# Ray Traversal

The ray traversal process identifies and handles intersections between a ray and geometries in an acceleration structure.

Ray traversal cannot be started by a Vulkan API command directly - a shader
must execute
`OpRayQueryProceedKHR`

or
a pipeline trace ray instruction
.
When the `rayTracingPipeline`

feature
is enabled, `OpTraceRayKHR`

can be used for ray tracing
in a ray tracing pipeline.
When the `rayQuery`

feature is enabled,
`OpRayQueryProceedKHR`

can be used in any shader stage.

## Ray Intersection Candidate Determination

Once tracing begins, rays are first tested against instances in a top-level acceleration structure. A ray that intersects an instance will be transformed into the space of the instance to continue traversal within that instance; therefore the transform matrix stored in the instance must be invertible.

In case multiple instances are intersected by a ray, the ray transformation into the space of the instance is invariant under the order in which these instances are encountered in the top-level acceleration structure.

Applying multiple forward and reverse transforms to a ray to transition from one instance to another could result in accumulated errors. Thus an implementation should behave as if the ray is transformed from the origin for each instance independently.

Next, rays are tested against geometries in a bottom-level acceleration structure to determine if a hit occurred between them, initially based only on their geometric properties (i.e. their vertices). The implementation performs similar operations to that of rasterization, but with the effective viewport determined by the parameters of the ray, and the geometry transformed into a space determined by that viewport.

The vertices of each primitive are transformed from acceleration structure
space * _{as}* to ray space

*according to the ray origin and direction as follows:*

_{r}$\mathbf{a}$ is the axis of rotation from the unnormalized ray direction vector $\mathbf{d}$ to the axis vector $\mathbf{k}$:

$\mathbf{a} = \begin{cases} \frac{\mathbf{d} \times \mathbf{k}}{|| \mathbf{d} \times \mathbf{k} ||} & \mathrm{if}\\; || \mathbf{d} \times \mathbf{k} || \ne 0 \\\ \left(\begin{array}{c} 0 \\\ 1 \\\ 0 \end{array} \right) & \mathrm{if}\\; || \mathbf{d} \times \mathbf{k} || = 0 \\\ \end{cases}$$\mathit{s}$ and $\mathit{c}$ are the sine and cosine of the angle of rotation about $\mathbf{a}$ from $\mathbf{d}$ to $\mathbf{k}$:

$\begin{aligned} c &= {{\mathbf{d} \cdot \mathbf{k}}\over{||\mathbf{d}||}} \\\ s &= \sqrt{1 - c^2} \end{aligned}$$\mathbf{k}$ is the unit vector:

$\mathbf{k} = \left( \begin{array}{c} 0 \\\ 0 \\\ -1 \end{array} \right)$$\mathbf{o}$ and $\mathbf{d}$ are the ray origin and
unnormalized direction, respectively; the vector described by x_{as},
y_{as}, and z_{as} is any position in acceleration structure
space; and the vector described by x_{r}, y_{r}, and z_{r} is
the same position in ray space.

An *intersection candidate* is a unique point of intersection between a ray
and a geometric primitive.
For any primitive that has within its bounds a position
$\mathbf{xyz\_{as}}$ such that

(where $t = {-{z\_r}\over{||\mathbf{d}||}}$), an intersection candidate exists.

Triangle primitive bounds consist of all points on the plane formed by the three vertices and within the bounds of the edges between the vertices, subject to the watertightness constraints below. AABB primitive bounds consist of all points within an implementation-defined bound which includes the specified box.

The bounds of the AABB including all points internal to the bound implies that a ray started within the AABB will hit that AABB.

The determination of this condition is performed in an implementation specific manner, and may be performed with floating-point operations. Due to the complexity and number of operations involved, inaccuracies are expected, particularly as the scale of values involved begins to diverge. Implementations should take efforts to maintain as much precision as possible.

One very common case is when geometries are close to each other at some
distance from the origin in acceleration structure space, where an effect
similar to `z-fighting`

is likely to be observed.
Applications can mitigate this by ensuring their detailed geometries remain
close to the origin.

Another likely case is when the origin of a ray is set to a position on a
previously intersected surface, and its t_{min} is zero or near zero;
an intersection may be detected on the emitting surface.
This case can usually be mitigated by offsetting t_{min} slightly.

For a motion primitive or a motion instance, the positions for intersection
are evaluated at the time specified in the `time`

parameter to
`OpTraceRayMotionNV`

by interpolating between the two endpoints as
specified for the given motion type.
If a motion acceleration structure is traced with `OpTraceRayKHR`

, it
behaves as a `OpTraceRayMotionNV`

with `time`

of 0.0.

In the case of AABB geometries, implementations may increase their size in an acceleration structure in order to mitigate precision issues. This may result in false positive intersections being reported to the application.

