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",{"type":10,"tag":692,"props":693,"children":694},"em",{},[695],{"type":16,"value":696},"interior\nvertices",{"type":16,"value":698}," that are positioned on the edge of the patch if an inner\ntessellation level is less than or equal to one.\nSuch vertices are considered distinct from vertices produced by subdividing\nthe outer edge of the patch, even if there are pairs of vertices with\nidentical coordinates.",{"type":10,"tag":48,"props":700,"children":702},{"id":701},"tessellation-primitive-order",[703],{"type":16,"value":704},"Tessellation Primitive Ordering",{"type":10,"tag":18,"props":706,"children":707},{},[708,710,716],{"type":16,"value":709},"Few guarantees are provided for the relative ordering of primitives produced\nby tessellation, as they pertain to ",{"type":10,"tag":24,"props":711,"children":713},{"href":712},"/chapters/drawing#drawing-primitive-order",[714],{"type":16,"value":715},"primitive\norder",{"type":16,"value":487},{"type":10,"tag":186,"props":718,"children":719},{},[720,725],{"type":10,"tag":190,"props":721,"children":722},{},[723],{"type":16,"value":724},"The output primitives generated from each input primitive are passed to\nsubsequent pipeline stages in an implementation-dependent order.",{"type":10,"tag":190,"props":726,"children":727},{},[728],{"type":16,"value":729},"All output primitives generated from a given input primitive are passed\nto subsequent pipeline stages before any output primitives generated\nfrom subsequent input primitives.",{"type":10,"tag":48,"props":731,"children":733},{"id":732},"tessellation-vertex-winding-order",[734],{"type":16,"value":735},"Tessellator Vertex Winding Order",{"type":10,"tag":18,"props":737,"children":738},{},[739,741,746,748,753,755,760,762,767,768,773,775,780,782,787],{"type":16,"value":740},"When the tessellator produces triangles (in the ",{"type":10,"tag":68,"props":742,"children":744},{"className":743},[],[745],{"type":16,"value":102},{"type":16,"value":747}," or ",{"type":10,"tag":68,"props":749,"children":751},{"className":750},[],[752],{"type":16,"value":110},{"type":16,"value":754},"\nmodes), the orientation of all triangles is specified with an\n",{"type":10,"tag":68,"props":756,"children":758},{"className":757},[],[759],{"type":16,"value":94},{"type":16,"value":761}," of ",{"type":10,"tag":68,"props":763,"children":765},{"className":764},[],[766],{"type":16,"value":281},{"type":16,"value":747},{"type":10,"tag":68,"props":769,"children":771},{"className":770},[],[772],{"type":16,"value":288},{"type":16,"value":774}," in the\ntessellation control or tessellation evaluation shaders.\nIf the order is ",{"type":10,"tag":68,"props":776,"children":778},{"className":777},[],[779],{"type":16,"value":281},{"type":16,"value":781},", the vertices of all generated triangles\nwill have clockwise ordering in (u,v) or (u,v,w) space.\nIf the order is ",{"type":10,"tag":68,"props":783,"children":785},{"className":784},[],[786],{"type":16,"value":288},{"type":16,"value":788},", the vertices will have\ncounter-clockwise ordering in that space.",{"type":10,"tag":18,"props":790,"children":791},{},[792],{"type":16,"value":793},"If the tessellation domain has an upper-left origin, the vertices of a\ntriangle have counter-clockwise ordering if",{"type":10,"tag":186,"props":795,"children":796},{},[797],{"type":10,"tag":190,"props":798,"children":799},{},[800,802,808,810,815,817,821,822,826,828,832,833,838,839,843,844,848,850,854,855,859,860,864,865],{"type":16,"value":801},"a = u",{"type":10,"tag":803,"props":804,"children":805},"sub",{},[806],{"type":16,"value":807},"0",{"type":16,"value":809}," v",{"type":10,"tag":803,"props":811,"children":812},{},[813],{"type":16,"value":814},"1",{"type":16,"value":816}," - u",{"type":10,"tag":803,"props":818,"children":819},{},[820],{"type":16,"value":814},{"type":16,"value":809},{"type":10,"tag":803,"props":823,"children":824},{},[825],{"type":16,"value":807},{"type":16,"value":827}," +  