8334},{"className":8333},[1188],[8335],{"type":10,"tag":181,"props":8336,"children":8339},{"className":8337,"style":8338},[1193],"height:0.8641em;",[8340],{"type":10,"tag":181,"props":8341,"children":8343},{"style":8342},"top:-3.113em;margin-right:0.05em;",[8344,8348],{"type":10,"tag":181,"props":8345,"children":8347},{"className":8346,"style":1615},[1203],[],{"type":10,"tag":181,"props":8349,"children":8351},{"className":8350},[1620,1621,1622,1623],[8352],{"type":10,"tag":181,"props":8353,"children":8355},{"className":8354},[1245,1623],[8356,8361,8366],{"type":10,"tag":181,"props":8357,"children":8359},{"className":8358},[1245,1290,1623],[8360],{"type":16,"value":6070},{"type":10,"tag":181,"props":8362,"children":8364},{"className":8363},[1648,1623],[8365],{"type":16,"value":388},{"type":10,"tag":181,"props":8367,"children":8369},{"className":8368},[1245,1623],[8370],{"type":16,"value":383},{"type":10,"tag":181,"props":8372,"children":8374},{"className":8373},[1245,1290],[8375],{"type":16,"value":249},{"type":10,"tag":181,"props":8377,"children":8379},{"className":8378,"style":1296},[1245],[8380],{"type":16,"value":255},{"type":10,"tag":181,"props":8382,"children":8384},{"className":8383},[1245],[8385,8390],{"type":10,"tag":181,"props":8386,"children":8388},{"className":8387,"style":1296},[1245,1290],[8389],{"type":16,"value":177},{"type":10,"tag":181,"props":8391,"children":8393},{"className":8392},[1593],[8394],{"type":10,"tag":181,"props":8395,"children":8397},{"className":8396},[1182],[8398],{"type":10,"tag":181,"props":8399,"children":8401},{"className":8400},[1188],[8402],{"type":10,"tag":181,"props":8403,"children":8406},{"className":8404,"style":8405},[1193],"height:0.8747em;",[8407],{"type":10,"tag":181,"props":8408,"children":8409},{"style":8342},[8410,8414],{"type":10,"tag":181,"props":8411,"children":8413},{"className":8412,"style":1615},[1203],[],{"type":10,"tag":181,"props":8415,"children":8417},{"className":8416},[1620,1621,1622,1623],[8418],{"type":10,"tag":181,"props":8419,"children":8421},{"className":8420},[1245,1290,1623],[8422],{"type":16,"value":3329},{"type":10,"tag":181,"props":8424,"children":8426},{"className":8425,"style":1329},[1245,1290],[8427],{"type":16,"value":282},{"type":10,"tag":181,"props":8429,"children":8431},{"className":8430,"style":1296},[1245],[8432],{"type":16,"value":255},{"type":10,"tag":181,"props":8434,"children":8436},{"className":8435},[1245],[8437,8442],{"type":10,"tag":181,"props":8438,"children":8440},{"className":8439,"style":1296},[1245,1290],[8441],{"type":16,"value":177},{"type":10,"tag":181,"props":8443,"children":8445},{"className":8444},[1593],[8446],{"type":10,"tag":181,"props":8447,"children":8449},{"className":8448},[1182],[8450],{"type":10,"tag":181,"props":8451,"children":8453},{"className":8452},[1188],[8454],{"type":10,"tag":181,"props":8455,"children":8457},{"className":8456,"style":8405},[1193],[8458],{"type":10,"tag":181,"props":8459,"children":8460},{"style":8342},[8461,8465],{"type":10,"tag":181,"props":8462,"children":8464},{"className":8463,"style":1615},[1203],[],{"type":10,"tag":181,"props":8466,"children":8468},{"className":8467},[1620,1621,1622,1623],[8469],{"type":10,"tag":181,"props":8470,"children":8472},{"className":8471},[1245,1623],[8473,8478,8483],{"type":10,"tag":181,"props":8474,"children":8476},{"className":8475},[1245,1290,1623],[8477],{"type":16,"value":3329},{"type":10,"tag":181,"props":8479,"children":8481},{"className":8480},[1648,1623],[8482],{"type":16,"value":8070},{"type":10,"tag":181,"props":8484,"children":8486},{"className":8485},[1245,1623],[8487],{"type":16,"value":383},{"type":10,"tag":181,"props":8489,"children":8491},{"className":8490,"style":1643},[1323],[],{"type":10,"tag":181,"props":8493,"children":8495},{"className":8494},[1648],[8496],{"type":16,"value":388},{"type":10,"tag":181,"props":8498,"children":8500},{"className":8499,"style":1643},[1323],[],{"type":10,"tag":181,"props":8502,"children":8504},{"className":8503},[1155],[8505,8510,8515,8520,8575,8580,8585],{"type":10,"tag":181,"props":8506,"children":8509},{"className":8507,"style":8508},[1160],"height:1.1847em;vertical-align:-0.31em;",[],{"type":10,"tag":181,"props":8511,"children":8513},{"className":8512},[1245,1290],[8514],{"type":16,"value":249},{"type":10,"tag":181,"props":8516,"children":8518},{"className":8517,"style":1296},[1245],[8519],{"type":16,"value":255},{"type":10,"tag":181,"props":8521,"children":8523},{"className":8522},[1245],[8524,8529],{"type":10,"tag":181,"props":8525,"children":8527},{"className":8526,"style":1296},[1245,1290],[8528],{"type":16,"value":177},{"type":10,"tag":181,"props":8530,"children":8532},{"className":8531},[1593],[8533],{"type":10,"tag":181,"props":8534,"children":8536},{"className":8535},[1182],[8537],{"type":10,"tag":181,"props":8538,"children":8540},{"className":8539},[1188],[8541],{"type":10,"tag":181,"props":8542,"children":8544},{"className":8543,"style":8405},[1193],[8545],{"type":10,"tag":181,"props":8546,"children":8547},{"style":8342},[8548,8552],{"type":10,"tag":181,"props":8549,"children":8551},{"className":8550,"style":1615},[1203],[],{"type":10,"tag":181,"props":8553,"children":8555},{"className":8554},[1620,1621,1622,1623],[8556],{"type":10,"tag":181,"props":8557,"children":8559},{"className":8558},[1245,1623],[8560,8565,8570],{"type":10,"tag":181,"props":8561,"children":8563},{"className":8562},[1245,1290,1623],[8564],{"type":16,"value":3329},{"type":10,"tag":181,"props":8566,"children":8568},{"className":8567},[1648,1623],[8569],{"type":16,"value":8070},{"type":10,"tag":181,"props":8571,"children":8573},{"className":8572},[1245,1623],[8574],{"type":16,"value":383},{"type":10,"tag":181,"props":8576,"children":8578},{"className":8577,"style":1329},[1245,1290],[8579],{"type":16,"value":282},{"type":10,"tag":181,"props":8581,"children":8583},{"className":8582,"style":1296},[1245],[8584],{"type":16,"value":255},{"type":10,"tag":181,"props":8586,"children":8588},{"className":8587},[1245],[8589,8594],{"type":10,"tag":181,"props":8590,"children":8592},{"className":8591,"style":1296},[1245,1290],[8593],{"type":16,"value":177},{"type":10,"tag":181,"props":8595,"children":8597},{"className":8596},[1593],[8598],{"type":10,"tag":181,"props":8599,"children":8601},{"className":8600},[1182],[8602],{"type":10,"tag":181,"props":8603,"children":8605},{"className":8604},[1188],[8606],{"type":10,"tag":181,"props":8607,"children":8609},{"className":8608,"style":8405},[1193],[8610],{"type":10,"tag":181,"props":8611,"children":8612},{"style":8342},[8613,8617],{"type":10,"tag":181,"props":8614,"children":8616},{"className":8615,"style":1615},[1203],[],{"type":10,"tag":181,"props":8618,"children":8620},{"className":8619},[1620,1621,1622,1623],[8621],{"type":10,"tag":181,"props":8622,"children":8624},{"className":8623},[1245,1290,1623],[8625],{"type":16,"value":3329},{"type":10,"tag":18,"props":8627,"children":8628},{},[8629,8631,8737,8738,8842],{"type":16,"value":8630},"where ",{"type":10,"tag":181,"props":8632,"children":8634},{"className":8633},[189],[8635,8672],{"type":10,"tag":181,"props":8636,"children":8638},{"className":8637},[194],[8639],{"type":10,"tag":197,"props":8640,"children":8641},{"xmlns":199},[8642],{"type":10,"tag":203,"props":8643,"children":8644},{},[8645,8667],{"type":10,"tag":207,"props":8646,"children":8647},{},[8648,8652,8656],{"type":10,"tag":245,"props":8649,"children":8650},{},[8651],{"type":16,"value":249},{"type":10,"tag":245,"props":8653,"children":8654},{"mathvariant":252},[8655],{"type":16,"value":255},{"type":10,"tag":362,"props":8657,"children":8658},{},[8659,8663],{"type":10,"tag":245,"props":8660,"children":8661},{},[8662],{"type":16,"value":177},{"type":10,"tag":245,"props":8664,"children":8665},{},[8666],{"type":16,"value":3329},{"type":10,"tag":1141,"props":8668,"children":8669},{"encoding":1143},[8670],{"type":16,"value":8671},"x\\_r^i",{"type":10,"tag":181,"props":8673,"children":8675},{"className":8674,"ariaHidden":216},[1150],[8676],{"type":10,"tag":181,"props":8677,"children":8679},{"className":8678},[1155],[8680,8685,8690,8695],{"type":10,"tag":181,"props":8681,"children":8684},{"className":8682,"style":8683},[1160],"height:1.1347em;vertical-align:-0.31em;",[],{"type":10,"tag":181,"props":8686,"children":8688},{"className":8687},[1245,1290],[8689],{"type":16,"value":249},{"type":10,"tag":181,"props":8691,"children":8693},{"className":8692,"style":1296},[1245],[8694],{"type":16,"value":255},{"type":10,"tag":181,"props":8696,"children":8698},{"className":8697},[1245],[8699,8704],{"type":10,"tag":181,"props":8700,"children":8702},{"className":8701,"style":1296},[1245,1290],[8703],{"type":16,"value":177},{"type":10,"tag":181,"props":8705,"children":8707},{"className":8706},[1593],[8708],{"type":10,"tag":181,"props":8709,"children":8711},{"className":8710},[1182],[8712],{"type":10,"tag":181,"props":8713,"children":8715},{"className":8714},[1188],[8716],{"type":10,"tag":181,"props":8717,"children":8720},{"className":8718,"style":8719},[1193],"height:0.8247em;",[8721],{"type":10,"tag":181,"props":8722,"children":8723},{"style":1610},[8724,8728],{"type":10,"tag":181,"props":8725,"children":8727},{"className":8726,"style":1615},[1203],[],{"type":10,"tag":181,"props":8729,"children":8731},{"className":8730},[1620,1621,1622,1623],[8732],{"type":10,"tag":181,"props":8733,"children":8735},{"className":8734},[1245,1290,1623],[8736],{"type":16,"value":3329},{"type":16,"value":4500},{"type":10,"tag":181,"props":8739,"children":8741},{"className":8740},[189],[8742,8779],{"type":10,"tag":181,"props":8743,"children":8745},{"className":8744},[194],[8746],{"type":10,"tag":197,"props":8747,"children":8748},{"xmlns":199},[8749],{"type":10,"tag":203,"props":8750,"children":8751},{},[8752,8774],{"type":10,"tag":207,"props":8753,"children":8754},{},[8755,8759,8763],{"type":10,"tag":245,"props":8756,"children":8757},{},[8758],{"type":16,"value":282},{"type":10,"tag":245,"props":8760,"children":8761},{"mathvariant":252},[8762],{"type":16,"value":255},{"type":10,"tag":362,"props":8764,"children":8765},{},[8766,8770],{"type":10,"tag":245,"props":8767,"children":8768},{},[8769],{"type":16,"value":177},{"type":10,"tag":245,"props":8771,"children":8772},{},[8773],{"type":16,"value":3329},{"type":10,"tag":1141,"props":8775,"children":8776},{"encoding":1143},[8777],{"type":16,"value":8778},"y\\_r^i",{"type":10,"tag":181,"props":8780,"children":8782},{"className":8781,"ariaHidden":216},[1150],[8783],{"type":10,"tag":181,"props":8784,"children":8786},{"className":8785},[1155],[8787,8791,8796,8801],{"type":10,"tag":181,"props":8788,"children":8790},{"className":8789,"style":8683},[1160],[],{"type":10,"tag":181,"props":8792,"children":8794},{"className":8793,"style":1329},[1245,1290],[8795],{"type":16,"value":282},{"type":10,"tag":181,"props":8797,"children":8799},{"className":8798,"style":1296},[1245],[8800],{"type":16,"value":255},{"type":10,"tag":181,"props":8802,"children":8804},{"className":8803},[1245],[8805,8810],{"type":10,"tag":181,"props":8806,"children":8808},{"className":8807,"style":1296},[1245,1290],[8809],{"type":16,"value":177},{"type":10,"tag":181,"props":8811,"children":8813},{"className":8812},[1593],[8814],{"type":10,"tag":181,"props":8815,"children":8817},{"className":8816},[1182],[8818],{"type":10,"tag":181,"props":8819,"children":8821},{"className":8820},[1188],[8822],{"type":10,"tag":181,"props":8823,"children":8825},{"className":8824,"style":8719},[1193],[8826],{"type":10,"tag":181,"props":8827,"children":8828},{"style":1610},[8829,8833],{"type":10,"tag":181,"props":8830,"children":8832},{"className":8831,"style":1615},[1203],[],{"type":10,"tag":181,"props":8834,"children":8836},{"className":8835},[1620,1621,1622,1623],[8837],{"type":10,"tag":181,"props":8838,"children":8840},{"className":8839},[1245,1290,1623],[8841],{"type":16,"value":3329},{"type":16,"value":8843}," are the x and y",{"type":10,"tag":18,"props":8845,"children":8846},{},[8847,8853],{"type":10,"tag":44,"props":8848,"children":8850},{"href":8849},"/chapters/ray-traversal#ray-intersection-candidate-determination",[8851],{"type":16,"value":8852},"ray space coordinates",{"type":16,"value":8854}," of the\nith vertex of the n-vertex polygon (vertices are numbered\nstarting at zero for the purposes of this computation) and i ⊕ 1\nis (i + 1) mod n.",{"type":10,"tag":18,"props":8856,"children":8857},{},[8858,8860,8866,8868,8872,8873,8879],{"type":16,"value":8859},"By default, if a is negative then the intersection is with the front\nface of the triangle, otherwise it is with the back face.\nIf ",{"type":10,"tag":35,"props":8861,"children":8863},{"className":8862},[],[8864],{"type":16,"value":8865},"VK_GEOMETRY_INSTANCE_TRIANGLE_FLIP_FACING_BIT_KHR",{"type":16,"value":8867}," is included in\n",{"type":10,"tag":44,"props":8869,"children":8870},{"href":7851},[8871],{"type":16,"value":7854},{"type":16,"value":7856},{"type":10,"tag":35,"props":8874,"children":8876},{"className":8875},[],[8877],{"type":16,"value":8878},"flags",{"type":16,"value":8880}," for the instance\ncontaining the intersected triangle, this determination is reversed.\nAdditionally, if a is 0, the intersection candidate is treated as not\nintersecting with any face, irrespective of the sign.",{"type":10,"tag":140,"props":8882,"children":8883},{},[8884],{"type":10,"tag":18,"props":8885,"children":8886},{},[8887,8889,8894,8896,8902],{"type":16,"value":8888},"In a left-handed coordinate system, an intersection will be with the front\nface of a triangle if the vertices of the triangle, as defined in index\norder, appear from the ray’s perspective in a clockwise rotation order.\n",{"type":10,"tag":35,"props":8890,"children":8892},{"className":8891},[],[8893],{"type":16,"value":8865},{"type":16,"value":8895}," was previously\nannotated as\n",{"type":10,"tag":35,"props":8897,"children":8899},{"className":8898},[],[8900],{"type":16,"value":8901},"VK_GEOMETRY_INSTANCE_TRIANGLE_FRONT_COUNTERCLOCKWISE_BIT_KHR",{"type":16,"value":8903}," because\nof this.",{"type":10,"tag":18,"props":8905,"children":8906},{},[8907,8909,8913,8915,8921,8923,8929,8931,8937],{"type":16,"value":8908},"If the ray was traced with a ",{"type":10,"tag":44,"props":8910,"children":8911},{"href":46},[8912],{"type":16,"value":7483},{"type":16,"value":8914}," instruction, the ",{"type":10,"tag":35,"props":8916,"children":8918},{"className":8917},[],[8919],{"type":16,"value":8920},"HitKindKHR",{"type":16,"value":8922}," built-in is set to\n",{"type":10,"tag":35,"props":8924,"children":8926},{"className":8925},[],[8927],{"type":16,"value":8928},"HitKindFrontFacingTriangleKHR",{"type":16,"value":8930}," if the intersection is with front-facing\ngeometry, and ",{"type":10,"tag":35,"props":8932,"children":8934},{"className":8933},[],[8935],{"type":16,"value":8936},"HitKindBackFacingTriangleKHR",{"type":16,"value":8938}," if the intersection is with\nback-facing geometry, for shader stages considering this intersection.",{"type":10,"tag":18,"props":8940,"children":8941},{},[8942,8944,8949,8951,8957],{"type":16,"value":8943},"If the ray was traced with ",{"type":10,"tag":35,"props":8945,"children":8947},{"className":8946},[],[8948],{"type":16,"value":40},{"type":16,"value":8950},",\n",{"type":10,"tag":35,"props":8952,"children":8954},{"className":8953},[],[8955],{"type":16,"value":8956},"OpRayQueryGetIntersectionFrontFaceKHR",{"type":16,"value":8958}," will return true for intersection\ncandidates with front faces, or false for back faces.",{"type":10,"tag":7546,"props":8960,"children":8962},{"id":8961},"culling",[8963],{"type":16,"value":8964},"Culling",{"type":10,"tag":18,"props":8966,"children":8967},{},[8968,8969,8974,8975,8980],{"type":16,"value":7745},{"type":10,"tag":35,"props":8970,"children":8972},{"className":8971},[],[8973],{"type":16,"value":7732},{"type":16,"value":7752},{"type":10,"tag":35,"props":8976,"children":8978},{"className":8977},[],[8979],{"type":16,"value":7758},{"type":16,"value":8981}," parameter\nof the ray trace instruction, and the intersection is determined as with the\nback face of a triangle primitive, the intersection is dropped, and no\nfurther processing of this intersection occurs.",{"type":10,"tag":18,"props":8983,"children":8984},{},[8985,8986,8991,8992,8997],{"type":16,"value":7745},{"type":10,"tag":35,"props":8987,"children":8989},{"className":8988},[],[8990],{"type":16,"value":7739},{"type":16,"value":7752},{"type":10,"tag":35,"props":8993,"children":8995},{"className":8994},[],[8996],{"type":16,"value":7758},{"type":16,"value":8998},"\nparameter of the ray trace instruction, and the intersection is determined\nas with the front face of a triangle primitive, the intersection is dropped,\nand no further processing of this intersection occurs.",{"type":10,"tag":18,"props":9000,"children":9001},{},[9002,9004,9010,9012,9016,9017,9022],{"type":16,"value":9003},"This culling is disabled if\n",{"type":10,"tag":35,"props":9005,"children":9007},{"className":9006},[],[9008],{"type":16,"value":9009},"VK_GEOMETRY_INSTANCE_TRIANGLE_FACING_CULL_DISABLE_BIT_KHR",{"type":16,"value":9011}," was included\nin ",{"type":10,"tag":44,"props":9013,"children":9014},{"href":7851},[9015],{"type":16,"value":7854},{"type":16,"value":7856},{"type":10,"tag":35,"props":9018,"children":9020},{"className":9019},[],[9021],{"type":16,"value":8878},{"type":16,"value":9023}," for the instance\nwhich the intersected geometry belongs to.",{"type":10,"tag":18,"props":9025,"children":9026},{},[9027],{"type":16,"value":9028},"Intersection candidates that have not intersected with any face (a ==\n0) are unconditionally culled, irrespective of ray flags and geometry\ninstance flags.",{"type":10,"tag":18,"props":9030,"children":9031},{},[9032,9034,9039,9040],{"type":16,"value":9033},"The ",{"type":10,"tag":35,"props":9035,"children":9037},{"className":9036},[],[9038],{"type":16,"value":7732},{"type":16,"value":4500},{"type":10,"tag":35,"props":9041,"children":9043},{"className":9042},[],[9044],{"type":16,"value":7739},{"type":10,"tag":18,"props":9046,"children":9047},{},[9048,9053],{"type":10,"tag":35,"props":9049,"children":9051},{"className":9050},[],[9052],{"type":16,"value":7758},{"type":16,"value":9054}," are mutually exclusive.",{"type":10,"tag":7546,"props":9056,"children":9058},{"id":9057},"_ray_opacity_culling",[9059],{"type":16,"value":9060},"Ray Opacity Culling",{"type":10,"tag":18,"props":9062,"children":9063},{},[9064,9066,9069,9071,9074],{"type":16,"value":9065},"Each geometry in the acceleration structure ",{"type":10,"tag":28,"props":9067,"children":9068},{"type":7363},[],{"type":16,"value":9070}," be considered either opaque\nor not.\nOpaque geometries continue through traversal as normal, whereas non-opaque\ngeometries need to be either confirmed or discarded by shader code.\nIntersection candidates ",{"type":10,"tag":28,"props":9072,"children":9073},{"type":74},[],{"type":16,"value":9075}," also be culled based on their opacity.",{"type":10,"tag":7546,"props":9077,"children":9079},{"id":9078},"determination-1",[9080],{"type":16,"value":7926},{"type":10,"tag":18,"props":9082,"children":9083},{},[9084,9086,9092,9094,9100,9101,9106],{"type":16,"value":9085},"Each individual intersection candidate is initially determined as opaque if\n",{"type":10,"tag":35,"props":9087,"children":9089},{"className":9088},[],[9090],{"type":16,"value":9091},"VK_GEOMETRY_OPAQUE_BIT_KHR",{"type":16,"value":9093}," was included in the\n",{"type":10,"tag":44,"props":9095,"children":9097},{"href":9096},"/man/VkAccelerationStructureGeometryKHR",[9098],{"type":16,"value":9099},"VkAccelerationStructureGeometryKHR",{"type":16,"value":7856},{"type":10,"tag":35,"props":9102,"children":9104},{"className":9103},[],[9105],{"type":16,"value":8878},{"type":16,"value":9107}," when the geometry it\nintersected with was built, otherwise it is considered non-opaque.",{"type":10,"tag":18,"props":9109,"children":9110},{},[9111,9113,9119],{"type":16,"value":9112},"If the geometry includes an opacity micromap, the opacity of the\nintersection at this point is instead derived as described in\n",{"type":10,"tag":44,"props":9114,"children":9116},{"href":9115},"/chapters/ray-traversal#ray-opacity-micromap",[9117],{"type":16,"value":9118},"Ray Opacity Micromap",{"type":16,"value":7572},{"type":10,"tag":18,"props":9121,"children":9122},{},[9123,9125,9131],{"type":16,"value":9124},"If the intersection candidate was generated by an ",{"type":10,"tag":44,"props":9126,"children":9128},{"href":9127},"/chapters/shaders#shaders-intersection",[9129],{"type":16,"value":9130},"intersection shader",{"type":16,"value":9132},", the intersection is initially considered to have\nopacity matching the AABB candidate that it was generated from.",{"type":10,"tag":18,"props":9134,"children":9135},{},[9136,9138,9144,9146,9150,9151,9156,9158,9164],{"type":16,"value":9137},"However, this opacity can be overridden when it is built into an instance.\nSetting ",{"type":10,"tag":35,"props":9139,"children":9141},{"className":9140},[],[9142],{"type":16,"value":9143},"VK_GEOMETRY_INSTANCE_FORCE_OPAQUE_BIT_KHR",{"type":16,"value":9145}," in\n",{"type":10,"tag":44,"props":9147,"children":9148},{"href":7851},[9149],{"type":16,"value":7854},{"type":16,"value":7856},{"type":10,"tag":35,"props":9152,"children":9154},{"className":9153},[],[9155],{"type":16,"value":8878},{"type":16,"value":9157}," will force all\ngeometries in the instance to be considered opaque.\nSimilarly, setting ",{"type":10,"tag":35,"props":9159,"children":9161},{"className":9160},[],[9162],{"type":16,"value":9163},"VK_GEOMETRY_INSTANCE_FORCE_NO_OPAQUE_BIT_KHR",{"type":16,"value":9165}," will\nforce all geometries in the instance to be considered non-opaque.",{"type":10,"tag":18,"props":9167,"children":9168},{},[9169,9171,9177,9178,9184,9186,9191,9193,9198,9200,9205],{"type":16,"value":9170},"This can again be overridden by including ",{"type":10,"tag":35,"props":9172,"children":9174},{"className":9173},[],[9175],{"type":16,"value":9176},"OpaqueKHR",{"type":16,"value":7675},{"type":10,"tag":35,"props":9179,"children":9181},{"className":9180},[],[9182],{"type":16,"value":9183},"NoOpaqueKHR",{"type":16,"value":9185},"\nin the ",{"type":10,"tag":35,"props":9187,"children":9189},{"className":9188},[],[9190],{"type":16,"value":7758},{"type":16,"value":9192}," parameter when tracing a ray.\n",{"type":10,"tag":35,"props":9194,"children":9196},{"className":9195},[],[9197],{"type":16,"value":9176},{"type":16,"value":9199}," forces all geometries to behave as if they are opaque,\nregardless of their build parameters.\nSimilarly, ",{"type":10,"tag":35,"props":9201,"children":9203},{"className":9202},[],[9204],{"type":16,"value":9183},{"type":16,"value":9206}," forces all geometries to behave as if they are\nnon-opaque.",{"type":10,"tag":18,"props":9208,"children":9209},{},[9210,9211,9216,9218,9224,9225,9228,9230,9235,9237,9242],{"type":16,"value":8943},{"type":10,"tag":35,"props":9212,"children":9214},{"className":9213},[],[9215],{"type":16,"value":40},{"type":16,"value":9217},", to determine the\nopacity of AABB intersection candidates,\n",{"type":10,"tag":35,"props":9219,"children":9221},{"className":9220},[],[9222],{"type":16,"value":9223},"OpRayQueryGetIntersectionCandidateAABBOpaqueKHR",{"type":16,"value":71},{"type":10,"tag":28,"props":9226,"children":9227},{"type":74},[],{"type":16,"value":9229}," be used.\nThis instruction will return ",{"type":10,"tag":35,"props":9231,"children":9233},{"className":9232},[],[9234],{"type":16,"value":216},{"type":16,"value":9236}," for opaque intersection candidates,\nand ",{"type":10,"tag":35,"props":9238,"children":9240},{"className":9239},[],[9241],{"type":16,"value":239},{"type":16,"value":9243}," for non-opaque intersection candidates.",{"type":10,"tag":7546,"props":9245,"children":9247},{"id":9246},"culling-1",[9248],{"type":16,"value":8964},{"type":10,"tag":18,"props":9250,"children":9251},{},[9252,9253,9259,9261,9266],{"type":16,"value":7745},{"type":10,"tag":35,"props":9254,"children":9256},{"className":9255},[],[9257],{"type":16,"value":9258},"CullOpaqueKHR",{"type":16,"value":9260}," is included in the ",{"type":10,"tag":35,"props":9262,"children":9264},{"className":9263},[],[9265],{"type":16,"value":7758},{"type":16,"value":9267}," parameter when tracing\na ray, an intersection with a geometry that is considered opaque is dropped,\nand no further processing occurs.",{"type":10,"tag":18,"props":9269,"children":9270},{},[9271,9272,9278,9279,9284],{"type":16,"value":7745},{"type":10,"tag":35,"props":9273,"children":9275},{"className":9274},[],[9276],{"type":16,"value":9277},"CullNoOpaqueKHR",{"type":16,"value":9260},{"type":10,"tag":35,"props":9280,"children":9282},{"className":9281},[],[9283],{"type":16,"value":7758},{"type":16,"value":9285}," parameter when\ntracing a ray, an intersection with a geometry that is considered non-opaque\nis dropped, and no further processing occurs.",{"type":10,"tag":18,"props":9287,"children":9288},{},[9289,9290,9295,9297,9302,9303,9308,9310,9315,9316,9321],{"type":16,"value":9033},{"type":10,"tag":35,"props":9291,"children":9293},{"className":9292},[],[9294],{"type":16,"value":9176},{"type":16,"value":9296},", ",{"type":10,"tag":35,"props":9298,"children":9300},{"className":9299},[],[9301],{"type":16,"value":9183},{"type":16,"value":9296},{"type":10,"tag":35,"props":9304,"children":9306},{"className":9305},[],[9307],{"type":16,"value":9258},{"type":16,"value":9309},", and\n",{"type":10,"tag":35,"props":9311,"children":9313},{"className":9312},[],[9314],{"type":16,"value":9277},{"type":16,"value":71},{"type":10,"tag":35,"props":9317,"children":9319},{"className":9318},[],[9320],{"type":16,"value":7758},{"type":16,"value":9054},{"type":10,"tag":7546,"props":9323,"children":9325},{"id":9324},"ray-opacity-micromap",[9326],{"type":16,"value":9118},{"type":10,"tag":18,"props":9328,"children":9329},{},[9330,9331,9337,9339,9342],{"type":16,"value":7597},{"type":10,"tag":35,"props":9332,"children":9334},{"className":9333},[],[9335],{"type":16,"value":9336},"VK_GEOMETRY_TYPE_TRIANGLES_KHR",{"type":16,"value":9338}," geometry in the acceleration\nstructure ",{"type":10,"tag":28,"props":9340,"children":9341},{"type":7363},[],{"type":16,"value":9343}," have an opacity micromap associated with it to give\nfiner-grained opacity information.",{"type":10,"tag":18,"props":9345,"children":9346},{},[9347,9349,9355,9357,9362],{"type":16,"value":9348},"If the intersection candidate is with a geometry with an associated opacity\nmicromap and ",{"type":10,"tag":35,"props":9350,"children":9352},{"className":9351},[],[9353],{"type":16,"value":9354},"VK_GEOMETRY_INSTANCE_DISABLE_OPACITY_MICROMAPS_EXT",{"type":16,"value":9356}," is not\nset in its instance then the micromap is used to determine geometry opacity\ninstead of the ",{"type":10,"tag":35,"props":9358,"children":9360},{"className":9359},[],[9361],{"type":16,"value":9091},{"type":16,"value":9363}," flag in the geometry.",{"type":10,"tag":18,"props":9365,"children":9366},{},[9367],{"type":16,"value":9368},"The opacity information in the micromap object is accessed using the\ncandidate intersection u and v coordinates.\nThe integer u and v are computed from ⌊u⌋\n+ ⌊v⌋, clamping ⌊u⌋ as needed to\nkeep the sum less than or equal to 1 \u003C\u003C subdivisionlevel.\nThese values are mapped into a linear index with a space filling curve which\nis defined recursively by traversing into the sub-triangle nearest vertex 0,\nthen the middle triangle with ordering flipped, then nearest vertex 1 then\nnearest vertex 2.",{"type":10,"tag":18,"props":9370,"children":9371},{},[9372],{"type":10,"tag":7350,"props":9373,"children":9377},{"alt":9374,"src":9375,"title":9376},"micromap subd","https://data.vkdoc.net/images/micromap-subd.svg","Example ordering for micromap data",[],{"type":10,"tag":140,"props":9379,"children":9380},{},[9381,9386],{"type":10,"tag":18,"props":9382,"children":9383},{},[9384],{"type":16,"value":9385},"This encoding is spatially coherent, purely hierarchical, and allows a\nbit-parallel conversion between barycentric address and index values.",{"type":10,"tag":18,"props":9387,"children":9388},{},[9389],{"type":16,"value":9390},"See the appendix for reference code implementing this mapping.",{"type":10,"tag":18,"props":9392,"children":9393},{},[9394,9396,9402,9404,9410],{"type":16,"value":9395},"The result of the opacity micromap lookup and operations is to treat the\nintersection as opaque, non-opaque, or ignored.\nThe interpretation of the values depends on\n",{"type":10,"tag":35,"props":9397,"children":9399},{"className":9398},[],[9400],{"type":16,"value":9401},"VK_GEOMETRY_INSTANCE_FORCE_OPACITY_MICROMAP_2_STATE_EXT",{"type":16,"value":9403}," in the\ninstance of the candidate intersection or\n",{"type":10,"tag":35,"props":9405,"children":9407},{"className":9406},[],[9408],{"type":16,"value":9409},"ForceOpacityMicromap2StateEXT",{"type":16,"value":9411}," ray flags on the ray.\nIf either is set, the opacity micromap information is interpreted in 2 state\noverride mode.\nIf the result of the micromap lookup is to treat the intersection candidate\nas ignored, no further processing of that candidate is done.",{"type":10,"tag":18,"props":9413,"children":9414},{},[9415,9417,9423],{"type":16,"value":9416},"If the associated opacity micromap has format\n",{"type":10,"tag":35,"props":9418,"children":9420},{"className":9419},[],[9421],{"type":16,"value":9422},"VK_OPACITY_MICROMAP_FORMAT_2_STATE_EXT",{"type":16,"value":9424},", each element of the micromap\nis represented by a single bit at the index derived above.",{"type":10,"tag":18,"props":9426,"children":9427},{},[9428,9429,9435],{"type":16,"value":9416},{"type":10,"tag":35,"props":9430,"children":9432},{"className":9431},[],[9433],{"type":16,"value":9434},"VK_OPACITY_MICROMAP_FORMAT_4_STATE_EXT",{"type":16,"value":9436},", each element is represented by\na two bit value at the index derived above.",{"type":10,"tag":9438,"props":9439,"children":9445},"table",{"className":9440},[9441,9442,9443,9444],"tableblock","frame-all","grid-all","stretch",[9446,9467,9508],{"type":10,"tag":9447,"props":9448,"children":9449},"colgroup",{},[9450,9455,9458,9461,9464],{"type":10,"tag":9451,"props":9452,"children":9454},"col",{"style":9453},"width: 20%;",[],{"type":10,"tag":9451,"props":9456,"children":9457},{"style":9453},[],{"type":10,"tag":9451,"props":9459,"children":9460},{"style":9453},[],{"type":10,"tag":9451,"props":9462,"children":9463},{"style":9453},[],{"type":10,"tag":9451,"props":9465,"children":9466},{"style":9453},[],{"type":10,"tag":9468,"props":9469,"children":9470},"thead",{},[9471],{"type":10,"tag":9472,"props":9473,"children":9474},"tr",{},[9475,9484,9490,9496,9502],{"type":10,"tag":9476,"props":9477,"children":9481},"th",{"className":9478},[9441,9479,9480],"halign-left","valign-top",[9482],{"type":16,"value":9483},"4 State value",{"type":10,"tag":9476,"props":9485,"children":9487},{"className":9486},[9441,9479,9480],[9488],{"type":16,"value":9489},"2 State value",{"type":10,"tag":9476,"props":9491,"children":9493},{"className":9492},[9441,9479,9480],[9494],{"type":16,"value":9495},"Special index value",{"type":10,"tag":9476,"props":9497,"children":9499},{"className":9498},[9441,9479,9480],[9500],{"type":16,"value":9501},"2 State override",{"type":10,"tag":9476,"props":9503,"children":9505},{"className":9504},[9441,9479,9480],[9506],{"type":16,"value":9507},"Result",{"type":10,"tag":9509,"props":9510,"children":9511},"tbody",{},[9512,9568,9620,9673,9724,9771,9818,9866],{"type":10,"tag":9472,"props":9513,"children":9514},{},[9515,9525,9534,9548,9558],{"type":10,"tag":9516,"props":9517,"children":9519},"td",{"className":9518},[9441,9479,9480],[9520],{"type":10,"tag":18,"props":9521,"children":9523},{"className":9522},[9441],[9524],{"type":16,"value":238},{"type":10,"tag":9516,"props":9526,"children":9528},{"className":9527},[9441,9479,9480],[9529],{"type":10,"tag":18,"props":9530,"children":9532},{"className":9531},[9441],[9533],{"type":16,"value":238},{"type":10,"tag":9516,"props":9535,"children":9537},{"className":9536},[9441,9479,9480],[9538],{"type":10,"tag":18,"props":9539,"children":9541},{"className":9540},[9441],[9542],{"type":10,"tag":9543,"props":9544,"children":9545},"literal",{},[9546],{"type":16,"value":9547},"VK_OPACITY_MICROMAP_SPECIAL_INDEX_FULLY_TRANSPARENT_EXT",{"type":10,"tag":9516,"props":9549,"children":9551},{"className":9550},[9441,9479,9480],[9552],{"type":10,"tag":18,"props":9553,"children":9555},{"className":9554},[9441],[9556],{"type":16,"value":9557},"Y",{"type":10,"tag":9516,"props":9559,"children":9561},{"className":9560},[9441,9479,9480],[9562],{"type":10,"tag":18,"props":9563,"children":9565},{"className":9564},[9441],[9566],{"type":16,"value":9567},"Ignored",{"type":10,"tag":9472,"props":9569,"children":9570},{},[9571,9580,9589,9601,9611],{"type":10,"tag":9516,"props":9572,"children":9574},{"className":9573},[9441,9479,9480],[9575],{"type":10,"tag":18,"props":9576,"children":9578},{"className":9577},[9441],[9579],{"type":16,"value":238},{"type":10,"tag":9516,"props":9581,"children":9583},{"className":9582},[9441,9479,9480],[9584],{"type":10,"tag":18,"props":9585,"children":9587},{"className":9586},[9441],[9588],{"type":16,"value":238},{"type":10,"tag":9516,"props":9590,"children":9592},{"className":9591},[9441,9479,9480],[9593],{"type":10,"tag":18,"props":9594,"children":9596},{"className":9595},[9441],[9597],{"type":10,"tag":9543,"props":9598,"children":9599},{},[9600],{"type":16,"value":9547},{"type":10,"tag":9516,"props":9602,"children":9604},{"className":9603},[9441,9479,9480],[9605],{"type":10,"tag":18,"props":9606,"children":9608},{"className":9607},[9441],[9609],{"type":16,"value":9610},"N",{"type":10,"tag":9516,"props":9612,"children":9614},{"className":9613},[9441,9479,9480],[9615],{"type":10,"tag":18,"props":9616,"children":9618},{"className":9617},[9441],[9619],{"type":16,"value":9567},{"type":10,"tag":9472,"props":9621,"children":9622},{},[9623,9632,9641,9654,9663],{"type":10,"tag":9516,"props":9624,"children":9626},{"className":9625},[9441,9479,9480],[9627],{"type":10,"tag":18,"props":9628,"children":9630},{"className":9629},[9441],[9631],{"type":16,"value":383},{"type":10,"tag":9516,"props":9633,"children":9635},{"className":9634},[9441,9479,9480],[9636],{"type":10,"tag":18,"props":9637,"children":9639},{"className":9638},[9441],[9640],{"type":16,"value":383},{"type":10,"tag":9516,"props":9642,"children":9644},{"className":9643},[9441,9479,9480],[9645],{"type":10,"tag":18,"props":9646,"children":9648},{"className":9647},[9441],[9649],{"type":10,"tag":9543,"props":9650,"children":9651},{},[9652],{"type":16,"value":9653},"VK_OPACITY_MICROMAP_SPECIAL_INDEX_FULLY_OPAQUE_EXT",{"type":10,"tag":9516,"props":9655,"children":9657},{"className":9656},[9441,9479,9480],[9658],{"type":10,"tag":18,"props":9659,"children":9661},{"className":9660},[9441],[9662],{"type":16,"value":9557},{"type":10,"tag":9516,"props":9664,"children":9666},{"className":9665},[9441,9479,9480],[9667],{"type":10,"tag":18,"props":9668,"children":9670},{"className":9669},[9441],[9671],{"type":16,"value":9672},"Opaque",{"type":10,"tag":9472,"props":9674,"children":9675},{},[9676,9685,9694,9706,9715],{"type":10,"tag":9516,"props":9677,"children":9679},{"className":9678},[9441,9479,9480],[9680],{"type":10,"tag":18,"props":9681,"children":9683},{"className":9682},[9441],[9684],{"type":16,"value":383},{"type":10,"tag":9516,"props":9686,"children":9688},{"className":9687},[9441,9479,9480],[9689],{"type":10,"tag":18,"props":9690,"children":9692},{"className":9691},[9441],[9693],{"type":16,"value":383},{"type":10,"tag":9516,"props":9695,"children":9697},{"className":9696},[9441,9479,9480],[9698],{"type":10,"tag":18,"props":9699,"children":9701},{"className":9700},[9441],[9702],{"type":10,"tag":9543,"props":9703,"children":9704},{},[9705],{"type":16,"value":9653},{"type":10,"tag":9516,"props":9707,"children":9709},{"className":9708},[9441,9479,9480],[9710],{"type":10,"tag":18,"props":9711,"children":9713},{"className":9712},[9441],[9714],{"type":16,"value":9610},{"type":10,"tag":9516,"props":9716,"children":9718},{"className":9717},[9441,9479,9480],[9719],{"type":10,"tag":18,"props":9720,"children":9722},{"className":9721},[9441],[9723],{"type":16,"value":9672},{"type":10,"tag":9472,"props":9725,"children":9726},{},[9727,9736,9740,9753,9762],{"type":10,"tag":9516,"props":9728,"children":9730},{"className":9729},[9441,9479,9480],[9731],{"type":10,"tag":18,"props":9732,"children":9734},{"className":9733},[9441],[9735],{"type":16,"value":374},{"type":10,"tag":9516,"props":9737,"children":9739},{"className":9738},[9441,9479,9480],[],{"type":10,"tag":9516,"props":9741,"children":9743},{"className":9742