u",{"type":10,"tag":803,"props":829,"children":830},{},[831],{"type":16,"value":814},{"type":16,"value":809},{"type":10,"tag":803,"props":834,"children":835},{},[836],{"type":16,"value":837},"2",{"type":16,"value":816},{"type":10,"tag":803,"props":840,"children":841},{},[842],{"type":16,"value":837},{"type":16,"value":809},{"type":10,"tag":803,"props":845,"children":846},{},[847],{"type":16,"value":814},{"type":16,"value":849},"\n+  u",{"type":10,"tag":803,"props":851,"children":852},{},[853],{"type":16,"value":837},{"type":16,"value":809},{"type":10,"tag":803,"props":856,"children":857},{},[858],{"type":16,"value":807},{"type":16,"value":816},{"type":10,"tag":803,"props":861,"children":862},{},[863],{"type":16,"value":807},{"type":16,"value":809},{"type":10,"tag":803,"props":866,"children":867},{},[868],{"type":16,"value":837},{"type":10,"tag":18,"props":870,"children":871},{},[872,874,879,881,885],{"type":16,"value":873},"is negative, and clockwise ordering if a is positive.\nu",{"type":10,"tag":803,"props":875,"children":876},{},[877],{"type":16,"value":878},"i",{"type":16,"value":880}," and v",{"type":10,"tag":803,"props":882,"children":883},{},[884],{"type":16,"value":878},{"type":16,"value":886}," are the u and v coordinates in\nnormalized parameter space of the ith vertex of the triangle.\nIf the tessellation domain has a lower-left origin, the vertices of a\ntriangle have counter-clockwise ordering if a is positive, and\nclockwise ordering if a is negative.",{"type":10,"tag":888,"props":889,"children":890},"note",{},[891,896],{"type":10,"tag":18,"props":892,"children":893},{},[894],{"type":16,"value":895},"The value a is proportional (with a positive factor) to the signed\narea of the triangle.",{"type":10,"tag":18,"props":897,"children":898},{},[899,901,906],{"type":16,"value":900},"In ",{"type":10,"tag":68,"props":902,"children":904},{"className":903},[],[905],{"type":16,"value":102},{"type":16,"value":907}," mode, even though the vertex coordinates have a w\nvalue, it does not participate directly in the computation of a, being\nan affine combination of u and v.",{"type":10,"tag":48,"props":909,"children":911},{"id":910},"tessellation-triangle-tessellation",[912],{"type":16,"value":913},"Triangle Tessellation",{"type":10,"tag":18,"props":915,"children":916},{},[917,919,924],{"type":16,"value":918},"If the tessellation primitive mode is ",{"type":10,"tag":68,"props":920,"children":922},{"className":921},[],[923],{"type":16,"value":102},{"type":16,"value":925},", an equilateral\ntriangle is subdivided into a collection of triangles covering the area of\nthe original triangle.\nFirst, the original triangle is subdivided into a collection of concentric\nequilateral triangles.\nThe edges of each of these triangles are subdivided, and the area between\neach triangle pair is filled by triangles produced by joining the vertices\non the subdivided edges.\nThe number of concentric triangles and the number of subdivisions along each\ntriangle except the outermost is derived from the first inner tessellation\nlevel.\nThe edges of the outermost triangle are subdivided independently, using the\nfirst, second, and third outer tessellation levels to control the number of\nsubdivisions of the u = 0 (left), v = 0 (bottom), and w =\n0 (right) edges, respectively.\nThe second inner tessellation level and the fourth outer tessellation level\nhave no effect in this mode.",{"type":10,"tag":18,"props":927,"children":928},{},[929,931,934,936,941],{"type":16,"value":930},"If the first inner tessellation level and all three outer tessellation\nlevels are exactly one after clamping and rounding, only a single triangle\nwith (u,v,w) coordinates of (0,0,1), (1,0,0), and\n(0,1,0) is generated.\nIf the inner tessellation level is one and any of the outer tessellation\nlevels is greater than one, the inner tessellation level is treated as\nthough it were originally specified as 1 +  ε and will\nresult in a two- or three-segment subdivision depending on the tessellation\nspacing.\nWhen used with fractional odd spacing, the three-segment subdivision ",{"type":10,"tag":33,"props":932,"children":933},{"type":137},[],{"type":16,"value":935},"\nproduce ",{"type":10,"tag":692,"props":937,"children":938},{},[939],{"type":16,"value":940},"inner vertices",{"type":16,"value":942}," positioned on the edge of the triangle.",{"type":10,"tag":18,"props":944,"children":945},{},[946,948,954],{"type":16,"value":947},"If any tessellation level is greater than one, tessellation begins by\nproducing a set of concentric inner triangles and subdividing their edges.