},[9441,9479,9480],[9744],{"type":10,"tag":18,"props":9745,"children":9747},{"className":9746},[9441],[9748],{"type":10,"tag":9543,"props":9749,"children":9750},{},[9751],{"type":16,"value":9752},"VK_OPACITY_MICROMAP_SPECIAL_INDEX_FULLY_UNKNOWN_TRANSPARENT_EXT",{"type":10,"tag":9516,"props":9754,"children":9756},{"className":9755},[9441,9479,9480],[9757],{"type":10,"tag":18,"props":9758,"children":9760},{"className":9759},[9441],[9761],{"type":16,"value":9557},{"type":10,"tag":9516,"props":9763,"children":9765},{"className":9764},[9441,9479,9480],[9766],{"type":10,"tag":18,"props":9767,"children":9769},{"className":9768},[9441],[9770],{"type":16,"value":9567},{"type":10,"tag":9472,"props":9772,"children":9773},{},[9774,9783,9787,9799,9808],{"type":10,"tag":9516,"props":9775,"children":9777},{"className":9776},[9441,9479,9480],[9778],{"type":10,"tag":18,"props":9779,"children":9781},{"className":9780},[9441],[9782],{"type":16,"value":374},{"type":10,"tag":9516,"props":9784,"children":9786},{"className":9785},[9441,9479,9480],[],{"type":10,"tag":9516,"props":9788,"children":9790},{"className":9789},[9441,9479,9480],[9791],{"type":10,"tag":18,"props":9792,"children":9794},{"className":9793},[9441],[9795],{"type":10,"tag":9543,"props":9796,"children":9797},{},[9798],{"type":16,"value":9752},{"type":10,"tag":9516,"props":9800,"children":9802},{"className":9801},[9441,9479,9480],[9803],{"type":10,"tag":18,"props":9804,"children":9806},{"className":9805},[9441],[9807],{"type":16,"value":9610},{"type":10,"tag":9516,"props":9809,"children":9811},{"className":9810},[9441,9479,9480],[9812],{"type":10,"tag":18,"props":9813,"children":9815},{"className":9814},[9441],[9816],{"type":16,"value":9817},"Non-opaque",{"type":10,"tag":9472,"props":9819,"children":9820},{},[9821,9831,9835,9848,9857],{"type":10,"tag":9516,"props":9822,"children":9824},{"className":9823},[9441,9479,9480],[9825],{"type":10,"tag":18,"props":9826,"children":9828},{"className":9827},[9441],[9829],{"type":16,"value":9830},"3",{"type":10,"tag":9516,"props":9832,"children":9834},{"className":9833},[9441,9479,9480],[],{"type":10,"tag":9516,"props":9836,"children":9838},{"className":9837},[9441,9479,9480],[9839],{"type":10,"tag":18,"props":9840,"children":9842},{"className":9841},[9441],[9843],{"type":10,"tag":9543,"props":9844,"children":9845},{},[9846],{"type":16,"value":9847},"VK_OPACITY_MICROMAP_SPECIAL_INDEX_FULLY_UNKNOWN_OPAQUE_EXT",{"type":10,"tag":9516,"props":9849,"children":9851},{"className":9850},[9441,9479,9480],[9852],{"type":10,"tag":18,"props":9853,"children":9855},{"className":9854},[9441],[9856],{"type":16,"value":9557},{"type":10,"tag":9516,"props":9858,"children":9860},{"className":9859},[9441,9479,9480],[9861],{"type":10,"tag":18,"props":9862,"children":9864},{"className":9863},[9441],[9865],{"type":16,"value":9672},{"type":10,"tag":9472,"props":9867,"children":9868},{},[9869,9878,9882,9894,9903],{"type":10,"tag":9516,"props":9870,"children":9872},{"className":9871},[9441,9479,9480],[9873],{"type":10,"tag":18,"props":9874,"children":9876},{"className":9875},[9441],[9877],{"type":16,"value":9830},{"type":10,"tag":9516,"props":9879,"children":9881},{"className":9880},[9441,9479,9480],[],{"type":10,"tag":9516,"props":9883,"children":9885},{"className":9884},[9441,9479,9480],[9886],{"type":10,"tag":18,"props":9887,"children":9889},{"className":9888},[9441],[9890],{"type":10,"tag":9543,"props":9891,"children":9892},{},[9893],{"type":16,"value":9847},{"type":10,"tag":9516,"props":9895,"children":9897},{"className":9896},[9441,9479,9480],[9898],{"type":10,"tag":18,"props":9899,"children":9901},{"className":9900},[9441],[9902],{"type":16,"value":9610},{"type":10,"tag":9516,"props":9904,"children":9906},{"className":9905},[9441,9479,9480],[9907],{"type":10,"tag":18,"props":9908,"children":9910},{"className":9909},[9441],[9911],{"type":16,"value":9817},{"type":10,"tag":118,"props":9913,"children":9915},{"id":9914},"ray-intersection-confirmation",[9916],{"type":16,"value":7521},{"type":10,"tag":18,"props":9918,"children":9919},{},[9920],{"type":16,"value":9921},"Depending on the opacity of intersected geometry and whether it is a\ntriangle or an AABB, candidate intersections are further processed to\ndetermine the eventual hit result.\nCandidates generated from AABB intersections run through the same\nconfirmation process as triangle hits.",{"type":10,"tag":7546,"props":9923,"children":9925},{"id":9924},"_aabb_intersection_candidates",[9926],{"type":16,"value":9927},"AABB Intersection Candidates",{"type":10,"tag":18,"props":9929,"children":9930},{},[9931,9933,9937,9939,9942],{"type":16,"value":9932},"For an intersection candidate with an AABB geometry generated by\n",{"type":10,"tag":44,"props":9934,"children":9935},{"href":8849},[9936],{"type":16,"value":123},{"type":16,"value":9938},", shader code is executed to\ndetermine whether any hits should be reported to the traversal\ninfrastructure; no further processing of this intersection candidate occurs.\nThe occurrence of an AABB intersection candidate does not guarantee the ray\nintersects the primitive bounds.\nTo avoid propagating false intersections the application ",{"type":10,"tag":28,"props":9940,"children":9941},{"type":7369},[],{"type":16,"value":9943}," verify the\nintersection candidate before reporting any hits.",{"type":10,"tag":18,"props":9945,"children":9946},{},[9947,9948,9952,9954,9958,9960,9966,9968,9974,9976,9982,9984,9990,9992,9998],{"type":16,"value":8908},{"type":10,"tag":44,"props":9949,"children":9950},{"href":46},[9951],{"type":16,"value":7483},{"type":16,"value":9953}," instruction, an ",{"type":10,"tag":44,"props":9955,"children":9956},{"href":9127},[9957],{"type":16,"value":9130},{"type":16,"value":9959}," is\ninvoked from the ",{"type":10,"tag":44,"props":9961,"children":9963},{"href":9962},"/chapters/ray-tracing#shader-binding-table",[9964],{"type":16,"value":9965},"Shader Binding Table",{"type":16,"value":9967}," according to the\n",{"type":10,"tag":44,"props":9969,"children":9971},{"href":9970},"/chapters/ray-tracing#shader-binding-table-indexing-rules",[9972],{"type":16,"value":9973},"specified indexing",{"type":16,"value":9975}," for the\nintersected geometry.\nIf this shader calls ",{"type":10,"tag":35,"props":9977,"children":9979},{"className":9978},[],[9980],{"type":16,"value":9981},"OpReportIntersectionKHR",{"type":16,"value":9983},", a new intersection\ncandidate is generated as described\n",{"type":10,"tag":44,"props":9985,"children":9987},{"href":9986},"/chapters/ray-traversal#aabb-intersection-candidate-generation",[9988],{"type":16,"value":9989},"below",{"type":16,"value":9991},".\nIf the intersection shader is ",{"type":10,"tag":35,"props":9993,"children":9995},{"className":9994},[],[9996],{"type":16,"value":9997},"VK_SHADER_UNUSED_KHR",{"type":16,"value":9999}," (which is only\nallowed for a zero shader group) then no further processing of the\nintersection candidate occurs.",{"type":10,"tag":10001,"props":10002,"children":10004},"anchor",{"id":10003},"aabb-intersection-candidate-generation",[],{"type":10,"tag":18,"props":10006,"children":10007},{},[10008,10010,10016,10018,10023,10025,10029,10031,10037],{"type":16,"value":10009},"Each new candidate generated as a result of this processing is a generated\nintersection candidate that intersects the AABB geometry, with a t\nvalue equal to the ",{"type":10,"tag":35,"props":10011,"children":10013},{"className":10012},[],[10014],{"type":16,"value":10015},"Hit",{"type":16,"value":10017}," parameter of the ",{"type":10,"tag":35,"props":10019,"children":10021},{"className":10020},[],[10022],{"type":16,"value":9981},{"type":16,"value":10024},"\ninstruction.\nThe new generated candidate is then independently run through\n",{"type":10,"tag":44,"props":10026,"children":10027},{"href":7518},[10028],{"type":16,"value":7521},{"type":16,"value":10030}," as a\n",{"type":10,"tag":44,"props":10032,"children":10034},{"href":10033},"/chapters/ray-traversal#ray-triangle-and-generated-intersection-candidates",[10035],{"type":16,"value":10036},"generated\nintersection",{"type":16,"value":7572},{"type":10,"tag":18,"props":10039,"children":10040},{},[10041,10042,10047,10049,10054,10056,10061,10063,10069,10071,10077,10078,10081,10083,10089,10091,10094,10096,10101,10103,10106,10108,10114,10116,10120,10122,10125],{"type":16,"value":8943},{"type":10,"tag":35,"props":10043,"children":10045},{"className":10044},[],[10046],{"type":16,"value":40},{"type":16,"value":10048},", control is returned to\nthe shader which executed ",{"type":10,"tag":35,"props":10050,"children":10052},{"className":10051},[],[10053],{"type":16,"value":40},{"type":16,"value":10055},", returning ",{"type":10,"tag":35,"props":10057,"children":10059},{"className":10058},[],[10060],{"type":16,"value":216},{"type":16,"value":10062},".\nThe resulting ray query has a candidate intersection type of\n",{"type":10,"tag":35,"props":10064,"children":10066},{"className":10065},[],[10067],{"type":16,"value":10068},"RayQueryCandidateIntersectionAABBKHR",{"type":16,"value":10070},".\n",{"type":10,"tag":35,"props":10072,"children":10074},{"className":10073},[],[10075],{"type":16,"value":10076},"OpRayQueryGenerateIntersectionKHR",{"type":16,"value":71},{"type":10,"tag":28,"props":10079,"children":10080},{"type":74},[],{"type":16,"value":10082}," be called to commit a new\nintersection candidate with committed intersection type of\n",{"type":10,"tag":35,"props":10084,"children":10086},{"className":10085},[],[10087],{"type":16,"value":10088},"RayQueryCommittedIntersectionGeneratedKHR",{"type":16,"value":10090},".\nFurther ray query processing ",{"type":10,"tag":28,"props":10092,"children":10093},{"type":74},[],{"type":16,"value":10095}," be continued by executing\n",{"type":10,"tag":35,"props":10097,"children":10099},{"className":10098},[],[10100],{"type":16,"value":40},{"type":16,"value":10102}," with the same ray query, or intersection ",{"type":10,"tag":28,"props":10104,"children":10105},{"type":74},[],{"type":16,"value":10107}," be\nterminated with ",{"type":10,"tag":35,"props":10109,"children":10111},{"className":10110},[],[10112],{"type":16,"value":10113},"OpRayQueryTerminateKHR",{"type":16,"value":10115},".\nUnlike rays traced with a ",{"type":10,"tag":44,"props":10117,"children":10118},{"href":46},[10119],{"type":16,"value":7483},{"type":16,"value":10121}," instruction, candidates generated in this way skip generated\nintersection candidate confirmation; applications ",{"type":10,"tag":28,"props":10123,"children":10124},{"type":7369},[],{"type":16,"value":10126}," make this\ndetermination before generating the intersection.",{"type":10,"tag":18,"props":10128,"children":10129},{},[10130,10132,10135],{"type":16,"value":10131},"This operation ",{"type":10,"tag":28,"props":10133,"children":10134},{"type":7363},[],{"type":16,"value":10136}," be executed multiple times for the same intersection\ncandidate.",{"type":10,"tag":7546,"props":10138,"children":10140},{"id":10139},"ray-triangle-and-generated-intersection-candidates",[10141],{"type":16,"value":10142},"Triangle and Generated Intersection Candidates",{"type":10,"tag":18,"props":10144,"children":10145},{},[10146,10148,10153,10155,10158],{"type":16,"value":10147},"For triangle and ",{"type":10,"tag":44,"props":10149,"children":10150},{"href":9986},[10151],{"type":16,"value":10152},"generated\nintersection candidates",{"type":16,"value":10154},", additional shader code ",{"type":10,"tag":28,"props":10156,"children":10157},{"type":7363},[],{"type":16,"value":10159}," be executed based on\nthe intersection’s opacity.",{"type":10,"tag":18,"props":10161,"children":10162},{},[10163],{"type":16,"value":10164},"If the intersection is opaque, the candidate is immediately confirmed as a\nvalid hit and passes to the next stage of processing.",{"type":10,"tag":18,"props":10166,"children":10167},{},[10168],{"type":16,"value":10169},"For non-opaque intersection candidates, shader code is executed to determine\nwhether a hit occurred or not.",{"type":10,"tag":18,"props":10171,"children":10172},{},[10173,10174,10178,10179,10185,10187,10191,10193,10199,10201,10205,10207,10212],{"type":16,"value":8908},{"type":10,"tag":44,"props":10175,"children":10176},{"href":46},[10177],{"type":16,"value":7483},{"type":16,"value":9953},{"type":10,"tag":44,"props":10180,"children":10182},{"href":10181},"/chapters/shaders#shaders-any-hit",[10183],{"type":16,"value":10184},"any-hit shader",{"type":16,"value":10186}," is invoked from\nthe ",{"type":10,"tag":44,"props":10188,"children":10189},{"href":9962},[10190],{"type":16,"value":9965},{"type":16,"value":10192}," according to the specified indexing.\nIf this shader calls ",{"type":10,"tag":35,"props":10194,"children":10196},{"className":10195},[],[10197],{"type":16,"value":10198},"OpIgnoreIntersectionKHR",{"type":16,"value":10200},", the candidate is dropped\nand no further processing of the candidate occurs.\nIf the ",{"type":10,"tag":44,"props":10202,"children":10203},{"href":10181},[10204],{"type":16,"value":10184},{"type":16,"value":10206}," identified is\n",{"type":10,"tag":35,"props":10208,"children":10210},{"className":10209},[],[10211],{"type":16,"value":9997},{"type":16,"value":10213},", the candidate is immediately confirmed as a\nvalid hit and passes to the next stage of processing.",{"type":10,"tag":18,"props":10215,"children":10216},{},[10217,10218,10223,10224,10229,10230,10235,10237,10243,10244,10250,10251,10254,10256,10262,10263,10266,10267,10272,10273,10276,10277,10282,10284,10289],{"type":16,"value":8943},{"type":10,"tag":35,"props":10219,"children":10221},{"className":10220},[],[10222],{"type":16,"value":40},{"type":16,"value":10048},{"type":10,"tag":35,"props":10225,"children":10227},{"className":10226},[],[10228],{"type":16,"value":40},{"type":16,"value":10055},{"type":10,"tag":35,"props":10231,"children":10233},{"className":10232},[],[10234],{"type":16,"value":216},{"type":16,"value":10236},".\nAs only triangle candidates participate in this operation with ray queries,\nthe resulting candidate intersection type is always\n",{"type":10,"tag":35,"props":10238,"children":10240},{"className":10239},[],[10241],{"type":16,"value":10242},"RayQueryCandidateIntersectionTriangleKHR",{"type":16,"value":10070},{"type":10,"tag":35,"props":10245,"children":10247},{"className":10246},[],[10248],{"type":16,"value":10249},"OpRayQueryConfirmIntersectionKHR",{"type":16,"value":71},{"type":10,"tag":28,"props":10252,"children":10253},{"type":74},[],{"type":16,"value":10255}," be called on the ray query to\nconfirm the candidate as a hit with committed intersection type of\n",{"type":10,"tag":35,"props":10257,"children":10259},{"className":10258},[],[10260],{"type":16,"value":10261},"RayQueryCommittedIntersectionTriangleKHR",{"type":16,"value":10090},{"type":10,"tag":28,"props":10264,"children":10265},{"type":74},[],{"type":16,"value":10095},{"type":10,"tag":35,"props":10268,"children":10270},{"className":10269},[],[10271],{"type":16,"value":40},{"type":16,"value":10102},{"type":10,"tag":28,"props":10274,"children":10275},{"type":74},[],{"type":16,"value":10107},{"type":10,"tag":35,"props":10278,"children":10280},{"className":10279},[],[10281],{"type":16,"value":10113},{"type":16,"value":10283},".\nIf ",{"type":10,"tag":35,"props":10285,"children":10287},{"className":10286},[],[10288],{"type":16,"value":10249},{"type":16,"value":10290}," has not been executed, the\ncandidate is dropped and no further processing of the candidate occurs.",{"type":10,"tag":18,"props":10292,"children":10293},{},[10294,10295,10298,10300,10306],{"type":16,"value":10131},{"type":10,"tag":28,"props":10296,"children":10297},{"type":7363},[],{"type":16,"value":10299}," be executed multiple times for the same intersection\ncandidate unless ",{"type":10,"tag":35,"props":10301,"children":10303},{"className":10302},[],[10304],{"type":16,"value":10305},"VK_GEOMETRY_NO_DUPLICATE_ANY_HIT_INVOCATION_BIT_KHR",{"type":16,"value":10307},"\nwas specified for the intersected geometry.",{"type":10,"tag":118,"props":10309,"children":10311},{"id":10310},"ray-closest-hit-determination",[10312],{"type":16,"value":7530},{"type":10,"tag":18,"props":10314,"children":10315},{},[10316,10318,10324,10326,10329],{"type":16,"value":10317},"Unless the ray was traced with the ",{"type":10,"tag":35,"props":10319,"children":10321},{"className":10320},[],[10322],{"type":16,"value":10323},"TerminateOnFirstHitKHR",{"type":16,"value":10325}," ray flag, the\nimplementation ",{"type":10,"tag":28,"props":10327,"children":10328},{"type":30},[],{"type":16,"value":10330}," track the closest confirmed hit until all geometries\nhave been tested and either confirmed or dropped.",{"type":10,"tag":18,"props":10332,"children":10333},{},[10334,10336,10340],{"type":16,"value":10335},"After an intersection candidate is confirmed, its t value is compared\nto t",{"type":10,"tag":163,"props":10337,"children":10338},{},[10339],{"type":16,"value":6936},{"type":16,"value":10341}," to determine which intersection is closer, where t is\nthe parametric distance along the ray at which the intersection occurred.",{"type":10,"tag":7558,"props":10343,"children":10344},{},[10345,10362,10373],{"type":10,"tag":7504,"props":10346,"children":10347},{},[10348,10350,10354,10356,10360],{"type":16,"value":10349},"If t \u003C t",{"type":10,"tag":163,"props":10351,"children":10352},{},[10353],{"type":16,"value":6936},{"type":16,"value":10355},", t",{"type":10,"tag":163,"props":10357,"children":10358},{},[10359],{"type":16,"value":6936},{"type":16,"value":10361}," is set to t and the candidate is\nset as the current closest hit.",{"type":10,"tag":7504,"props":10363,"children":10364},{},[10365,10367,10371],{"type":16,"value":10366},"If t > t",{"type":10,"tag":163,"props":10368,"children":10369},{},[10370],{"type":16,"value":6936},{"type":16,"value":10372},", the candidate is dropped and no further processing\nof that candidate occurs.",{"type":10,"tag":7504,"props":10374,"children":10375},{},[10376,10378,10382,10384,10387],{"type":16,"value":10377},"If t = t",{"type":10,"tag":163,"props":10379,"children":10380},{},[10381],{"type":16,"value":6936},{"type":16,"value":10383},", the candidate ",{"type":10,"tag":28,"props":10385,"children":10386},{"type":7363},[],{"type":16,"value":10388}," be set as the current closest\nhit or dropped.",{"type":10,"tag":18,"props":10390,"children":10391},{},[10392,10393,10398,10399,10404],{"type":16,"value":7745},{"type":10,"tag":35,"props":10394,"children":10396},{"className":10395},[],[10397],{"type":16,"value":10323},{"type":16,"value":7752},{"type":10,"tag":35,"props":10400,"children":10402},{"className":10401},[],[10403],{"type":16,"value":7758},{"type":16,"value":10405}," used to trace\nthe ray, once the first hit is confirmed, the ray trace is terminated.",{"type":10,"tag":118,"props":10407,"children":10409},{"id":10408},"ray-result-determination",[10410],{"type":16,"value":7539},{"type":10,"tag":18,"props":10412,"children":10413},{},[10414],{"type":16,"value":10415},"Once all candidates have finished processing the prior stages, or if the ray\nis forcibly terminated, the final result of the ray trace is determined.",{"type":10,"tag":18,"props":10417,"children":10418},{},[10419,10421,10425],{"type":16,"value":10420},"If a closest hit result was identified by ",{"type":10,"tag":44,"props":10422,"children":10423},{"href":7527},[10424],{"type":16,"value":7530},{"type":16,"value":10426},",\na closest hit has occurred, otherwise the final result is a miss.",{"type":10,"tag":18,"props":10428,"children":10429},{},[10430,10432,10436,10438,10441,10443,10449,10451,10455,10456,10460,10462,10466,10468,10474,10476,10481,10483,10488],{"type":16,"value":10431},"For rays traced with ",{"type":10,"tag":44,"props":10433,"children":10434},{"href":46},[10435],{"type":16,"value":49},{"type":16,"value":10437},"\ninstructions which ",{"type":10,"tag":28,"props":10439,"children":10440},{"type":74},[],{"type":16,"value":10442}," invoke a closest hit shader, if a closest hit result\nwas identified, a ",{"type":10,"tag":44,"props":10444,"children":10446},{"href":10445},"/chapters/shaders#shaders-closest-hit",[10447],{"type":16,"value":10448},"closest hit shader",{"type":16,"value":10450}," is invoked\nfrom the ",{"type":10,"tag":44,"props":10452,"children":10453},{"href":9962},[10454],{"type":16,"value":9965},{"type":16,"value":9967},{"type":10,"tag":44,"props":10457,"children":10458},{"href":9970},[10459],{"type":16,"value":9973},{"type":16,"value":10461}," for the\nintersected geometry.\nControl returns to the shader that executed the\n",{"type":10,"tag":44,"props":10463,"children":10464},{"href":46},[10465],{"type":16,"value":49},{"type":16,"value":10467}," instruction once this\nshader returns.\nThis shader is skipped if either the ray flags included\n",{"type":10,"tag":35,"props":10469,"children":10471},{"className":10470},[],[10472],{"type":16,"value":10473},"SkipClosestHitShaderKHR",{"type":16,"value":10475},", or if the ",{"type":10,"tag":44,"props":10477,"children":10478},{"href":10445},[10479],{"type":16,"value":10480},"closest hit\nshader",{"type":16,"value":10482}," identified is ",{"type":10,"tag":35,"props":10484,"children":10486},{"className":10485},[],[10487],{"type":16,"value":9997},{"type":16,"value":7572},{"type":10,"tag":18,"props":10490,"children":10491},{},[10492,10494,10498,10500,10506,10508,10514,10516,10521],{"type":16,"value":10493},"For rays traced with a ",{"type":10,"tag":44,"props":10495,"children":10496},{"href":46},[10497],{"type":16,"value":49},{"type":16,"value":10499},"\ninstruction where no hit result was identified, the ",{"type":10,"tag":44,"props":10501,"children":10503},{"href":10502},"/chapters/shaders#shaders-miss",[10504],{"type":16,"value":10505},"miss\nshader",{"type":16,"value":10507}," identified by the ",{"type":10,"tag":35,"props":10509,"children":10511},{"className":10510},[],[10512],{"type":16,"value":10513},"Miss Index",{"type":16,"value":10515}," parameter of the instruction is\ninvoked.\nControl returns to the shader that executed the pipeline trace ray\ninstruction once this shader returns.\nThis shader is skipped if the miss shader identified is\n",{"type":10,"tag":35,"props":10517,"children":10519},{"className":10518},[],[10520],{"type":16,"value":9997},{"type":16,"value":7572},{"type":10,"tag":18,"props":10523,"children":10524},{},[10525,10526,10531,10532,10537,10538,10543,10545,10549,10551,10556,10558,10563,10565,10571],{"type":16,"value":8943},{"type":10,"tag":35,"props":10527,"children":10529},{"className":10528},[],[10530],{"type":16,"value":40},{"type":16,"value":10048},{"type":10,"tag":35,"props":10533,"children":10535},{"className":10534},[],[10536],{"type":16,"value":40},{"type":16,"value":10055},{"type":10,"tag":35,"props":10539,"children":10541},{"className":10540},[],[10542],{"type":16,"value":239},{"type":16,"value":10544},".\nIf a closest hit was identified by ",{"type":10,"tag":44,"props":10546,"children":10547},{"href":7527},[10548],{"type":16,"value":7530},{"type":16,"value":10550},", the\nray query will now have a committed intersection type of\n",{"type":10,"tag":35,"props":10552,"children":10554},{"className":10553},[],[10555],{"type":16,"value":10088},{"type":16,"value":10557}," or\n",{"type":10,"tag":35,"props":10559,"children":10561},{"className":10560},[],[10562],{"type":16,"value":10261},{"type":16,"value":10564},".\nIf no closest hit was identified, the committed intersection type will be\n",{"type":10,"tag":35,"props":10566,"children":10568},{"className":10567},[],[10569],{"type":16,"value":10570},"RayQueryCommittedIntersectionNoneKHR",{"type":16,"value":7572},{"type":10,"tag":18,"props":10573,"children":10574},{},[10575],{"type":16,"value":10576},"No further processing of a ray query occurs after this result is determined.",{"title":10578,"searchDepth":10579,"depth":10579,"links":10580},"",2,[10581,10585,10596,10600,10601],{"id":120,"depth":10579,"text":123,"children":10582},[10583],{"id":7548,"depth":10584,"text":7551},3,{"id":7645,"depth":10579,"text":7512,"children":10586},[10587,10588,10589,10590,10591,10592,10593,10594,10595],{"id":7655,"depth":10584,"text":7658},{"id":7835,"depth":10584,"text":7838},{"id":7894,"depth":10584,"text":7897},{"id":7923,"depth":10584,"text":7926},{"id":8961,"depth":10584,"text":8964},{"id":9057,"depth":10584,"text":9060},{"id":9078,"depth":10584,"text":7926},{"id":9246,"depth":10584,"text":8964},{"id":9324,"depth":10584,"text":9118},{"id":9914,"depth":10579,"text":7521,"children":10597},[10598,10599],{"id":9924,"depth":10584,"text":9927},{"id":10139,"depth":10584,"text":10142},{"id":10310,"depth":10579,"text":7530},{"id":10408,"depth":10579,"text":7539},"markdown","chapters-ray-traversal",[10605,10610,10614,10617,10620,10624,10628,10632,10636,10640,10644,10648,10652,10656,10660,10664,10668,10672,10676,10680,10684,10688,10692,10696,10700,10704,10708,10712,10716,10720,10724,10728,10732,10736,10740,10744,10748,10752,10756,10758,10762,10766,10770,10774,10778,10782,10786,10790,10794,10798,10802,10806,10809,10812,10815,10818,10821,10824,10827],{"index":10606,"title":10607,"id":10608,"appendix":10609},0,"Preamble","preamble",false,{"index":10611,"title":10612,"id":10613,"appendix":10609},1,"Introduction","introduction",{"index":10579,"title":10615,"id":10616,"appendix":10609},"Fundamentals","fundamentals",{"index":10584,"title":10618,"id":10619,"appendix":10609},"Initialization","initialization",{"index":10621,"title":10622,"id":10623,"appendix":10609},4,"Devices and Queues","devsandqueues",{"index":10625,"title":10626,"id":10627,"appendix":10609},5,"Command Buffers","commandbuffers",{"index":10629,"title":10630,"id":10631,"appendix":10609},6,"Synchronization and Cache Control","synchronization",{"index":10633,"title":10634,"id":10635,"appendix":10609},7,"Render Pass","renderpass",{"index":10637,"title":10638,"id":10639,"appendix":10609},8,"Shaders","shaders",{"index":10641,"title":10642,"id":10643,"appendix":10609},9,"Pipelines","pipelines",{"index":10645,"title":10646,"id":10647,"appendix":10609},10,"Memory Allocation","memory",{"index":10649,"title":10650,"id":10651,"appendix":10609},11,"Resource Creation","resources",{"index":10653,"title":10654,"id":10655,"appendix":10609},12,"Samplers","samplers",{"index":10657,"title":10658,"id":10659,"appendix":10609},13,"Resource Descriptors","descriptorsets",{"index":10661,"title":10662,"id":10663,"appendix":10609},14,"Shader Interfaces","interfaces",{"index":10665,"title":10666,"id":10667,"appendix":10609},15,"Image Operations","textures",{"index":10669,"title":10670,"id":10671,"appendix":10609},16,"Fragment Density Map Operations","fragmentdensitymapops",{"index":10673,"title":10674,"id":10675,"appendix":10609},17,"Queries","queries",{"index":10677,"title":10678,"id":10679,"appendix":10609},18,"Clear Commands","clears",{"index":10681,"title":10682,"id":10683,"appendix":10609},19,"Copy Commands","copies",{"index":10685,"title":10686,"id":10687,"appendix":10609},20,"Drawing Commands","drawing",{"index":10689,"title":10690,"id":10691,"appendix":10609},21,"Fixed-Function Vertex Processing","fxvertex",{"index":10693,"title":10694,"id":10695,"appendix":10609},22,"Tessellation","tessellation",{"index":10697,"title":10698,"id":10699,"appendix":10609},23,"Geometry Shading","geometry",{"index":10701,"title":10702,"id":10703,"appendix":10609},24,"Mesh Shading","mesh",{"index":10705,"title":10706,"id":10707,"appendix":10609},25,"Cluster Culling Shading","cluster-culling",{"index":10709,"title":10710,"id":10711,"appendix":10609},26,"Fixed-Function Vertex Post-Processing","vertexpostproc",{"index":10713,"title":10714,"id":10715,"appendix":10609},27,"Rasterization","primsrast",{"index":10717,"title":10718,"id":10719,"appendix":10609},28,"Fragment Operations","fragops",{"index":10721,"title":10722,"id":10723,"appendix":10609},29,"The Framebuffer","framebuffer",{"index":10725,"title":10726,"id":10727,"appendix":10609},30,"Dispatching Commands","dispatch",{"index":10729,"title":10730,"id":10731,"appendix":10609},31,"Device-Generated Commands","device-generated-commands",{"index":10733,"title":10734,"id":10735,"appendix":10609},32,"Sparse Resources","sparsememory",{"index":10737,"title":10738,"id":10739,"appendix":10609},33,"Window System Integration (WSI)","wsi",{"index":10741,"title":10742,"id":10743,"appendix":10609},34,"Deferred Host Operations","deferred-host-operations",{"index":10745,"title":10746,"id":10747,"appendix":10609},35,"Private Data","private-data",{"index":10749,"title":10750,"id":10751,"appendix":10609},36,"Acceleration Structures","acceleration-structure",{"index":10753,"title":10754,"id":10755,"appendix":10609},37,"Micromap","micromap",{"index":10757,"title":4,"id":13,"appendix":10609},38,{"index":10759,"title":10760,"id":10761,"appendix":10609},39,"Ray Tracing","ray-tracing",{"index":10763,"title":10764,"id":10765,"appendix":10609},40,"Memory Decompression","memory-decompression",{"index":10767,"title":10768,"id":10769,"appendix":10609},41,"Video Coding","video-coding",{"index":10771,"title":10772,"id":10773,"appendix":10609},42,"Optical Flow","opticalflow",{"index":10775,"title":10776,"id":10777,"appendix":10609},43,"Execution Graphs","executiongraphs",{"index":10779,"title":10780,"id":10781,"appendix":10609},44,"Extending Vulkan","extendingvulkan",{"index":10783,"title":10784,"id":10785,"appendix":10609},45,"Features","features",{"index":10787,"title":10788,"id":10789,"appendix":10609},46,"Limits","limits",{"index":10791,"title":10792,"id":10793,"appendix":10609},47,"Formats","formats",{"index":10795,"title":10796,"id":10797,"appendix":10609},48,"Additional Capabilities","capabilities",{"index":10799,"title":10800,"id":10801,"appendix":10609},49,"Debugging","debugging",{"index":10606,"title":10803,"id":10804,"appendix":10805},"Vulkan Environment for SPIR-V","spirvenv",true,{"index":10611,"title":10807,"id":10808,"appendix":10805},"Memory Model","memory-model",{"index":10579,"title":10810,"id":10811,"appendix":10805},"Compressed Image Formats","compressed_image_formats",{"index":10584,"title":10813,"id":10814,"appendix":10805},"Core Revisions (Informative)","versions",{"index":10621,"title":10816,"id":10817,"appendix":10805},"Layers & Extensions (Informative)","extensions",{"index":10625,"title":10819,"id":10820,"appendix":10805},"API Boilerplate","boilerplate",{"index":10629,"title":10822,"id":10823,"appendix":10805},"Invariance","invariance",{"index":10633,"title":10825,"id":10826,"appendix":10805},"Lexicon","lexicon",{"index":10637,"title":10828,"id":10829,"appendix":10805},"Credits (Informative)","credits",[10831,10839,10843,10848,10852,10857,10860,10863,10866,10870,10874,10877,10880,10883,10885,10887,10890,10893,10897,10899,10903,10905,10908,10910,10913,10921,10925,10931,10935,10940,10942,10946,10952,10958,10964,10966,10969,10975,10978,10982,10988,10992,10996,11001,11005,11008,11011,11017,11020,11023,11027,11031,11035,11038,11040,11044,11049,11055,11058,11062,11065,11071,11074,11078,11081,11085,11088,11092,11095,11100,11104,11107,11112,11115,11118,11121,11125,11130,11135,11139,11143,11147,11151,11155,11159,11163,11166,11169,11173,11176,11179,11182,11186,11191,11195,11198,11202,11207,11211,11216,11219,11222,11227,11232,11236,11239,11243,11248,11251,11256,11261,11264,11267,11271,11275,11279,11284,11288,11291,11296,11300,11303,11307,11311,11315,11318,11320,11324,11327,11330,11333,11336,11339,11342,11345,11348,11351,11355,11359,11362,11365,11368,11371,11374,11377,11381,11385,11389,11392,11396,11399,11402,11405,11407,11411,11416,11420,11424,11426,11430,11433,11440,11444,11448,11452,11458,11461,11465,11469,11472,11475,11479,11484,11490,11494,11496,11501,11504,11509,11513,11518,11522,11526,11528,11531,11534,11536,11541,11544,11547,11552,11556,11560,11565,11569,11573,11575,11577,11580,11582,11585,11588,11592,11596,11598,11602,11605,11609,11612,11614,11617,11621,11623,11627,11630,11633,11636,11640,11643,11646,11648,11651,11653,11656,11660,11663,11665,11667,11669,11671,11675,11677,11680,11685,11689,11692,11694,11697,11699,11703,11706,11709,11712,11716,11719,11724,11728,11731,11735,11738,11741,11745,11749,11751,11756,11759,11763,11766,11769,11772,11774,11777,11781,11784,11788,11791,11795,11799,11802,11805,11808,11811,11815,11817,11820,11822,11827,11828,11832,11835,11838,11841,11844,11846,11850,11853,11856,11859,11863,11865,11867,11871,11873,11876,11880,11884,11886,11890,11893,11896,11899,11902,11906,11911,11916,11920,11926,11930,11933,11937,11941,11944,11948,11952,11955,11959,11962,11967,11971,11973,11979,11982,11985,11988,11992,11995,11999,12003,12007,12009,12012,12014,12017,12019,12021,12024,12027,12030,12033,12036,12039,12041,12045,12049,12053,12057,12060,12063,12067,12070,12074,12076,12080,12084,12087,12090,12093,12096,12099,12102,12105,12108,12111,12114,12117,12120,12123,12126,12130,12133,12137,12141,12144,12147,12150,12153,12156,12159,12163,12166,12169,12175,12179,12183,12187],{"number":10832,"type":10833,"author":10834,"provisional":10805,"depends":10835,"platform":10836,"contact":10837,"extension":10838,"proposal":10805},135,"device","AMD","(((VK_KHR_get_physical_device_properties2,VK_VERSION_1_1)+VK_KHR_synchronization2),VK_VERSION_1_3)+VK_KHR_pipeline_library+VK_KHR_spirv_1_4","provisional","Tobias Hector @tobski","VK_AMDX_shader_enqueue",{"number":10840,"type":10833,"author":10834,"provisional":10609,"contact":10841,"extension":10842,"proposal":10805},477,"Stu Smith","VK_AMD_anti_lag",{"number":10844,"type":10833,"author":10834,"provisional":10609,"specialuse":10845,"contact":10846,"extension":10847,"proposal":10609},180,"devtools","Daniel Rakos @drakos-amd","VK_AMD_buffer_marker",{"number":10849,"type":10833,"author":10834,"provisional":10609,"depends":10850,"contact":10837,"extension":10851,"proposal":10609},230,"VK_KHR_get_physical_device_properties2,VK_VERSION_1_1","VK_AMD_device_coherent_memory",{"number":10853,"type":10833,"author":10834,"provisional":10609,"depends":10854,"contact":10855,"extension":10856,"proposal":10609},214,"(VK_KHR_get_physical_device_properties2,VK_VERSION_1_1)+VK_KHR_get_surface_capabilities2+VK_KHR_swapchain","Matthaeus G. Chajdas @anteru","VK_AMD_display_native_hdr",{"number":10741,"type":10833,"author":10834,"promotedto":10858,"provisional":10609,"contact":10846,"extension":10859,"proposal":10609},"VK_KHR_draw_indirect_count","VK_AMD_draw_indirect_count",{"number":10709,"type":10833,"author":10834,"provisional":10609,"contact":10861,"extension":10862,"proposal":10609},"Dominik Witczak @dominikwitczakamd","VK_AMD_gcn_shader",{"number":10753,"type":10833,"author":10834,"deprecatedby":10864,"provisional":10609,"contact":10861,"extension":10865,"proposal":10609},"VK_KHR_shader_float16_int8","VK_AMD_gpu_shader_half_float",{"number":10867,"type":10833,"author":10834,"deprecatedby":10864,"provisional":10609,"contact":10868,"extension":10869,"proposal":10609},133,"Qun Lin @linqun","VK_AMD_gpu_shader_int16",{"number":10871,"type":10833,"author":10834,"provisional":10609,"contact":10872,"extension":10873,"proposal":10609},190,"Martin Dinkov @mdinkov","VK_AMD_memory_overallocation_behavior",{"number":10875,"type":10833,"author":10834,"provisional":10609,"contact":10855,"extension":10876,"proposal":10609},137,"VK_AMD_mixed_attachment_samples",{"number":10749,"type":10833,"author":10834,"obsoletedby":10878,"provisional":10609,"contact":10855,"extension":10879,"proposal":10609},"VK_KHR_maintenance1","VK_AMD_negative_viewport_height",{"number":10881,"type":10833,"author":10834,"provisional":10609,"contact":10855,"extension":10882,"proposal":10609},184,"VK_AMD_pipeline_compiler_control",{"number":10681,"type":10833,"author":10834,"provisional":10609,"contact":10846,"extension":10884,"proposal":10609},"VK_AMD_rasterization_order",{"number":10757,"type":10833,"author":10834,"provisional":10609,"contact":10861,"extension":10886,"proposal":10609},"VK_AMD_shader_ballot",{"number":10888,"type":10833,"author":10834,"provisional":10609,"depends":10850,"contact":10872,"extension":10889,"proposal":10609},186,"VK_AMD_shader_core_properties",{"number":10891,"type":10833,"author":10834,"provisional":10609,"depends":10889,"contact":10855,"extension":10892,"proposal":10609},228,"VK_AMD_shader_core_properties2",{"number":10894,"type":10833,"author":10895,"provisional":10609,"depends":10850,"contact":10837,"extension":10896,"proposal":10805},322,"EXT","VK_AMD_shader_early_and_late_fragment_tests",{"number":10693,"type":10833,"author":10834,"provisional":10609,"contact":10868,"extension":10898,"proposal":10609},"VK_AMD_shader_explicit_vertex_parameter",{"number":10900,"type":10833,"author":10834,"provisional":10609,"contact":10901,"extension":10902,"proposal":10609},138,"Aaron Hagan @AaronHaganAMD","VK_AMD_shader_fragment_mask",{"number":10791,"type":10833,"author":10834,"provisional":10609,"contact":10861,"extension":10904,"proposal":10609},"VK_AMD_shader_image_load_store_lod",{"number":10775,"type":10833,"author":10834,"provisional":10609,"specialuse":10845,"contact":10906,"extension":10907,"proposal":10609},"Jaakko Konttinen @jaakkoamd","VK_AMD_shader_info",{"number":10689,"type":10833,"author":10834,"provisional":10609,"contact":10868,"extension":10909,"proposal":10609},"VK_AMD_shader_trinary_minmax",{"number":10771,"type":10833,"author":10834,"provisional":10609,"depends":10850,"contact":10911,"extension":10912,"proposal":10609},"Rex Xu @amdrexu","VK_AMD_texture_gather_bias_lod",{"number":10914,"type":10833,"author":10915,"provisional":10609,"depends":10916,"platform":10917,"specialuse":10918,"contact":10919,"extension":10920,"proposal":10805},469,"ANDROID","VK_ANDROID_external_memory_android_hardware_buffer","android","glemulation","Chris Forbes @chrisforbes","VK_ANDROID_external_format_resolve",{"number":10922,"type":10833,"author":10915,"provisional":10609,"depends":10923,"platform":10917,"contact":10924,"extension":10916,"proposal":10609},130,"((VK_KHR_sampler_ycbcr_conversion+VK_KHR_external_memory+VK_KHR_dedicated_allocation),VK_VERSION_1_1)+VK_EXT_queue_family_foreign","Jesse Hall @critsec",{"number":10926,"type":10833,"author":10927,"promotedto":10928,"provisional":10609,"depends":10850,"contact":10929,"extension":10930,"proposal":10609},343,"ARM","VK_EXT_rasterization_order_attachment_access","Jan-Harald Fredriksen @janharaldfredriksen-arm","VK_ARM_rasterization_order_attachment_access",{"number":10932,"type":10833,"author":10927,"provisional":10609,"depends":10933,"contact":10929,"extension":10934,"proposal":10805},425,"((VK_KHR_get_physical_device_properties2,VK_VERSION_1_1)+VK_KHR_synchronization2),VK_VERSION_1_3","VK_ARM_render_pass_striped",{"number":10936,"type":10833,"author":10927,"provisional":10609,"depends":10937,"contact":10938,"extension":10939,"proposal":10609},418,"VK_ARM_shader_core_builtins","Kevin Petit @kpet","VK_ARM_scheduling_controls",{"number":10941,"type":10833,"author":10927,"provisional":10609,"depends":10850,"contact":10938,"extension":10937,"proposal":10609},498,{"number":10943,"type":10833,"author":10927,"provisional":10609,"depends":10944,"contact":10929,"extension":10945,"proposal":10609},416,"VK_VERSION_1_1","VK_ARM_shader_core_properties",{"number":10947,"type":10833,"author":10895,"promotedto":10948,"provisional":10609,"depends":10850,"ratified":10949,"contact":10950,"extension":10951,"proposal":10609},341,"VK_VERSION_1_3","vulkansc","Joshua Ashton @Joshua-Ashton","VK_EXT_4444_formats",{"number":10953,"type":10954,"author":10895,"provisional":10609,"depends":10955,"contact":10956,"extension":10957,"proposal":10609},286,"instance","VK_EXT_direct_mode_display","Drew DeVault sir@cmpwn.com","VK_EXT_acquire_drm_display",{"number":10959,"type":10954,"author":10960,"provisional":10609,"depends":10955,"platform":10961,"contact":10962,"extension":10963,"proposal":10609},90,"NV","xlib_xrandr","James Jones @cubanismo","VK_EXT_acquire_xlib_display",{"extension":10965,"proposal":10609},"VK_EXT_application_parameters",{"number":10967,"type":10833,"author":10927,"provisional":10609,"depends":10850,"contact":10929,"extension":10968,"proposal":10609},68,"VK_EXT_astc_decode_mode",{"number":10970,"type":10833,"author":10895,"provisional":10609,"depends":10971,"ratified":10972,"contact":10973,"extension":10974,"proposal":10805},525,"(VK_KHR_get_physical_device_properties2,VK_VERSION_1_1)+VK_EXT_attachment_feedback_loop_layout","vulkan","Mike Blumenkrantz @zmike","VK_EXT_attachment_feedback_loop_dynamic_state",{"number":10976,"type":10833,"author":10895,"provisional":10609,"depends":10850,"ratified":10972,"contact":10950,"extension":10977,"proposal":10805},340,"VK_EXT_attachment_feedback_loop_layout",{"number":10979,"type":10833,"author":10960,"provisional":10609,"depends":10850,"ratified":10972,"contact":10980,"extension":10981,"proposal":10609},149,"Jeff Bolz @jeffbolznv","VK_EXT_blend_operation_advanced",{"number":10983,"type":10833,"author":10895,"provisional":10609,"depends":10984,"specialuse":10985,"contact":10986,"extension":10987,"proposal":10609},412,"VK_EXT_custom_border_color","glemulation,d3demulation","Piers Daniell @pdaniell-nv","VK_EXT_border_color_swizzle",{"number":10989,"type":10833,"author":10960,"deprecatedby":10990,"provisional":10609,"depends":10850,"contact":10980,"extension":10991,"proposal":10609},245,"VK_KHR_buffer_device_address","VK_EXT_buffer_device_address",{"number":10993,"type":10833,"author":10895,"promotedto":10994,"provisional":10609,"depends":10850,"contact":10846,"extension":10995,"proposal":10805},185,"VK_KHR_calibrated_timestamps","VK_EXT_calibrated_timestamps",{"number":10997,"type":10833,"author":10895,"provisional":10609,"depends":10850,"ratified":10998,"contact":10999,"extension":11000,"proposal":10609},382,"vulkan,vulkansc","Sharif Elcott @selcott","VK_EXT_color_write_enable",{"number":11002,"type":10833,"author":10960,"provisional":10609,"depends":10850,"contact":11003,"extension":11004,"proposal":10609},82,"Vikram Kushwaha @vkushwaha","VK_EXT_conditional_rendering",{"number":11006,"type":10833,"author":10960,"provisional":10609,"depends":10850,"ratified":10972,"contact":10986,"extension":11007,"proposal":10609},102,"VK_EXT_conservative_rasterization",{"number":11009,"type":10833,"author":10895,"provisional":10609,"depends":10850,"ratified":10998,"specialuse":10985,"contact":11010,"extension":10984,"proposal":10609},288,"Liam Middlebrook @liam-middlebrook",{"number":10697,"type":10833,"author":11012,"promotedto":11013,"provisional":10609,"depends":11014,"specialuse":10801,"contact":11015,"extension":11016,"proposal":10609},"Baldur Karlsson","VK_EXT_debug_utils","VK_EXT_debug_report","Baldur Karlsson @baldurk","VK_EXT_debug_marker",{"number":10653,"type":10954,"author":11018,"deprecatedby":11013,"provisional":10609,"specialuse":10801,"contact":11019,"extension":11014,"proposal":10609},"GOOGLE","Courtney Goeltzenleuchter @courtney-g",{"number":11021,"type":10954,"author":10895,"provisional":10609,"specialuse":10801,"contact":11022,"extension":11013,"proposal":10609},129,"Mark Young @marky-lunarg",{"number":11024,"type":10833,"author":10895,"provisional":10609,"depends":10850,"ratified":10972,"specialuse":11025,"contact":10950,"extension":11026,"proposal":10805},284,"d3demulation","VK_EXT_depth_bias_control",{"number":11028,"type":10833,"author":10895,"provisional":10609,"depends":10850,"contact":11029,"extension":11030,"proposal":10609},422,"Graeme Leese @gnl21","VK_EXT_depth_clamp_zero_one",{"number":11032,"type":10833,"author":10895,"provisional":10609,"depends":10850,"ratified":10972,"specialuse":10918,"contact":11033,"extension":11034,"proposal":10609},356,"Shahbaz Youssefi @syoussefi","VK_EXT_depth_clip_control",{"number":11036,"type":10833,"author":10895,"provisional":10609,"depends":10850,"ratified":10998,"specialuse":11025,"contact":10986,"extension":11037,"proposal":10609},103,"VK_EXT_depth_clip_enable",{"number":10661,"type":10833,"author":10960,"provisional":10609,"ratified":10998,"contact":10986,"extension":11039,"proposal":10609},"VK_EXT_depth_range_unrestricted",{"number":11041,"type":10833,"author":10895,"provisional":10609,"depends":11042,"contact":10837,"extension":11043,"proposal":10805},317,"((((VK_KHR_get_physical_device_properties2,VK_VERSION_1_1)+VK_KHR_buffer_device_address+VK_EXT_descriptor_indexing),VK_VERSION_1_2)+VK_KHR_synchronization2),VK_VERSION_1_3","VK_EXT_descriptor_buffer",{"number":11045,"type":10833,"author":10960,"promotedto":11046,"provisional":10609,"depends":11047,"contact":10980,"extension":11048,"proposal":10609},162,"VK_VERSION_1_2","(VK_KHR_get_physical_device_properties2+VK_KHR_maintenance3),VK_VERSION_1_1","VK_EXT_descriptor_indexing",{"number":11050,"type":10833,"author":10895,"provisional":10609,"depends":11051,"specialuse":11052,"contact":11053,"extension":11054,"proposal":10609},355,"(VK_KHR_get_physical_device_properties2,VK_VERSION_1_1)+VK_EXT_debug_utils","debugging,devtools","Ralph Potter gitlab:@r_potter","VK_EXT_device_address_binding_report",{"number":11056,"type":10833,"author":10895,"provisional":10609,"depends":10850,"contact":11053,"extension":11057,"proposal":10805},342,"VK_EXT_device_fault",{"number":11059,"type":10833,"author":10895,"provisional":10609,"depends":10850,"ratified":10972,"specialuse":10845,"contact":11060,"extension":11061,"proposal":10609},285,"Yiwei Zhang @zhangyiwei","VK_EXT_device_memory_report",{"number":11063,"type":10954,"author":10960,"provisional":10609,"depends":11064,"contact":10962,"extension":10955,"proposal":10609},89,"VK_KHR_display",{"number":11066,"type":10954,"author":10895,"provisional":10609,"depends":11067,"platform":11068,"contact":11069,"extension":11070,"proposal":10609},347,"VK_KHR_surface","directfb","Nicolas Caramelli @caramelli","VK_EXT_directfb_surface",{"number":11072,"type":10833,"author":10960,"provisional":10609,"depends":10850,"ratified":10998,"contact":10986,"extension":11073,"proposal":10609},100,"VK_EXT_discard_rectangles",{"number":11075,"type":10833,"author":10960,"provisional":10609,"depends":11076,"ratified":10972,"contact":10962,"extension":11077,"proposal":10609},92,"VK_EXT_display_surface_counter+VK_KHR_swapchain","VK_EXT_display_control",{"number":11079,"type":10954,"author":10960,"provisional":10609,"depends":11064,"ratified":10972,"contact":10962,"extension":11080,"proposal":10609},91,"VK_EXT_display_surface_counter",{"number":11082,"type":10833,"author":10895,"provisional":10609,"depends":11083,"ratified":10972,"contact":10986,"extension":11084,"proposal":10805},500,"((VK_KHR_get_physical_device_properties2,VK_VERSION_1_1)+VK_KHR_dynamic_rendering),VK_VERSION_1_3","VK_EXT_dynamic_rendering_unused_attachments",{"number":11086,"type":10833,"author":10895,"promotedto":10948,"provisional":10609,"depends":10850,"ratified":10949,"contact":10986,"extension":11087,"proposal":10609},268,"VK_EXT_extended_dynamic_state",{"number":11089,"type":10833,"author":10895,"promotedto":10948,"provisional":10609,"depends":10850,"ratified":10949,"contact":11090,"extension":11091,"proposal":10609},378,"Vikram Kushwaha @vkushwaha-nv","VK_EXT_extended_dynamic_state2",{"number":11093,"type":10833,"author":10960,"provisional":10609,"depends":10850,"ratified":10972,"contact":10986,"extension":11094,"proposal":10805},456,"VK_EXT_extended_dynamic_state3",{"number":11096,"type":10833,"author":10895,"provisional":10609,"depends":11097,"ratified":10972,"contact":11098,"extension":11099,"proposal":10805},454,"VK_KHR_external_memory,VK_VERSION_1_1","Lina Versace @versalinyaa","VK_EXT_external_memory_acquire_unmodified",{"number":11101,"type":10833,"author":10895,"provisional":10609,"depends":11102,"ratified":10998,"contact":11098,"extension":11103,"proposal":10609},126,"VK_KHR_external_memory_fd","VK_EXT_external_memory_dma_buf",{"number":11105,"type":10833,"author":10895,"provisional":10609,"depends":11097,"ratified":10998,"contact":10846,"extension":11106,"proposal":10609},179,"VK_EXT_external_memory_host",{"number":11108,"type":10833,"author":11109,"provisional":10609,"ratified":10972,"contact":11110,"extension":11111,"proposal":10609},171,"QCOM","Matthew Netsch @mnetsch","VK_EXT_filter_cubic",{"number":11113,"type":10833,"author":10895,"provisional":10609,"depends":10850,"contact":11110,"extension":11114,"proposal":10609},219,"VK_EXT_fragment_density_map",{"number":11116,"type":10833,"author":10895,"provisional":10609,"depends":11114,"contact":11110,"extension":11117,"proposal":10609},333,"VK_EXT_fragment_density_map2",{"number":11119,"type":10833,"author":10895,"provisional":10609,"depends":10850,"contact":10986,"extension":11120,"proposal":10609},252,"VK_EXT_fragment_shader_interlock",{"number":11122,"type":10833,"author":10895,"provisional":10609,"ratified":10972,"contact":11123,"extension":11124,"proposal":10805},376,"James Fitzpatrick @jamesfitzpatrick","VK_EXT_frame_boundary",{"number":11126,"type":10833,"author":10895,"provisional":10609,"depends":11127,"platform":11128,"ratified":10972,"contact":10962,"extension":11129,"proposal":10609},256,"(VK_KHR_get_physical_device_properties2,VK_VERSION_1_1)+VK_KHR_surface+VK_KHR_get_surface_capabilities2+VK_KHR_swapchain","win32","VK_EXT_full_screen_exclusive",{"number":11131,"type":10833,"author":10895,"promotedto":11132,"provisional":10609,"contact":11133,"extension":11134,"proposal":10609},175,"VK_KHR_global_priority","Andres Rodriguez @lostgoat","VK_EXT_global_priority",{"number":11136,"type":10833,"author":10895,"promotedto":11132,"provisional":10609,"depends":11137,"contact":11060,"extension":11138,"proposal":10609},389,"VK_EXT_global_priority+(VK_KHR_get_physical_device_properties2,VK_VERSION_1_1)","VK_EXT_global_priority_query",{"number":11140,"type":10833,"author":10834,"provisional":10609,"depends":11141,"contact":10837,"extension":11142,"proposal":10805},321,"(VK_KHR_get_physical_device_properties2,VK_VERSION_1_1)+VK_KHR_pipeline_library","VK_EXT_graphics_pipeline_library",{"number":11144,"type":10833,"author":11018,"provisional":10609,"depends":11145,"ratified":10998,"contact":11019,"extension":11146,"proposal":10609},106,"VK_KHR_swapchain","VK_EXT_hdr_metadata",{"number":11148,"type":10954,"author":10895,"provisional":10609,"depends":11067,"contact":11149,"extension":11150,"proposal":10609},257,"Lisa Wu @chengtianww","VK_EXT_headless_surface",{"number":11152,"type":10833,"author":10895,"provisional":10609,"depends":11153,"ratified":10972,"contact":11033,"extension":11154,"proposal":10805},271,"((VK_KHR_get_physical_device_properties2,VK_VERSION_1_1)+VK_KHR_copy_commands2+VK_KHR_format_feature_flags2),VK_VERSION_1_3","VK_EXT_host_image_copy",{"number":11156,"type":10833,"author":10895,"promotedto":11046,"provisional":10609,"depends":10850,"contact":11157,"extension":11158,"proposal":10609},262,"Bas Nieuwenhuizen @BNieuwenhuizen","VK_EXT_host_query_reset",{"number":11160,"type":10833,"author":10895,"provisional":10609,"depends":11161,"specialuse":10918,"contact":10973,"extension":11162,"proposal":10609},394,"(VK_KHR_maintenance1+VK_KHR_get_physical_device_properties2),VK_VERSION_1_1","VK_EXT_image_2d_view_of_3d",{"number":11164,"type":10833,"author":10895,"provisional":10609,"depends":10850,"contact":10929,"extension":11165,"proposal":10805},339,"VK_EXT_image_compression_control",{"number":11167,"type":10833,"author":10895,"provisional":10609,"depends":11165,"contact":10929,"extension":11168,"proposal":10609},438,"VK_EXT_image_compression_control_swapchain",{"number":11170,"type":10833,"author":10895,"provisional":10609,"depends":11171,"ratified":10972,"contact":11098,"extension":11172,"proposal":10609},159,"(((VK_KHR_bind_memory2+VK_KHR_get_physical_device_properties2+VK_KHR_sampler_ycbcr_conversion),VK_VERSION_1_1)+VK_KHR_image_format_list),VK_VERSION_1_2","VK_EXT_image_drm_format_modifier",{"number":11174,"type":10833,"author":10895,"promotedto":10948,"provisional":10609,"depends":10850,"ratified":10949,"contact":11029,"extension":11175,"proposal":10609},336,"VK_EXT_image_robustness",{"number":11177,"type":10833,"author":10895,"provisional":10609,"depends":11161,"specialuse":11025,"contact":10973,"extension":11178,"proposal":10805},419,"VK_EXT_image_sliced_view_of_3d",{"number":11180,"type":10833,"author":10895,"provisional":10609,"depends":10850,"contact":10950,"extension":11181,"proposal":10609},392,"VK_EXT_image_view_min_lod",{"number":11183,"type":10833,"author":10895,"promotedto":11184,"provisional":10609,"depends":10850,"contact":10986,"extension":11185,"proposal":10609},266,"VK_KHR_index_type_uint8","VK_EXT_index_type_uint8",{"number":11187,"type":10833,"author":10895,"promotedto":10948,"provisional":10609,"depends":11188,"contact":11189,"extension":11190,"proposal":10609},139,"(VK_KHR_get_physical_device_properties2+VK_KHR_maintenance1),VK_VERSION_1_1","Daniel Rakos @aqnuep","VK_EXT_inline_uniform_block",{"number":11192,"type":10954,"author":10895,"provisional":10609,"ratified":10972,"contact":11193,"extension":11194,"proposal":10805},497,"Christophe Riccio @christophe","VK_EXT_layer_settings",{"number":11196,"type":10833,"author":10895,"provisional":10609,"depends":10850,"specialuse":10918,"contact":11033,"extension":11197,"proposal":10805},466,"VK_EXT_legacy_dithering",{"number":11199,"type":10833,"author":10895,"provisional":10609,"depends":11200,"ratified":10972,"specialuse":10918,"contact":10973,"extension":11201,"proposal":10805},496,"VK_EXT_vertex_input_dynamic_state","VK_EXT_legacy_vertex_attributes",{"number":11203,"type":10833,"author":10895,"promotedto":11204,"provisional":10609,"depends":10850,"specialuse":11205,"contact":10980,"extension":11206,"proposal":10609},260,"VK_KHR_line_rasterization","cadsupport","VK_EXT_line_rasterization",{"number":11208,"type":10833,"author":10895,"promotedto":11209,"provisional":10609,"ratified":10972,"contact":11033,"extension":11210,"proposal":10609},401,"VK_KHR_load_store_op_none","VK_EXT_load_store_op_none",{"number":11212,"type":10833,"author":10895,"provisional":10609,"depends":11213,"ratified":10972,"contact":11214,"extension":11215,"proposal":10805},273,"VK_KHR_map_memory2","Faith Ekstrand @gfxstrand","VK_EXT_map_memory_placed",{"number":11217,"type":10833,"author":10895,"provisional":10609,"depends":10850,"ratified":10972,"contact":10980,"extension":11218,"proposal":10609},238,"VK_EXT_memory_budget",{"number":11220,"type":10833,"author":10895,"provisional":10609,"depends":10850,"ratified":10972,"contact":10980,"extension":11221,"proposal":10609},239,"VK_EXT_memory_priority",{"number":11223,"type":10833,"author":10895,"provisional":10609,"depends":11224,"contact":11225,"extension":11226,"proposal":10805},329,"VK_KHR_spirv_1_4","Christoph Kubisch @pixeljetstream","VK_EXT_mesh_shader",{"number":11228,"type":10833,"author":10895,"provisional":10609,"platform":11229,"contact":11230,"extension":11231,"proposal":10805},312,"metal","Bill Hollings @billhollings","VK_EXT_metal_objects",{"number":11233,"type":10954,"author":10895,"provisional":10609,"depends":11067,"platform":11229,"contact":11234,"extension":11235,"proposal":10609},218,"Dzmitry Malyshau @kvark","VK_EXT_metal_surface",{"number":11237,"type":10833,"author":10895,"provisional":10609,"depends":10850,"contact":10973,"extension":11238,"proposal":10609},393,"VK_EXT_multi_draw",{"number":11240,"type":10833,"author":10895,"provisional":10609,"depends":11241,"contact":11033,"extension":11242,"proposal":10805},377,"(VK_KHR_create_renderpass2+VK_KHR_depth_stencil_resolve),VK_VERSION_1_2","VK_EXT_multisampled_render_to_single_sampled",{"number":11244,"type":10833,"author":10895,"provisional":10609,"depends":11245,"specialuse":11025,"contact":11246,"extension":11247,"proposal":10805},495,"VK_KHR_maintenance3","Joshua Ashton @Joshua-Ashton,Hans-Kristian Arntzen @HansKristian-Work","VK_EXT_mutable_descriptor_type",{"number":11249,"type":10833,"author":10895,"provisional":10609,"depends":10850,"ratified":10972,"contact":10986,"extension":11250,"proposal":10609},452,"VK_EXT_nested_command_buffer",{"number":11252,"type":10833,"author":10895,"provisional":10609,"depends":10850,"specialuse":11253,"contact":11254,"extension":11255,"proposal":10805},423,"d3demulation,glemulation","Georg Lehmann @DadSchoorse","VK_EXT_non_seamless_cube_map",{"number":11257,"type":10833,"author":10895,"provisional":10609,"depends":11258,"ratified":10972,"contact":11259,"extension":11260,"proposal":10805},397,"VK_KHR_acceleration_structure+(VK_KHR_synchronization2,VK_VERSION_1_3)","Christoph Kubisch @pixeljetstream, Eric Werness","VK_EXT_opacity_micromap",{"number":11262,"type":10833,"author":10895,"provisional":10609,"depends":11221,"contact":10986,"extension":11263,"proposal":10609},413,"VK_EXT_pageable_device_local_memory",{"number":11265,"type":10833,"author":10895,"provisional":10609,"depends":10850,"ratified":10998,"contact":10855,"extension":11266,"proposal":10609},213,"VK_EXT_pci_bus_info",{"number":11268,"type":10833,"author":10895,"provisional":10609,"depends":10850,"contact":11269,"extension":11270,"proposal":10609},354,"Simon Ser @emersion","VK_EXT_physical_device_drm",{"number":11272,"type":10833,"author":10834,"promotedto":10948,"provisional":10609,"depends":10850,"contact":11273,"extension":11274,"proposal":10609},298,"Gregory Grebe @grgrebe_amd","VK_EXT_pipeline_creation_cache_control",{"number":11276,"type":10833,"author":11018,"promotedto":10948,"provisional":10609,"specialuse":10845,"contact":11277,"extension":11278,"proposal":10609},193,"Jean-Francois Roy @jfroy","VK_EXT_pipeline_creation_feedback",{"number":11280,"type":10833,"author":10895,"provisional":10609,"depends":11281,"contact":11282,"extension":11283,"proposal":10805},499,"VK_KHR_ray_tracing_pipeline+VK_KHR_pipeline_library","Hans-Kristian Arntzen @HansKristian-Work","VK_EXT_pipeline_library_group_handles",{"number":11285,"type":10833,"author":10895,"provisional":10609,"depends":10850,"contact":11286,"extension":11287,"proposal":10609},373,"Mukund Keshava @mkeshavanv","VK_EXT_pipeline_properties",{"number":11289,"type":10833,"author":10895,"provisional":10609,"depends":10850,"contact":11033,"extension":11290,"proposal":10805},467,"VK_EXT_pipeline_protected_access",{"number":11292,"type":10833,"author":11293,"provisional":10609,"depends":10850,"contact":11294,"extension":11295,"proposal":10609},69,"IMG","Jarred Davies","VK_EXT_pipeline_robustness",{"number":11297,"type":10833,"author":10960,"provisional":10609,"ratified":10972,"contact":11298,"extension":11299,"proposal":10609},156,"Daniel Koch @dgkoch","VK_EXT_post_depth_coverage",{"number":11301,"type":10833,"author":10895,"provisional":10609,"depends":10850,"ratified":10972,"specialuse":10918,"contact":11033,"extension":11302,"proposal":10609},357,"VK_EXT_primitive_topology_list_restart",{"number":11304,"type":10833,"author":10895,"provisional":10609,"depends":11305,"specialuse":10918,"contact":11033,"extension":11306,"proposal":10805},383,"VK_EXT_transform_feedback","VK_EXT_primitives_generated_query",{"number":11308,"type":10833,"author":10960,"promotedto":10948,"provisional":10609,"depends":10850,"contact":11309,"extension":11310,"proposal":10609},296,"Matthew Rusch @mattruschnv","VK_EXT_private_data",{"number":11312,"type":10833,"author":10895,"provisional":10609,"depends":10850,"ratified":10972,"specialuse":10918,"contact":11313,"extension":11314,"proposal":10609},255,"Jesse Hall @jessehall","VK_EXT_provoking_vertex",{"number":11316,"type":10833,"author":10895,"provisional":10609,"depends":11097,"ratified":10998,"contact":11098,"extension":11317,"proposal":10609},127,"VK_EXT_queue_family_foreign",{"number":11319,"type":10833,"author":10927,"provisional":10609,"depends":10850,"contact":10929,"extension":10928,"proposal":10805},464,{"number":11321,"type":10833,"author":10895,"provisional":10609,"depends":11322,"contact":10929,"extension":11323,"proposal":10609},345,"VK_KHR_sampler_ycbcr_conversion,VK_VERSION_1_1","VK_EXT_rgba10x6_formats",{"number":11325,"type":10833,"author":10895,"provisional":10609,"depends":10850,"ratified":10998,"contact":11010,"extension":11326,"proposal":10609},287,"VK_EXT_robustness2",{"number":11328,"type":10833,"author":10834,"provisional":10609,"depends":10850,"ratified":10998,"contact":10846,"extension":11329,"proposal":10609},144,"VK_EXT_sample_locations",{"number":11331,"type":10833,"author":10960,"promotedto":11046,"provisional":10609,"depends":10850,"contact":10980,"extension":11332,"proposal":10609},131,"VK_EXT_sampler_filter_minmax",{"number":11334,"type":10833,"author":10895,"promotedto":11046,"provisional":10609,"depends":10850,"contact":10837,"extension":11335,"proposal":10609},222,"VK_EXT_scalar_block_layout",{"number":11337,"type":10833,"author":10895,"promotedto":11046,"provisional":10609,"contact":10846,"extension":11338,"proposal":10609},247,"VK_EXT_separate_stencil_usage",{"number":11340,"type":10833,"author":10960,"provisional":10609,"depends":10850,"ratified":10998,"contact":11090,"extension":11341,"proposal":10609},261,"VK_EXT_shader_atomic_float",{"number":11343,"type":10833,"author":10895,"provisional":10609,"depends":11341,"ratified":10972,"contact":11214,"extension":11344,"proposal":10609},274,"VK_EXT_shader_atomic_float2",{"number":11346,"type":10833,"author":10895,"promotedto":10948,"provisional":10609,"depends":10850,"ratified":10949,"contact":10980,"extension":11347,"proposal":10609},277,"VK_EXT_shader_demote_to_helper_invocation",{"number":11349,"type":10833,"author":10895,"provisional":10609,"depends":10850,"ratified":10972,"contact":10837,"extension":11350,"proposal":10609},235,"VK_EXT_shader_image_atomic_int64",{"number":11352,"type":10833,"author":10895,"provisional":10609,"depends":11353,"contact":11282,"extension":11354,"proposal":10805},463,"((VK_KHR_get_physical_device_properties2,VK_VERSION_1_1)+VK_EXT_pipeline_creation_cache_control),VK_VERSION_1_3","VK_EXT_shader_module_identifier",{"number":11356,"type":10833,"author":10895,"provisional":10609,"depends":11083,"ratified":10972,"contact":11357,"extension":11358,"proposal":10805},483,"Daniel Story @daniel-story","VK_EXT_shader_object",{"number":11360,"type":10833,"author":10895,"provisional":10609,"ratified":10972,"contact":10938,"extension":11361,"proposal":10805},565,"VK_EXT_shader_replicated_composites",{"number":11363,"type":10833,"author":10895,"provisional":10609,"ratified":10998,"contact":10861,"extension":11364,"proposal":10609},141,"VK_EXT_shader_stencil_export",{"number":11366,"type":10833,"author":10960,"deprecatedby":11046,"provisional":10609,"contact":11298,"extension":11367,"proposal":10609},65,"VK_EXT_shader_subgroup_ballot",{"number":11369,"type":10833,"author":10960,"deprecatedby":10944,"provisional":10609,"contact":11298,"extension":11370,"proposal":10609},66,"VK_EXT_shader_subgroup_vote",{"number":11372,"type":10833,"author":10895,"provisional":10609,"depends":10948,"ratified":10972,"contact":10929,"extension":11373,"proposal":10805},396,"VK_EXT_shader_tile_image",{"number":11375,"type":10833,"author":10960,"promotedto":11046,"provisional":10609,"contact":11298,"extension":11376,"proposal":10609},163,"VK_EXT_shader_viewport_index_layer",{"number":11378,"type":10833,"author":10895,"promotedto":10948,"provisional":10609,"depends":10944,"ratified":10949,"contact":11379,"extension":11380,"proposal":10609},226,"Neil Henning @sheredom","VK_EXT_subgroup_size_control",{"number":11382,"type":10833,"author":10895,"provisional":10609,"depends":10850,"contact":11383,"extension":11384,"proposal":10805},459,"Ting Wei @catweiting","VK_EXT_subpass_merge_feedback",{"number":11386,"type":10954,"author":10895,"provisional":10609,"depends":11387,"contact":11033,"extension":11388,"proposal":10805},275,"VK_KHR_surface+VK_KHR_get_surface_capabilities2","VK_EXT_surface_maintenance1",{"number":11390,"type":10954,"author":11018,"provisional":10609,"depends":11067,"contact":11019,"extension":11391,"proposal":10609},105,"VK_EXT_swapchain_colorspace",{"number":11393,"type":10833,"author":10895,"provisional":10609,"depends":11394,"contact":11033,"extension":11395,"proposal":10805},276,"VK_KHR_swapchain+VK_EXT_surface_maintenance1+(VK_KHR_get_physical_device_properties2,VK_VERSION_1_1)","VK_EXT_swapchain_maintenance1",{"number":11397,"type":10833,"author":10895,"promotedto":10948,"provisional":10609,"depends":10850,"ratified":10949,"contact":10980,"extension":11398,"proposal":10609},282,"VK_EXT_texel_buffer_alignment",{"number":11400,"type":10833,"author":10927,"promotedto":10948,"provisional":10609,"depends":10850,"ratified":10949,"contact":10929,"extension":11401,"proposal":10609},67,"VK_EXT_texture_compression_astc_hdr",{"number":11403,"type":10833,"author":10895,"promotedto":10948,"provisional":10609,"contact":10837,"extension":11404,"proposal":10609},246,"VK_EXT_tooling_info",{"number":10721,"type":10833,"author":10960,"provisional":10609,"depends":10850,"ratified":10972,"specialuse":11406,"contact":10986,"extension":11305,"proposal":10609},"glemulation,d3demulation,devtools",{"number":11408,"type":10833,"author":11018,"provisional":10609,"contact":11409,"extension":11410,"proposal":10609},161,"Cort Stratton @cdwfs","VK_EXT_validation_cache",{"number":11412,"type":10954,"author":11413,"deprecatedby":11194,"provisional":10609,"specialuse":10801,"contact":11414,"extension":11415,"proposal":10609},248,"LUNARG","Karl Schultz @karl-lunarg","VK_EXT_validation_features",{"number":11417,"type":10954,"author":11018,"deprecatedby":11194,"provisional":10609,"specialuse":10801,"contact":11418,"extension":11419,"proposal":10609},62,"Tobin Ehlis @tobine","VK_EXT_validation_flags",{"number":11421,"type":10833,"author":10960,"promotedto":11422,"provisional":10609,"depends":10850,"contact":11003,"extension":11423,"proposal":10609},191,"VK_KHR_vertex_attribute_divisor","VK_EXT_vertex_attribute_divisor",{"number":11425,"type":10833,"author":10895,"provisional":10609,"depends":10850,"ratified":10972,"contact":10986,"extension":11200,"proposal":10609},353,{"number":11427,"type":10833,"author":10895,"promotedto":10948,"provisional":10609,"depends":11322,"ratified":10949,"contact":11428,"extension":11429,"proposal":10609},331,"Tony Zlatinski @tzlatinski","VK_EXT_ycbcr_2plane_444_formats",{"number":11431,"type":10833,"author":10895,"provisional":10609,"depends":11322,"ratified":10998,"contact":10986,"extension":11432,"proposal":10609},253,"VK_EXT_ycbcr_image_arrays",{"number":11434,"type":10833,"author":11435,"provisional":10609,"depends":11436,"platform":11437,"contact":11438,"extension":11439,"proposal":10609},367,"FUCHSIA","VK_FUCHSIA_external_memory+(VK_KHR_sampler_ycbcr_conversion,VK_VERSION_1_1)","fuchsia","John Rosasco @rosasco","VK_FUCHSIA_buffer_collection",{"number":11441,"type":10833,"author":11435,"provisional":10609,"depends":11442,"platform":11437,"contact":11438,"extension":11443,"proposal":10609},365,"(VK_KHR_external_memory_capabilities+VK_KHR_external_memory),VK_VERSION_1_1","VK_FUCHSIA_external_memory",{"number":11445,"type":10833,"author":11435,"provisional":10609,"depends":11446,"platform":11437,"contact":11438,"extension":11447,"proposal":10609},366,"VK_KHR_external_semaphore_capabilities+VK_KHR_external_semaphore","VK_FUCHSIA_external_semaphore",{"number":11449,"type":10954,"author":11435,"provisional":10609,"depends":11067,"platform":11437,"contact":11450,"extension":11451,"proposal":10609},215,"Craig Stout @cdotstout","VK_FUCHSIA_imagepipe_surface",{"number":11453,"type":10833,"author":11454,"provisional":10609,"depends":11455,"platform":11456,"contact":11277,"extension":11457,"proposal":10609},192,"GGP","VK_KHR_swapchain+VK_GGP_stream_descriptor_surface","ggp","VK_GGP_frame_token",{"number":11459,"type":10954,"author":11454,"provisional":10609,"depends":11067,"platform":11456,"contact":11277,"extension":11460,"proposal":10609},50,"VK_GGP_stream_descriptor_surface",{"number":11462,"type":10833,"author":11018,"provisional":10609,"contact":11463,"extension":11464,"proposal":10609},225,"Hai Nguyen @chaoticbob","VK_GOOGLE_decorate_string",{"number":11466,"type":10833,"author":11018,"provisional":10609,"depends":11145,"contact":11467,"extension":11468,"proposal":10609},93,"Ian Elliott @ianelliottus","VK_GOOGLE_display_timing",{"number":11470,"type":10833,"author":11018,"provisional":10609,"contact":11463,"extension":11471,"proposal":10609},224,"VK_GOOGLE_hlsl_functionality1",{"number":11473,"type":10954,"author":11018,"provisional":10609,"depends":11067,"specialuse":10918,"contact":11033,"extension":11474,"proposal":10805},434,"VK_GOOGLE_surfaceless_query",{"number":11476,"type":10833,"author":11018,"provisional":10609,"contact":11477,"extension":11478,"proposal":10609},290,"Kaye Mason @chaleur","VK_GOOGLE_user_type",{"number":11480,"type":10833,"author":11481,"provisional":10609,"depends":10850,"contact":11482,"extension":11483,"proposal":10805},405,"HUAWEI","Yuchang Wang @richard_Wang2","VK_HUAWEI_cluster_culling_shader",{"number":11485,"type":10833,"author":11486,"provisional":10609,"depends":11487,"contact":11488,"extension":11489,"proposal":10805},371,"Huawei","VK_KHR_ray_tracing_pipeline+(VK_KHR_synchronization2,VK_VERSION_1_3)","Pan Gao @PanGao-h","VK_HUAWEI_invocation_mask",{"number":11491,"type":10833,"author":11481,"provisional":10609,"depends":11492,"contact":11488,"extension":11493,"proposal":10609},370,"((VK_KHR_create_renderpass2,VK_VERSION_1_2)+VK_KHR_synchronization2),VK_VERSION_1_3","VK_HUAWEI_subpass_shading",{"number":10669,"type":10833,"author":11293,"provisional":10609,"contact":10837,"extension":11495,"proposal":10609},"VK_IMG_filter_cubic",{"number":11497,"type":10833,"author":11293,"deprecatedby":11498,"provisional":10609,"contact":11499,"extension":11500,"proposal":10609},55,null,"Stuart Smith","VK_IMG_format_pvrtc",{"number":11502,"type":10833,"author":11293,"provisional":10609,"depends":10850,"specialuse":10918,"contact":11123,"extension":11503,"proposal":10609},111,"VK_IMG_relaxed_line_rasterization",{"number":11505,"type":10833,"author":11506,"provisional":10609,"specialuse":10845,"contact":11507,"extension":11508,"proposal":10609},211,"INTEL","Lionel Landwerlin @llandwerlin","VK_INTEL_performance_query",{"number":11510,"type":10833,"author":11506,"provisional":10609,"depends":10850,"contact":11511,"extension":11512,"proposal":10609},210,"Ian Romanick @ianromanick","VK_INTEL_shader_integer_functions2",{"number":11514,"type":10833,"author":11515,"promotedto":10944,"provisional":10609,"depends":11516,"ratified":10972,"contact":10929,"extension":11517,"proposal":10609},84,"KHR","(VK_KHR_get_physical_device_properties2+VK_KHR_storage_buffer_storage_class),VK_VERSION_1_1","VK_KHR_16bit_storage",{"number":11519,"type":10833,"author":11515,"promotedto":11046,"provisional":10609,"depends":11516,"ratified":10972,"contact":11520,"extension":11521,"proposal":10609},178,"Alexander Galazin @alegal-arm","VK_KHR_8bit_storage",{"number":11523,"type":10833,"author":11515,"provisional":10609,"depends":11524,"ratified":10972,"contact":11298,"extension":11525,"proposal":10609},151,"((VK_VERSION_1_1+VK_EXT_descriptor_indexing+VK_KHR_buffer_device_address),VK_VERSION_1_2)+VK_KHR_deferred_host_operations","VK_KHR_acceleration_structure",{"number":10641,"type":10954,"author":11515,"provisional":10609,"depends":11067,"platform":10917,"ratified":10972,"contact":10924,"extension":11527,"proposal":10609},"VK_KHR_android_surface",{"number":11529,"type":10833,"author":11515,"promotedto":10944,"provisional":10609,"ratified":10972,"contact":10837,"extension":11530,"proposal":10609},158,"VK_KHR_bind_memory2",{"number":11532,"type":10833,"author":11515,"promotedto":11046,"provisional":10609,"depends":11533,"ratified":10972,"contact":10980,"extension":10990,"proposal":10609},258,"(VK_KHR_get_physical_device_properties2+VK_KHR_device_group),VK_VERSION_1_1",{"number":11535,"type":10833,"author":11515,"provisional":10609,"depends":10850,"ratified":10998,"contact":11189,"extension":10994,"proposal":10609},544,{"number":11537,"type":10833,"author":11515,"provisional":10609,"depends":11538,"ratified":10972,"contact":11539,"extension":11540,"proposal":10805},512,"VK_KHR_get_physical_device_properties2","Jean-Noe Morissette @MagicPoncho","VK_KHR_compute_shader_derivatives",{"number":11542,"type":10833,"author":11515,"provisional":10609,"depends":10850,"ratified":10972,"contact":10938,"extension":11543,"proposal":10805},507,"VK_KHR_cooperative_matrix",{"number":11545,"type":10833,"author":11515,"promotedto":10948,"provisional":10609,"depends":10850,"ratified":10998,"contact":11110,"extension":11546,"proposal":10609},338,"VK_KHR_copy_commands2",{"number":11548,"type":10833,"author":11515,"promotedto":11046,"provisional":10609,"depends":11549,"ratified":10972,"contact":11550,"extension":11551,"proposal":10609},110,"(VK_KHR_multiview+VK_KHR_maintenance2),VK_VERSION_1_1","Tobias Hector @tobias","VK_KHR_create_renderpass2",{"number":11553,"type":10833,"author":11515,"promotedto":10944,"provisional":10609,"depends":11554,"ratified":10972,"contact":10962,"extension":11555,"proposal":10609},128,"VK_KHR_get_memory_requirements2,VK_VERSION_1_1","VK_KHR_dedicated_allocation",{"number":11557,"type":10833,"author":11515,"provisional":10609,"ratified":10972,"contact":11558,"extension":11559,"proposal":10609},269,"Josh Barczak @jbarczak","VK_KHR_deferred_host_operations",{"number":11561,"type":10833,"author":11515,"promotedto":11046,"provisional":10609,"depends":11562,"ratified":10972,"contact":11563,"extension":11564,"proposal":10609},200,"VK_KHR_create_renderpass2,VK_VERSION_1_2","Jan-Harald Fredriksen @janharald","VK_KHR_depth_stencil_resolve",{"number":11566,"type":10833,"author":11515,"promotedto":10944,"provisional":10609,"ratified":10972,"contact":11567,"extension":11568,"proposal":10609},86,"Markus Tavenrath @mtavenrath","VK_KHR_descriptor_update_template",{"number":11570,"type":10833,"author":11515,"promotedto":10944,"provisional":10609,"depends":11571,"ratified":10972,"contact":10980,"extension":11572,"proposal":10609},61,"VK_KHR_device_group_creation","VK_KHR_device_group",{"number":11574,"type":10954,"author":11515,"promotedto":10944,"provisional":10609,"ratified":10972,"contact":10980,"extension":11571,"proposal":10609},71,{"number":10584,"type":10954,"author":11515,"provisional":10609,"depends":11067,"ratified":10998,"contact":11576,"extension":11064,"proposal":10609},"James Jones @cubanismo,Norbert Nopper @FslNopper",{"number":10621,"type":10833,"author":11515,"provisional":10609,"depends":11578,"ratified":10998,"contact":10962,"extension":11579,"proposal":10609},"VK_KHR_swapchain+VK_KHR_display","VK_KHR_display_swapchain",{"number":11581,"type":10833,"author":11515,"promotedto":11046,"provisional":10609,"ratified":10972,"contact":10986,"extension":10858,"proposal":10609},170,{"number":11583,"type":10833,"author":11515,"promotedto":11046,"provisional":10609,"depends":10850,"ratified":10972,"contact":10846,"extension":11584,"proposal":10609},197,"VK_KHR_driver_properties",{"number":10783,"type":10833,"author":11515,"promotedto":10948,"provisional":10609,"depends":11586,"ratified":10972,"contact":10837,"extension":11587,"proposal":10805},"((VK_KHR_get_physical_device_properties2,VK_VERSION_1_1)+VK_KHR_depth_stencil_resolve),VK_VERSION_1_2","VK_KHR_dynamic_rendering",{"number":11589,"type":10833,"author":10834,"provisional":10609,"depends":11590,"ratified":10972,"contact":10837,"extension":11591,"proposal":10805},233,"VK_KHR_dynamic_rendering,VK_VERSION_1_3","VK_KHR_dynamic_rendering_local_read",{"number":11593,"type":10833,"author":11515,"promotedto":10944,"provisional":10609,"depends":11594,"ratified":10972,"contact":10924,"extension":11595,"proposal":10609},114,"VK_KHR_external_fence_capabilities","VK_KHR_external_fence",{"number":11597,"type":10954,"author":11515,"promotedto":10944,"provisional":10609,"depends":10850,"ratified":10972,"contact":10924,"extension":11594,"proposal":10609},113,{"number":11599,"type":10833,"author":11515,"provisional":10609,"depends":11600,"ratified":10998,"contact":10924,"extension":11601,"proposal":10609},116,"VK_KHR_external_fence,VK_VERSION_1_1","VK_KHR_external_fence_fd",{"number":11603,"type":10833,"author":11515,"provisional":10609,"depends":11595,"platform":11128,"ratified":10972,"contact":10924,"extension":11604,"proposal":10609},115,"VK_KHR_external_fence_win32",{"number":11606,"type":10833,"author":11515,"promotedto":10944,"provisional":10609,"depends":11607,"ratified":10972,"contact":10962,"extension":11608,"proposal":10609},73,"VK_KHR_external_memory_capabilities,VK_VERSION_1_1","VK_KHR_external_memory",{"number":11610,"type":10954,"author":11515,"promotedto":10944,"provisional":10609,"depends":10850,"ratified":10972,"contact":10962,"extension":11611,"proposal":10609},72,"VK_KHR_external_memory_capabilities",{"number":11613,"type":10833,"author":11515,"provisional":10609,"depends":11097,"ratified":10998,"contact":10962,"extension":11102,"proposal":10609},75,{"number":11615,"type":10833,"author":11515,"provisional":10609,"depends":11097,"platform":11128,"ratified":10972,"contact":10962,"extension":11616,"proposal":10609},74,"VK_KHR_external_memory_win32",{"number":11618,"type":10833,"author":11515,"promotedto":10944,"provisional":10609,"depends":11619,"ratified":10972,"contact":10962,"extension":11620,"proposal":10609},78,"VK_KHR_external_semaphore_capabilities","VK_KHR_external_semaphore",{"number":11622,"type":10954,"author":11515,"promotedto":10944,"provisional":10609,"depends":10850,"ratified":10972,"contact":10962,"extension":11619,"proposal":10609},77,{"number":11624,"type":10833,"author":11515,"provisional":10609,"depends":11625,"ratified":10998,"contact":10962,"extension":11626,"proposal":10609},80,"VK_KHR_external_semaphore,VK_VERSION_1_1","VK_KHR_external_semaphore_fd",{"number":11628,"type":10833,"author":11515,"provisional":10609,"depends":11620,"platform":11128,"ratified":10972,"contact":10962,"extension":11629,"proposal":10609},79,"VK_KHR_external_semaphore_win32",{"number":11631,"type":10833,"author":11515,"promotedto":10948,"provisional":10609,"depends":10850,"ratified":10972,"contact":11507,"extension":11632,"proposal":10609},361,"VK_KHR_format_feature_flags2",{"number":11634,"type":10833,"author":11515,"provisional":10609,"depends":10850,"ratified":10972,"contact":10841,"extension":11635,"proposal":10805},323,"VK_KHR_fragment_shader_barycentric",{"number":11637,"type":10833,"author":11515,"provisional":10609,"depends":11638,"ratified":10998,"contact":10837,"extension":11639,"proposal":10805},227,"((VK_KHR_get_physical_device_properties2,VK_VERSION_1_1)+VK_KHR_create_renderpass2),VK_VERSION_1_2","VK_KHR_fragment_shading_rate",{"number":11641,"type":10954,"author":11515,"provisional":10609,"depends":11064,"ratified":10998,"contact":10962,"extension":11642,"proposal":10609},122,"VK_KHR_get_display_properties2",{"number":11644,"type":10833,"author":11515,"promotedto":10944,"provisional":10609,"ratified":10972,"contact":11214,"extension":11645,"proposal":10609},147,"VK_KHR_get_memory_requirements2",{"number":11647,"type":10954,"author":11515,"promotedto":10944,"provisional":10609,"ratified":10972,"contact":10980,"extension":11538,"proposal":10609},60,{"number":11649,"type":10954,"author":11515,"provisional":10609,"depends":11067,"ratified":10998,"contact":10962,"extension":11650,"proposal":10609},120,"VK_KHR_get_surface_capabilities2",{"number":11652,"type":10833,"author":11515,"provisional":10609,"depends":10850,"ratified":10998,"contact":10837,"extension":11132,"proposal":10609},189,{"number":11654,"type":10833,"author":11515,"promotedto":11046,"provisional":10609,"ratified":10972,"contact":11214,"extension":11655,"proposal":10609},148,"VK_KHR_image_format_list",{"number":11657,"type":10833,"author":11515,"promotedto":11046,"provisional":10609,"depends":11658,"ratified":10972,"contact":11550,"extension":11659,"proposal":10609},109,"(((VK_KHR_get_physical_device_properties2+VK_KHR_maintenance2),VK_VERSION_1_1)+VK_KHR_image_format_list),VK_VERSION_1_2","VK_KHR_imageless_framebuffer",{"number":11661,"type":10833,"author":11515,"provisional":10609,"depends":11145,"ratified":10998,"contact":11467,"extension":11662,"proposal":10609},85,"VK_KHR_incremental_present",{"number":11664,"type":10833,"author":11515,"provisional":10609,"depends":10850,"ratified":10998,"contact":10986,"extension":11184,"proposal":10609},534,{"number":11666,"type":10833,"author":11515,"provisional":10609,"depends":10850,"ratified":10998,"contact":10986,"extension":11204,"proposal":10609},535,{"number":11668,"type":10833,"author":11515,"provisional":10609,"ratified":10972,"contact":11033,"extension":11209,"proposal":10805},527,{"number":11670,"type":10833,"author":11515,"promotedto":10944,"provisional":10609,"ratified":10972,"contact":10986,"extension":10878,"proposal":10609},70,{"number":11672,"type":10833,"author":11515,"promotedto":10944,"provisional":10609,"ratified":10972,"contact":11673,"extension":11674,"proposal":10609},118,"Michael Worcester @michaelworcester","VK_KHR_maintenance2",{"number":11676,"type":10833,"author":11515,"promotedto":10944,"provisional":10609,"depends":10850,"ratified":10972,"contact":10980,"extension":11245,"proposal":10609},169,{"number":11678,"type":10833,"author":11515,"promotedto":10948,"provisional":10609,"depends":10944,"ratified":10972,"contact":10986,"extension":11679,"proposal":10609},414,"VK_KHR_maintenance4",{"number":11681,"type":10833,"author":11515,"provisional":10609,"depends":11682,"ratified":10972,"contact":11683,"extension":11684,"proposal":10805},471,"(VK_VERSION_1_1+VK_KHR_dynamic_rendering),VK_VERSION_1_3","Stu Smith @stu-s","VK_KHR_maintenance5",{"number":11686,"type":10833,"author":11515,"provisional":10609,"depends":10944,"ratified":10972,"contact":11687,"extension":11688,"proposal":10805},546,"Jon Leech @oddhack","VK_KHR_maintenance6",{"number":11690,"type":10833,"author":11515,"provisional":10609,"depends":10944,"ratified":10972,"contact":10973,"extension":11691,"proposal":10805},563,"VK_KHR_maintenance7",{"number":11693,"type":10833,"author":11515,"provisional":10609,"ratified":10972,"contact":11214,"extension":11213,"proposal":10805},272,{"number":11695,"type":10833,"author":11515,"promotedto":10944,"provisional":10609,"depends":10850,"ratified":10972,"contact":10980,"extension":11696,"proposal":10609},54,"VK_KHR_multiview",{"extension":11698,"proposal":10609},"VK_KHR_object_refresh",{"number":11700,"type":10833,"author":11515,"provisional":10609,"depends":10850,"ratified":10998,"specialuse":10845,"contact":11701,"extension":11702,"proposal":10609},117,"Alon Or-bach @alonorbach","VK_KHR_performance_query",{"number":11704,"type":10833,"author":11515,"provisional":10609,"depends":11684,"ratified":10972,"contact":11683,"extension":11705,"proposal":10805},484,"VK_KHR_pipeline_binary",{"number":11707,"type":10833,"author":11515,"provisional":10609,"depends":10850,"ratified":10972,"specialuse":10845,"contact":11214,"extension":11708,"proposal":10609},270,"VK_KHR_pipeline_executable_properties",{"number":11710,"type":10833,"author":11515,"provisional":10609,"ratified":10972,"contact":11225,"extension":11711,"proposal":10609},291,"VK_KHR_pipeline_library",{"number":11713,"type":10954,"author":11515,"provisional":10609,"ratified":10972,"contact":11714,"extension":11715,"proposal":10609},395,"Charles Giessen @charles-lunarg","VK_KHR_portability_enumeration",{"number":11717,"type":10833,"author":11515,"provisional":10805,"depends":10850,"platform":10836,"ratified":10972,"contact":11230,"extension":11718,"proposal":10609},164,"VK_KHR_portability_subset",{"number":11720,"type":10833,"author":11515,"provisional":10609,"depends":11721,"ratified":10972,"contact":11722,"extension":11723,"proposal":10609},295,"VK_KHR_swapchain+VK_KHR_get_physical_device_properties2,VK_VERSION_1_1","Keith Packard @keithp","VK_KHR_present_id",{"number":11725,"type":10833,"author":11515,"provisional":10609,"depends":11726,"ratified":10972,"contact":11722,"extension":11727,"proposal":10609},249,"VK_KHR_swapchain+VK_KHR_present_id","VK_KHR_present_wait",{"number":11729,"type":10833,"author":11515,"provisional":10609,"depends":10850,"ratified":10972,"contact":10980,"extension":11730,"proposal":10609},81,"VK_KHR_push_descriptor",{"number":11732,"type":10833,"author":11515,"provisional":10609,"depends":11733,"ratified":10972,"contact":11298,"extension":11734,"proposal":10609},349,"VK_KHR_spirv_1_4+VK_KHR_acceleration_structure","VK_KHR_ray_query",{"number":11736,"type":10833,"author":11515,"provisional":10609,"depends":11525,"ratified":10972,"contact":11298,"extension":11737,"proposal":10609},387,"VK_KHR_ray_tracing_maintenance1",{"number":11739,"type":10833,"author":11515,"provisional":10609,"depends":11733,"ratified":10972,"contact":11298,"extension":11740,"proposal":10609},348,"VK_KHR_ray_tracing_pipeline",{"number":11742,"type":10833,"author":11515,"provisional":10609,"depends":11525,"ratified":10972,"contact":11743,"extension":11744,"proposal":10805},482,"Eric Werness","VK_KHR_ray_tracing_position_fetch",{"number":11746,"type":10833,"author":11515,"promotedto":10944,"provisional":10609,"ratified":10972,"contact":11747,"extension":11748,"proposal":10609},145,"John Kessenich @johnkslang","VK_KHR_relaxed_block_layout",{"number":10665,"type":10833,"author":11515,"promotedto":11046,"provisional":10609,"ratified":10972,"contact":10837,"extension":11750,"proposal":10609},"VK_KHR_sampler_mirror_clamp_to_edge",{"number":11752,"type":10833,"author":11515,"promotedto":10944,"provisional":10609,"depends":11753,"ratified":10972,"contact":11754,"extension":11755,"proposal":10609},157,"(VK_KHR_maintenance1+VK_KHR_bind_memory2+VK_KHR_get_memory_requirements2+VK_KHR_get_physical_device_properties2),VK_VERSION_1_1","Andrew Garrard @fluppeteer","VK_KHR_sampler_ycbcr_conversion",{"number":11757,"type":10833,"author":11515,"promotedto":11046,"provisional":10609,"depends":11638,"ratified":10972,"contact":10986,"extension":11758,"proposal":10609},242,"VK_KHR_separate_depth_stencil_layouts",{"number":11760,"type":10833,"author":11515,"promotedto":11046,"provisional":10609,"depends":10850,"ratified":10972,"contact":11761,"extension":11762,"proposal":10609},181,"Aaron Hagan @ahagan","VK_KHR_shader_atomic_int64",{"number":11764,"type":10833,"author":11515,"provisional":10609,"depends":10850,"ratified":10998,"contact":11761,"extension":11765,"proposal":10609},182,"VK_KHR_shader_clock",{"number":11767,"type":10833,"author":11515,"promotedto":10944,"provisional":10609,"ratified":10972,"contact":11298,"extension":11768,"proposal":10609},64,"VK_KHR_shader_draw_parameters",{"number":11770,"type":10833,"author":11515,"provisional":10609,"depends":10850,"ratified":10972,"contact":10938,"extension":11771,"proposal":10805},545,"VK_KHR_shader_expect_assume",{"number":11773,"type":10833,"author":11515,"promotedto":11046,"provisional":10609,"depends":10850,"ratified":10972,"contact":11520,"extension":10864,"proposal":10609},83,{"number":11775,"type":10833,"author":11515,"promotedto":11046,"provisional":10609,"depends":10850,"ratified":10972,"contact":11520,"extension":11776,"proposal":10609},198,"VK_KHR_shader_float_controls",{"number":11778,"type":10833,"author":11515,"provisional":10609,"depends":11779,"ratified":10972,"contact":11029,"extension":11780,"proposal":10805},529,"VK_VERSION_1_1+VK_KHR_shader_float_controls","VK_KHR_shader_float_controls2",{"number":11782,"type":10833,"author":11515,"promotedto":10948,"provisional":10609,"depends":10850,"ratified":10972,"contact":10938,"extension":11783,"proposal":10805},281,"VK_KHR_shader_integer_dot_product",{"number":11785,"type":10833,"author":11515,"provisional":10609,"depends":10944,"ratified":10972,"contact":11786,"extension":11787,"proposal":10805},435,"Alan Baker @alan-baker","VK_KHR_shader_maximal_reconvergence",{"number":11789,"type":10833,"author":11515,"promotedto":10948,"provisional":10609,"ratified":10972,"contact":11015,"extension":11790,"proposal":10609},294,"VK_KHR_shader_non_semantic_info",{"number":11792,"type":10833,"author":11515,"provisional":10609,"depends":11793,"ratified":10972,"contact":10837,"extension":11794,"proposal":10805},236,"VK_VERSION_1_1+VK_KHR_vulkan_memory_model+VK_KHR_shader_maximal_reconvergence","VK_KHR_shader_quad_control",{"number":11796,"type":10833,"author":11515,"provisional":10609,"ratified":10972,"contact":11797,"extension":11798,"proposal":10805},559,"Nathan Gauër @Keenuts","VK_KHR_shader_relaxed_extended_instruction",{"number":11800,"type":10833,"author":11515,"promotedto":11046,"provisional":10609,"depends":10944,"ratified":10972,"contact":11379,"extension":11801,"proposal":10609},176,"VK_KHR_shader_subgroup_extended_types",{"number":11803,"type":10833,"author":11515,"provisional":10609,"ratified":10972,"contact":10938,"extension":11804,"proposal":10805},417,"VK_KHR_shader_subgroup_rotate",{"number":11806,"type":10833,"author":11515,"provisional":10609,"depends":10944,"ratified":10972,"contact":11786,"extension":11807,"proposal":10609},324,"VK_KHR_shader_subgroup_uniform_control_flow",{"number":11809,"type":10833,"author":11515,"promotedto":10948,"provisional":10609,"depends":10850,"ratified":10998,"contact":10924,"extension":11810,"proposal":10609},216,"VK_KHR_shader_terminate_invocation",{"number":11812,"type":10833,"author":11515,"provisional":10609,"depends":11813,"ratified":10998,"contact":11701,"extension":11814,"proposal":10609},112,"VK_KHR_swapchain+VK_KHR_get_surface_capabilities2+(VK_KHR_get_physical_device_properties2,VK_VERSION_1_1)","VK_KHR_shared_presentable_image",{"number":11816,"type":10833,"author":11515,"promotedto":11046,"provisional":10609,"depends":11779,"ratified":10972,"contact":10924,"extension":11224,"proposal":10609},237,{"number":11818,"type":10833,"author":11515,"promotedto":10944,"provisional":10609,"ratified":10972,"contact":11520,"extension":11819,"proposal":10609},132,"VK_KHR_storage_buffer_storage_class",{"number":10611,"type":10954,"author":11515,"provisional":10609,"ratified":10998,"contact":11821,"extension":11067,"proposal":10609},"James Jones @cubanismo,Ian Elliott @ianelliottus",{"number":11823,"type":10954,"author":11515,"provisional":10609,"depends":11824,"ratified":10972,"contact":11825,"extension":11826,"proposal":10609},240,"VK_VERSION_1_1+VK_KHR_get_surface_capabilities2","Sandeep Shinde @sashinde","VK_KHR_surface_protected_capabilities",{"number":10579,"type":10833,"author":11515,"provisional":10609,"depends":11067,"ratified":10998,"contact":11821,"extension":11145,"proposal":10609},{"number":11829,"type":10833,"author":11515,"provisional":10609,"depends":11830,"ratified":10998,"contact":10846,"extension":11831,"proposal":10609},201,"VK_KHR_swapchain+(VK_KHR_maintenance2,VK_VERSION_1_1)+(VK_KHR_image_format_list,VK_VERSION_1_2)","VK_KHR_swapchain_mutable_format",{"number":11833,"type":10833,"author":11515,"promotedto":10948,"provisional":10609,"depends":10850,"ratified":10998,"contact":10837,"extension":11834,"proposal":10609},315,"VK_KHR_synchronization2",{"number":11836,"type":10833,"author":11515,"promotedto":11046,"provisional":10609,"depends":10850,"ratified":10972,"contact":11214,"extension":11837,"proposal":10609},208,"VK_KHR_timeline_semaphore",{"number":11839,"type":10833,"author":11515,"promotedto":11046,"provisional":10609,"depends":10850,"ratified":10972,"contact":11029,"extension":11840,"proposal":10609},254,"VK_KHR_uniform_buffer_standard_layout",{"number":11842,"type":10833,"author":11515,"promotedto":10944,"provisional":10609,"depends":11516,"ratified":10972,"contact":10924,"extension":11843,"proposal":10609},121,"VK_KHR_variable_pointers",{"number":11845,"type":10833,"author":11515,"provisional":10609,"depends":10850,"ratified":10998,"contact":11033,"extension":11422,"proposal":10805},526,{"number":11847,"type":10833,"author":11515,"provisional":10609,"depends":11848,"ratified":10972,"contact":11189,"extension":11849,"proposal":10805},513,"VK_KHR_video_decode_queue","VK_KHR_video_decode_av1",{"number":10767,"type":10833,"author":11515,"provisional":10609,"depends":11848,"ratified":10972,"contact":11851,"extension":11852,"proposal":10805},"peter.fang@amd.com","VK_KHR_video_decode_h264",{"number":11854,"type":10833,"author":11515,"provisional":10609,"depends":11848,"ratified":10972,"contact":11851,"extension":11855,"proposal":10805},188,"VK_KHR_video_decode_h265",{"number":10705,"type":10833,"author":11515,"provisional":10609,"depends":11857,"ratified":10972,"contact":11858,"extension":11848,"proposal":10805},"VK_KHR_video_queue+(VK_KHR_synchronization2,VK_VERSION_1_3)","jake.beju@amd.com",{"number":10759,"type":10833,"author":11515,"provisional":10609,"depends":11860,"ratified":10972,"contact":11861,"extension":11862,"proposal":10805},"VK_KHR_video_encode_queue","Ahmed