\nFirst, the three outer edges are temporarily subdivided using the clamped\nand rounded first inner tessellation level and the specified tessellation\nspacing, generating n segments.\nFor the outermost inner triangle, the inner triangle is degenerate — a\nsingle point at the center of the triangle — if n is two.\nOtherwise, for each corner of the outer triangle, an inner triangle corner\nis produced at the intersection of two lines extended perpendicular to the\ncorner’s two adjacent edges running through the vertex of the subdivided\nouter edge nearest that corner.\nIf n is three, the edges of the inner triangle are not subdivided and\nit is the final triangle in the set of concentric triangles.\nOtherwise, each edge of the inner triangle is divided into n - 2\nsegments, with the n - 1 vertices of this subdivision produced by\nintersecting the inner edge with lines perpendicular to the edge running\nthrough the n - 1 innermost vertices of the subdivision of the outer\nedge.\nOnce the outermost inner triangle is subdivided, the previous subdivision\nprocess repeats itself, using the generated triangle as an outer triangle.\nThis subdivision process is illustrated in ",{"type":10,"tag":24,"props":949,"children":951},{"href":950},"/404#img-innertri",[952],{"type":16,"value":953},"Inner Triangle\nTessellation",{"type":16,"value":487},{"type":10,"tag":18,"props":956,"children":957},{},[958],{"type":10,"tag":492,"props":959,"children":963},{"alt":960,"src":961,"title":962},"innertri","https://data.vkdoc.net/images/innertri.svg","Inner Triangle Tessellation",[],{"type":10,"tag":18,"props":965,"children":966},{},[967],{"type":16,"value":968},"Once all the concentric triangles are produced and their edges are\nsubdivided, the area between each pair of adjacent inner triangles is filled\ncompletely with a set of non-overlapping triangles.\nIn this subdivision, two of the three vertices of each triangle are taken\nfrom adjacent vertices on a subdivided edge of one triangle; the third is\none of the vertices on the corresponding edge of the other triangle.\nIf the innermost triangle is degenerate (i.e., a point), the triangle\ncontaining it is subdivided into six triangles by connecting each of the six\nvertices on that triangle with the center point.\nIf the innermost triangle is not degenerate, that triangle is added to the\nset of generated triangles as-is.",{"type":10,"tag":18,"props":970,"children":971},{},[972],{"type":16,"value":973},"After the area corresponding to any inner triangles is filled, the\ntessellator generates triangles to cover the area between the outermost\ntriangle and the outermost inner triangle.\nTo do this, the temporary subdivision of the outer triangle edge above is\ndiscarded.\nInstead, the u = 0, v = 0, and w = 0 edges are subdivided\naccording to the first, second, and third outer tessellation levels,\nrespectively, and the tessellation spacing.\nThe original subdivision of the first inner triangle is retained.\nThe area between the outer and first inner triangles is completely filled by\nnon-overlapping triangles as described above.\nIf the first (and only) inner triangle is degenerate, a set of triangles is\nproduced by connecting each vertex on the outer triangle edges with the\ncenter point.",{"type":10,"tag":18,"props":975,"children":976},{},[977],{"type":16,"value":978},"After all triangles are generated, each vertex in the subdivided triangle is\nassigned a barycentric (u,v,w) coordinate based on its location relative to\nthe three vertices of the outer triangle.",{"type":10,"tag":18,"props":980,"children":981},{},[982],{"type":16,"value":983},"The algorithm used to subdivide the triangular domain in (u,v,w) space into\nindividual triangles is implementation-dependent.\nHowever, the set of triangles produced will completely cover the domain, and\nno portion of the domain will be covered by multiple triangles.",{"type":10,"tag":18,"props":985,"children":986},{},[987,989,995,997,1002],{"type":16,"value":988},"Output triangles are generated with a topology similar to\n",{"type":10,"tag":24,"props":990,"children":992},{"href":991},"/chapters/drawing#drawing-triangle-lists",[993],{"type":16,"value":994},"triangle lists",{"type":16,"value":996},", except that the order in which\neach triangle is generated, and the order in which the vertices are\ngenerated for each triangle, are implementation-dependent.\nHowever, the order of vertices in each triangle is consistent across the\ndomain as described in ",{"type":10,"tag":24,"props":998,"children":1000},{"href":999},"/chapters/tessellation#tessellation-vertex-winding-order",[1001],{"type":16,"value":735},{"type":16,"value":487},{"type":10,"tag":48,"props":1004,"children":1006},{"id":1005},"tessellation-quad-tessellation",[1007],{"type":16,"value":1008},"Quad Tessellation",{"type":10,"tag":18,"props":1010,"children":1011},{},[1012,1013,1018],{"type":16,"value":918},{"type":10,"tag":68,"props":1014,"children":1016},{"className":1015},[],[1017],{"type":16,"value":110},{"type":16,"value":1019},", a rectangle is subdivided\ninto a collection of triangles covering the area of the original rectangle.\nFirst, the original rectangle is subdivided into a regular mesh of\nrectangles, where the number of rectangles along the u = 0 and u\n= 1 (vertical) and v = 0 and v = 1 (horizontal) edges are\nderived from the first and second inner tessellation levels, respectively.\nAll rectangles, except those adjacent to one of the outer rectangle edges,\nare decomposed into triangle pairs.\nThe outermost rectangle edges are subdivided independently, using the first,\nsecond, third, and fourth outer tessellation levels to control the number of\nsubdivisions of the u = 0 (left), v = 0 (bottom), u = 1\n(right), and v = 1 (top) edges, respectively.\nThe area between the inner rectangles of the mesh and the outer rectangle\nedges are filled by triangles produced by joining the vertices on the\nsubdivided outer edges to the vertices on the edge of the inner rectangle\nmesh.",{"type":10,"tag":18,"props":1021,"children":1022},{},[1023,1025,1028,1029,1033],{"type":16,"value":1024},"If both clamped inner tessellation levels and all four clamped outer\ntessellation levels are exactly one, only a single triangle pair covering\nthe outer rectangle is generated.\nOtherwise, if either clamped inner tessellation level is one, that\ntessellation level is treated as though it was originally specified as\n1 +  ε and will result in a two- or three-segment\nsubdivision depending on the tessellation spacing.\nWhen used with fractional odd spacing, the three-segment subdivision ",{"type":10,"tag":33,"props":1026,"children":1027},{"type":137},[],{"type":16,"value":935},{"type":10,"tag":692,"props":1030,"children":1031},{},[1032],{"type":16,"value":940},{"type":16,"value":1034}," positioned on the edge of the rectangle.",{"type":10,"tag":18,"props":1036,"children":1037},{},[1038,1040,1045,1047,1053],{"type":16,"value":1039},"If any tessellation level is greater than one, tessellation begins by\nsubdividing the u = 0 and u = 1 edges of the outer rectangle\ninto m segments using the clamped and rounded first inner tessellation\nlevel and the tessellation spacing.\nThe v = 0 and v = 1 edges are subdivided into n segments\nusing the second inner tessellation level.\nEach vertex on the u = 0 and v = 0 edges are joined with the\ncorresponding vertex on the u = 1 and v = 1 edges to produce a\nset of vertical and horizontal lines that divide the rectangle into a grid\nof smaller rectangles.\nThe primitive generator emits a pair of non-overlapping triangles covering\neach such rectangle not adjacent to an edge of the outer rectangle.\nThe boundary of the region covered by these triangles forms an inner\nrectangle, the edges of which are subdivided by the grid vertices that lie\non the edge.\nIf either m or n is two, the inner rectangle is degenerate, and\none or both of the rectangle’s ",{"type":10,"tag":692,"props":1041,"children":1042},{},[1043],{"type":16,"value":1044},"edges",{"type":16,"value":1046}," consist of a single point.