Abdelkhalek @aabdelkh","VK_KHR_video_encode_h264",{"number":10763,"type":10833,"author":11515,"provisional":10609,"depends":11860,"ratified":10972,"contact":11861,"extension":11864,"proposal":10805},"VK_KHR_video_encode_h265",{"number":11866,"type":10833,"author":11515,"provisional":10609,"depends":11857,"ratified":10972,"contact":11861,"extension":11860,"proposal":10805},300,{"number":11868,"type":10833,"author":11515,"provisional":10609,"depends":11869,"ratified":10972,"contact":11189,"extension":11870,"proposal":10805},516,"VK_KHR_video_queue","VK_KHR_video_maintenance1",{"number":10701,"type":10833,"author":11515,"provisional":10609,"depends":11872,"ratified":10972,"contact":11428,"extension":11869,"proposal":10805},"(VK_VERSION_1_1+VK_KHR_synchronization2),VK_VERSION_1_3",{"number":11874,"type":10833,"author":11515,"promotedto":11046,"provisional":10609,"depends":10850,"ratified":10972,"contact":10980,"extension":11875,"proposal":10609},212,"VK_KHR_vulkan_memory_model",{"number":10633,"type":10954,"author":11515,"provisional":10609,"depends":11067,"platform":11877,"ratified":10972,"contact":11878,"extension":11879,"proposal":10609},"wayland","Jesse Hall @critsec,Ian Elliott @ianelliottus","VK_KHR_wayland_surface",{"number":11881,"type":10833,"author":11515,"provisional":10609,"depends":11616,"platform":11128,"ratified":10972,"contact":11882,"extension":11883,"proposal":10609},76,"Carsten Rohde @crohde","VK_KHR_win32_keyed_mutex",{"number":10645,"type":10954,"author":11515,"provisional":10609,"depends":11067,"platform":11128,"ratified":10972,"contact":11878,"extension":11885,"proposal":10609},"VK_KHR_win32_surface",{"number":11887,"type":10833,"author":11515,"provisional":10609,"depends":10850,"ratified":10972,"contact":11888,"extension":11889,"proposal":10609},337,"Caio Marcelo de Oliveira Filho @cmarcelo","VK_KHR_workgroup_memory_explicit_layout",{"number":10629,"type":10954,"author":11515,"provisional":10609,"depends":11067,"platform":11891,"ratified":10972,"contact":11878,"extension":11892,"proposal":10609},"xcb","VK_KHR_xcb_surface",{"number":10625,"type":10954,"author":11515,"provisional":10609,"depends":11067,"platform":11894,"ratified":10972,"contact":11878,"extension":11895,"proposal":10609},"xlib","VK_KHR_xlib_surface",{"number":11897,"type":10833,"author":11515,"promotedto":10948,"provisional":10609,"depends":10850,"ratified":10972,"contact":11786,"extension":11898,"proposal":10609},326,"VK_KHR_zero_initialize_workgroup_memory",{"number":11900,"type":10954,"author":11413,"provisional":10609,"contact":11714,"extension":11901,"proposal":10805},460,"VK_LUNARG_direct_driver_loading",{"number":11903,"type":10833,"author":11904,"provisional":10609,"depends":10850,"specialuse":11025,"contact":11282,"extension":11905,"proposal":10609},576,"MESA","VK_MESA_image_alignment_control",{"number":11907,"type":10833,"author":11908,"provisional":10609,"depends":10850,"contact":11909,"extension":11910,"proposal":10805},531,"MSFT","Jesse Natalie @jenatali","VK_MSFT_layered_driver",{"number":11912,"type":10954,"author":11913,"deprecatedby":11235,"provisional":10609,"depends":11067,"platform":11914,"contact":11230,"extension":11915,"proposal":10609},123,"MVK","ios","VK_MVK_ios_surface",{"number":11917,"type":10954,"author":11913,"deprecatedby":11235,"provisional":10609,"depends":11067,"platform":11918,"contact":11230,"extension":11919,"proposal":10609},124,"macos","VK_MVK_macos_surface",{"number":11921,"type":10954,"author":11922,"provisional":10609,"depends":11067,"platform":11923,"contact":11924,"extension":11925,"proposal":10609},63,"NN","vi","Mathias Heyer gitlab:@mheyer","VK_NN_vi_surface",{"number":10725,"type":10833,"author":11927,"provisional":10609,"contact":11928,"extension":11929,"proposal":10609},"NVX","Eric Werness @ewerness-nv,Liam Middlebrook @liam-middlebrook","VK_NVX_binary_import",{"number":10729,"type":10833,"author":11927,"provisional":10609,"contact":11931,"extension":11932,"proposal":10609},"Eric Werness @ewerness-nv","VK_NVX_image_view_handle",{"number":11934,"type":10833,"author":11927,"provisional":10609,"depends":11935,"contact":10980,"extension":11936,"proposal":10609},98,"VK_KHR_multiview,VK_VERSION_1_1","VK_NVX_multiview_per_view_attributes",{"number":11938,"type":10833,"author":10960,"provisional":10609,"depends":10955,"platform":11128,"contact":11939,"extension":11940,"proposal":10609},346,"Jeff Juliano @jjuliano","VK_NV_acquire_winrt_display",{"number":11942,"type":10833,"author":10960,"provisional":10609,"contact":11931,"extension":11943,"proposal":10609},88,"VK_NV_clip_space_w_scaling",{"number":11945,"type":10833,"author":10960,"provisional":10609,"contact":11946,"extension":11947,"proposal":10609},560,"Lujin Wang @lujinwangnv","VK_NV_command_buffer_inheritance",{"number":11949,"type":10833,"author":10960,"promotedto":11540,"provisional":10609,"depends":10850,"contact":11950,"extension":11951,"proposal":10609},202,"Pat Brown @nvpbrown","VK_NV_compute_shader_derivatives",{"number":11953,"type":10833,"author":10960,"provisional":10609,"depends":10850,"contact":10980,"extension":11954,"proposal":10609},250,"VK_NV_cooperative_matrix",{"number":11956,"type":10833,"author":10960,"provisional":10609,"depends":11957,"contact":11090,"extension":11958,"proposal":10609},427,"((VK_KHR_get_physical_device_properties2,VK_VERSION_1_1)+VK_KHR_buffer_device_address),VK_VERSION_1_2","VK_NV_copy_memory_indirect",{"number":11960,"type":10833,"author":10960,"provisional":10609,"depends":10850,"contact":11298,"extension":11961,"proposal":10609},51,"VK_NV_corner_sampled_image",{"number":11963,"type":10833,"author":10960,"provisional":10609,"depends":11964,"contact":11965,"extension":11966,"proposal":10609},251,"VK_NV_framebuffer_mixed_samples+(VK_KHR_get_physical_device_properties2,VK_VERSION_1_1)","Kedarnath Thangudu @kthangudu","VK_NV_coverage_reduction_mode",{"number":11968,"type":10833,"author":10960,"provisional":10805,"contact":11969,"extension":11970,"proposal":10609},308,"Tristan Lorach @tlorach","VK_NV_cuda_kernel_launch",{"number":10713,"type":10833,"author":10960,"deprecatedby":11555,"provisional":10609,"contact":10980,"extension":11972,"proposal":10609},"VK_NV_dedicated_allocation",{"number":11974,"type":10833,"author":11975,"provisional":10609,"depends":11976,"contact":11977,"extension":11978,"proposal":10609},241,"NVIDIA","(VK_KHR_dedicated_allocation+VK_KHR_get_physical_device_properties2),VK_VERSION_1_1","Nuno Subtil @nsubtil","VK_NV_dedicated_allocation_image_aliasing",{"number":11980,"type":10833,"author":10960,"provisional":10609,"depends":10944,"contact":10986,"extension":11981,"proposal":10609},547,"VK_NV_descriptor_pool_overallocation",{"number":11983,"type":10833,"author":11975,"provisional":10609,"depends":10850,"contact":11977,"extension":11984,"proposal":10609},207,"VK_NV_device_diagnostic_checkpoints",{"number":11986,"type":10833,"author":10960,"provisional":10609,"depends":10850,"contact":11965,"extension":11987,"proposal":10609},301,"VK_NV_device_diagnostics_config",{"number":11989,"type":10833,"author":10960,"provisional":10609,"depends":11990,"contact":11225,"extension":11991,"proposal":10609},278,"(VK_VERSION_1_1+VK_KHR_buffer_device_address),VK_VERSION_1_2","VK_NV_device_generated_commands",{"number":11993,"type":10833,"author":10960,"provisional":10609,"depends":11991,"contact":11090,"extension":11994,"proposal":10609},429,"VK_NV_device_generated_commands_compute",{"number":11996,"type":10833,"author":10960,"provisional":10805,"depends":11260,"platform":10836,"contact":11997,"extension":11998,"proposal":10609},398,"Christoph Kubisch @pixeljetstream, Eric Werness @ewerness-nv","VK_NV_displacement_micromap",{"number":12000,"type":10833,"author":10960,"provisional":10609,"contact":12001,"extension":12002,"proposal":10609},493,"Russell Chou @russellcnv","VK_NV_extended_sparse_address_space",{"number":12004,"type":10833,"author":10960,"deprecatedby":11608,"provisional":10609,"depends":12005,"contact":10962,"extension":12006,"proposal":10609},57,"VK_NV_external_memory_capabilities","VK_NV_external_memory",{"number":12008,"type":10954,"author":10960,"deprecatedby":11611,"provisional":10609,"contact":10962,"extension":12005,"proposal":10609},56,{"number":12010,"type":10833,"author":10960,"provisional":10609,"depends":11097,"contact":11882,"extension":12011,"proposal":10609},372,"VK_NV_external_memory_rdma",{"extension":12013,"proposal":10609},"VK_NV_external_memory_sci_buf",{"number":12015,"type":10833,"author":10960,"deprecatedby":11616,"provisional":10609,"depends":12006,"platform":11128,"contact":10962,"extension":12016,"proposal":10609},58,"VK_NV_external_memory_win32",{"extension":12018,"proposal":10609},"VK_NV_external_sci_sync",{"extension":12020,"proposal":10609},"VK_NV_external_sci_sync2",{"number":12022,"type":10833,"author":10960,"provisional":10609,"contact":10980,"extension":12023,"proposal":10609},154,"VK_NV_fill_rectangle",{"number":12025,"type":10833,"author":10960,"provisional":10609,"contact":10980,"extension":12026,"proposal":10609},150,"VK_NV_fragment_coverage_to_color",{"number":12028,"type":10833,"author":10960,"promotedto":11635,"provisional":10609,"depends":10850,"contact":11950,"extension":12029,"proposal":10609},204,"VK_NV_fragment_shader_barycentric",{"number":12031,"type":10833,"author":10960,"provisional":10609,"depends":11639,"contact":11950,"extension":12032,"proposal":10609},327,"VK_NV_fragment_shading_rate_enums",{"number":12034,"type":10833,"author":10960,"provisional":10609,"contact":10980,"extension":12035,"proposal":10609},153,"VK_NV_framebuffer_mixed_samples",{"number":12037,"type":10833,"author":10960,"provisional":10609,"contact":11298,"extension":12038,"proposal":10609},96,"VK_NV_geometry_shader_passthrough",{"number":10657,"type":10833,"author":10960,"deprecatedby":11498,"provisional":10609,"contact":10986,"extension":12040,"proposal":10609},"VK_NV_glsl_shader",{"number":12042,"type":10833,"author":10960,"provisional":10609,"depends":10850,"contact":12043,"extension":12044,"proposal":10609},279,"David Zhao Akeley @akeley98","VK_NV_inherited_viewport_scissor",{"number":12046,"type":10833,"author":11975,"provisional":10609,"depends":10850,"contact":12047,"extension":12048,"proposal":10609},431,"sourav parmar @souravpNV","VK_NV_linear_color_attachment",{"number":12050,"type":10833,"author":10960,"provisional":10609,"contact":12051,"extension":12052,"proposal":10609},311,"Charles Hansen @cshansen","VK_NV_low_latency",{"number":12054,"type":10833,"author":10960,"provisional":10609,"depends":12055,"contact":12051,"extension":12056,"proposal":10609},506,"VK_VERSION_1_2,VK_KHR_timeline_semaphore","VK_NV_low_latency2",{"number":12058,"type":10833,"author":10960,"provisional":10609,"depends":11957,"contact":11090,"extension":12059,"proposal":10609},428,"VK_NV_memory_decompression",{"number":12061,"type":10833,"author":10960,"provisional":10609,"depends":10850,"contact":11225,"extension":12062,"proposal":10609},203,"VK_NV_mesh_shader",{"number":12064,"type":10833,"author":10960,"provisional":10609,"depends":12065,"contact":11882,"extension":12066,"proposal":10609},465,"((VK_KHR_get_physical_device_properties2,VK_VERSION_1_1)+VK_KHR_format_feature_flags2+VK_KHR_synchronization2),VK_VERSION_1_3","VK_NV_optical_flow",{"number":12068,"type":10833,"author":10960,"provisional":10609,"depends":11688,"contact":10986,"extension":12069,"proposal":10609},517,"VK_NV_per_stage_descriptor_set",{"number":12071,"type":10833,"author":10960,"provisional":10609,"depends":11127,"contact":12072,"extension":12073,"proposal":10609},293,"Liya Li @liyli","VK_NV_present_barrier",{"extension":12075,"proposal":10609},"VK_NV_private_vendor_info",{"number":12077,"type":10833,"author":10960,"provisional":10609,"contact":12078,"extension":12079,"proposal":10609},556,"Rodrigo Locatti @rlocatti","VK_NV_raw_access_chains",{"number":12081,"type":10833,"author":10960,"deprecatedby":11740,"provisional":10609,"depends":12082,"contact":11931,"extension":12083,"proposal":10609},166,"(VK_KHR_get_physical_device_properties2+VK_KHR_get_memory_requirements2),VK_VERSION_1_1","VK_NV_ray_tracing",{"number":12085,"type":10833,"author":10960,"provisional":10609,"depends":11740,"contact":11931,"extension":12086,"proposal":10609},491,"VK_NV_ray_tracing_invocation_reorder",{"number":12088,"type":10833,"author":10960,"provisional":10609,"depends":11740,"contact":11743,"extension":12089,"proposal":10609},328,"VK_NV_ray_tracing_motion_blur",{"number":12091,"type":10833,"author":10960,"provisional":10609,"contact":11090,"extension":12092,"proposal":10805},569,"VK_NV_ray_tracing_validation",{"number":12094,"type":10833,"author":10960,"provisional":10609,"depends":10850,"contact":11965,"extension":12095,"proposal":10609},167,"VK_NV_representative_fragment_test",{"number":12097,"type":10833,"author":10960,"provisional":10609,"contact":10986,"extension":12098,"proposal":10609},95,"VK_NV_sample_mask_override_coverage",{"number":12100,"type":10833,"author":10960,"provisional":10609,"depends":10850,"contact":11950,"extension":12101,"proposal":10609},206,"VK_NV_scissor_exclusive",{"number":12103,"type":10833,"author":10960,"provisional":10609,"contact":10980,"extension":12104,"proposal":10609},564,"VK_NV_shader_atomic_float16_vector",{"number":12106,"type":10833,"author":10960,"provisional":10609,"depends":10850,"contact":11950,"extension":12107,"proposal":10609},205,"VK_NV_shader_image_footprint",{"number":12109,"type":10833,"author":10960,"provisional":10609,"depends":10944,"contact":11298,"extension":12110,"proposal":10609},155,"VK_NV_shader_sm_builtins",{"number":12112,"type":10833,"author":10960,"provisional":10609,"depends":10944,"contact":10980,"extension":12113,"proposal":10609},199,"VK_NV_shader_subgroup_partitioned",{"number":12115,"type":10833,"author":10960,"provisional":10609,"depends":10850,"contact":11950,"extension":12116,"proposal":10609},165,"VK_NV_shading_rate_image",{"number":12118,"type":10833,"author":10960,"provisional":10609,"contact":11298,"extension":12119,"proposal":10609},97,"VK_NV_viewport_array2",{"number":12121,"type":10833,"author":10960,"provisional":10609,"contact":10986,"extension":12122,"proposal":10609},99,"VK_NV_viewport_swizzle",{"number":12124,"type":10833,"author":10960,"promotedto":11883,"provisional":10609,"depends":12016,"platform":11128,"contact":11882,"extension":12125,"proposal":10609},59,"VK_NV_win32_keyed_mutex",{"number":12127,"type":10833,"author":11109,"provisional":10609,"depends":12128,"contact":11110,"extension":12129,"proposal":10609},522,"(VK_EXT_filter_cubic)+(VK_VERSION_1_2,VK_EXT_sampler_filter_minmax)","VK_QCOM_filter_cubic_clamp",{"number":12131,"type":10833,"author":11109,"provisional":10609,"depends":11111,"contact":11110,"extension":12132,"proposal":10609},520,"VK_QCOM_filter_cubic_weights",{"number":12134,"type":10833,"author":11109,"provisional":10609,"depends":12135,"contact":11110,"extension":12136,"proposal":10609},426,"(VK_KHR_get_physical_device_properties2,VK_VERSION_1_1)+VK_EXT_fragment_density_map","VK_QCOM_fragment_density_map_offset",{"number":12138,"type":10833,"author":11109,"provisional":10609,"depends":12139,"contact":11110,"extension":12140,"proposal":10805},441,"VK_KHR_format_feature_flags2,VK_VERSION_1_3","VK_QCOM_image_processing",{"number":12142,"type":10833,"author":11109,"provisional":10609,"depends":12140,"contact":11110,"extension":12143,"proposal":10609},519,"VK_QCOM_image_processing2",{"number":12145,"type":10833,"author":11109,"provisional":10609,"contact":11110,"extension":12146,"proposal":10609},511,"VK_QCOM_multiview_per_view_render_areas",{"number":12148,"type":10833,"author":11109,"provisional":10609,"depends":10850,"contact":11110,"extension":12149,"proposal":10609},489,"VK_QCOM_multiview_per_view_viewports",{"number":12151,"type":10833,"author":11109,"provisional":10609,"contact":11110,"extension":12152,"proposal":10609},172,"VK_QCOM_render_pass_shader_resolve",{"number":12154,"type":10833,"author":11109,"provisional":10609,"contact":11110,"extension":12155,"proposal":10609},302,"VK_QCOM_render_pass_store_ops",{"number":12157,"type":10833,"author":11109,"provisional":10609,"contact":11110,"extension":12158,"proposal":10609},283,"VK_QCOM_render_pass_transform",{"number":12160,"type":10833,"author":11109,"provisional":10609,"depends":12161,"contact":11110,"extension":12162,"proposal":10609},334,"VK_KHR_copy_commands2,VK_VERSION_1_3","VK_QCOM_rotated_copy_commands",{"number":12164,"type":10833,"author":11109,"provisional":10609,"depends":10850,"contact":11110,"extension":12165,"proposal":10805},485,"VK_QCOM_tile_properties",{"number":12167,"type":10833,"author":11109,"provisional":10609,"contact":11110,"extension":12168,"proposal":10609},521,"VK_QCOM_ycbcr_degamma",{"number":12170,"type":10833,"author":12171,"provisional":10609,"depends":10923,"platform":12172,"contact":12173,"extension":12174,"proposal":10609},530,"QNX","screen","Mike Gorchak @mgorchak-blackberry, Aaron Ruby @aruby-blackberry","VK_QNX_external_memory_screen_buffer",{"number":12176,"type":10954,"author":12171,"provisional":10609,"depends":11067,"platform":12172,"contact":12177,"extension":12178,"proposal":10609},379,"Mike Gorchak @mgorchak-blackberry","VK_QNX_screen_surface",{"number":12180,"type":10833,"author":12181,"provisional":10609,"depends":10850,"contact":11053,"extension":12182,"proposal":10609},486,"SEC","VK_SEC_amigo_profiling",{"number":12184,"type":10833,"author":12185,"provisional":10609,"depends":10850,"specialuse":11025,"contact":11282,"extension":12186,"proposal":10609},421,"VALVE","VK_VALVE_descriptor_set_host_mapping",{"number":12188,"type":10833,"author":12185,"promotedto":11247,"provisional":10609,"depends":11245,"specialuse":11025,"contact":11246,"extension":12189,"proposal":10609},352,"VK_VALVE_mutable_descriptor_type",1725732631833]