\nThis subdivision is illustrated in Figure ",{"type":10,"tag":24,"props":1048,"children":1050},{"href":1049},"/404#img-innerquad",[1051],{"type":16,"value":1052},"Inner Quad\nTessellation",{"type":16,"value":487},{"type":10,"tag":18,"props":1055,"children":1056},{},[1057],{"type":10,"tag":492,"props":1058,"children":1062},{"alt":1059,"src":1060,"title":1061},"innerquad","https://data.vkdoc.net/images/innerquad.svg","Inner Quad Tessellation",[],{"type":10,"tag":18,"props":1064,"children":1065},{},[1066,1068,1071,1073,1078],{"type":16,"value":1067},"After the area corresponding to the inner rectangle is filled, the\ntessellator ",{"type":10,"tag":33,"props":1069,"children":1070},{"type":131},[],{"type":16,"value":1072}," produce triangles to cover the area between the inner and\nouter rectangles.\nTo do this, the subdivision of the outer rectangle edge above is discarded.\nInstead, the u = 0, v = 0, u = 1, and v = 1 edges\nare subdivided according to the first, second, third, and fourth outer\ntessellation levels, respectively, and the tessellation spacing.\nThe original subdivision of the inner rectangle is retained.\nThe area between the outer and inner rectangles is completely filled by\nnon-overlapping triangles.\nTwo of the three vertices of each triangle are adjacent vertices on a\nsubdivided edge of one rectangle; the third is one of the vertices on the\ncorresponding edge of the other rectangle.\nIf either edge of the innermost rectangle is degenerate, the area near the\ncorresponding outer edges is filled by connecting each vertex on the outer\nedge with the single vertex making up the ",{"type":10,"tag":692,"props":1074,"children":1075},{},[1076],{"type":16,"value":1077},"inner edge",{"type":16,"value":487},{"type":10,"tag":18,"props":1080,"children":1081},{},[1082],{"type":16,"value":1083},"The algorithm used to subdivide the rectangular domain in (u,v) space into\nindividual triangles is implementation-dependent.\nHowever, the set of triangles produced will completely cover the domain, and\nno portion of the domain will be covered by multiple triangles.",{"type":10,"tag":18,"props":1085,"children":1086},{},[1087,1088,1092,1093,1097],{"type":16,"value":988},{"type":10,"tag":24,"props":1089,"children":1090},{"href":991},[1091],{"type":16,"value":994},{"type":16,"value":996},{"type":10,"tag":24,"props":1094,"children":1095},{"href":999},[1096],{"type":16,"value":735},{"type":16,"value":487},{"type":10,"tag":48,"props":1099,"children":1101},{"id":1100},"tessellation-isoline-tessellation",[1102],{"type":16,"value":1103},"Isoline Tessellation",{"type":10,"tag":18,"props":1105,"children":1106},{},[1107,1108,1113,1115,1120],{"type":16,"value":918},{"type":10,"tag":68,"props":1109,"children":1111},{"className":1110},[],[1112],{"type":16,"value":118},{"type":16,"value":1114},", a set of independent\nhorizontal line segments is drawn.\nThe segments are arranged into connected strips called ",{"type":10,"tag":692,"props":1116,"children":1117},{},[1118],{"type":16,"value":1119},"isolines",{"type":16,"value":1121},", where the\nvertices of each isoline have a constant v coordinate and u coordinates\ncovering the full range [0,1].\nThe number of isolines generated is derived from the first outer\ntessellation level; the number of segments in each isoline is derived from\nthe second outer tessellation level.\nBoth inner tessellation levels and the third and fourth outer tessellation\nlevels have no effect in this mode.",{"type":10,"tag":18,"props":1123,"children":1124},{},[1125,1127,1603],{"type":16,"value":1126},"As with quad tessellation above, isoline tessellation begins with a\nrectangle.\nThe u = 0 and u = 1 edges of the rectangle are subdivided\naccording to the first outer tessellation level.\nFor the purposes of this subdivision, the tessellation spacing mode is\nignored and treated as equal_spacing.\nAn isoline is drawn connecting each vertex on the u = 0 rectangle edge\nto the corresponding vertex on the u = 1 rectangle edge, except that\nno line is drawn between (0,1) and (1,1).\nIf the number of isolines on 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