For triangle intersection candidates, the b and c

barycentric coordinates on the triangle
where the above condition is met are made available to future shading.
If the ray was traced with a pipeline trace
ray instruction, these values are available as a vector of 2 32-bit
floating-point values in the `HitAttributeKHR`

storage class.

Once an intersection candidate is determined, it proceeds through the following operations, in order:

- Ray Intersection Culling
- Ray Intersection Confirmation
- Ray Closest Hit Determination
- Ray Result Determination

The sections below describe the exact details of these tests. There is no ordering guarantee between operations performed on different intersection candidates.

### Watertightness

For a set of triangles with identical transforms, within a single instance:

- Any set of two or more triangles where all triangles have one vertex
with an identical position value, that vertex is a
*shared vertex*. - Any set of two triangles with two shared vertices that were specified in
the same winding order in each triangle have
a
*shared edge*defined by those vertices.

A *closed fan* is a set of three or more triangles where:

- All triangles in the set have the same shared vertex as one of their vertices.
- All edges that include the above vertex are shared edges.
- All above shared edges are shared by exactly two triangles from the set.
- No two triangles in the set intersect, except at shared edges.
- Every triangle in the set is joined to every other triangle in the set by a series of the above shared edges.

Implementations should not double-hit or miss when a ray intersects a shared edge, or a shared vertex of a closed fan.

## Ray Intersection Culling

Candidate intersections go through several phases of culling before confirmation as an actual hit. There is no particular ordering dependency between the different culling operations.

### Ray Primitive Culling

If the `rayTraversalPrimitiveCulling`

or `rayQuery`

features are enabled, the `SkipTrianglesKHR`

and
`SkipAABBsKHR`

ray flags can be specified when tracing a ray.
`SkipTrianglesKHR`

and `SkipAABBsKHR`

are mutually exclusive.
`SkipTrianglesKHR`

is also mutually exclusive with
`CullBackFacingTrianglesKHR`

and `CullFrontFacingTrianglesKHR`

.

If `SkipTrianglesKHR`

was included in the `Ray Flags`

operand of the ray
trace instruction, and the intersection is with a triangle primitive, the
intersection is dropped, and no further processing of this intersection
occurs.
If `VK_PIPELINE_CREATE_RAY_TRACING_SKIP_TRIANGLES_BIT_KHR`

was included
in the pipeline, traversal with pipeline
trace ray instructions will all behave as if `SkipTrianglesKHR`

was
included in their `Ray Flags`

operand.

If `SkipAABBsKHR`

was included in the `Ray Flags`

operand of the ray
trace instruction, and the intersection is with an AABB primitive, the
intersection is dropped, and no further processing of this intersection
occurs.
If `VK_PIPELINE_CREATE_RAY_TRACING_SKIP_AABBS_BIT_KHR`

was included in
the pipeline, traversal with pipeline trace
ray instructions will all behave as if `SkipAABBsKHR`

was included in
their `Ray Flags`

operand.

### Ray Mask Culling

Instances can be made invisible to particular rays based on the value of
VkAccelerationStructureInstanceKHR::`mask`

used to add that
instance to a top-level acceleration structure, and the `Cull Mask`

parameter used to trace the ray.

For the instance which is intersected, if `mask`

& `Cull Mask`

==
0, the intersection is dropped, and no further processing occurs.

### Ray Face Culling

As in polygon rasterization, one of the stages of ray traversal is to determine if a triangle primitive is back- or front-facing, and primitives can be culled based on that facing.

If the intersection candidate is with an AABB primitive, this operation is skipped.

### Determination

When a ray intersects a triangle primitive, the order that vertices are specified for the polygon affects whether the ray intersects the front or back face. Front or back facing is determined in the same way as they are for rasterization, based on the sign of the polygon’s area but using the ray space coordinates instead of framebuffer coordinates. One way to compute this area is:

$a = -{1 \over 2}\sum\_{i=0}^{n-1} x\_r^i y\_r^{i \oplus 1} - x\_r^{i \oplus 1} y\_r^i$where $x\_r^i$ and $y\_r^i$ are the x and y

ray space coordinates of the ith vertex of the n-vertex polygon (vertices are numbered starting at zero for the purposes of this computation) and i ⊕ 1 is (i + 1) mod n.

By default, if a is negative then the intersection is with the front
face of the triangle, otherwise it is with the back face.
If `VK_GEOMETRY_INSTANCE_TRIANGLE_FLIP_FACING_BIT_KHR`

is included in
VkAccelerationStructureInstanceKHR::`flags`

for the instance
containing the intersected triangle, this determination is reversed.
Additionally, if a is 0, the intersection candidate is treated as not
intersecting with any face, irrespective of the sign.

In a left-handed coordinate system, an intersection will be with the front
face of a triangle if the vertices of the triangle, as defined in index
order, appear from the ray’s perspective in a clockwise rotation order.
`VK_GEOMETRY_INSTANCE_TRIANGLE_FLIP_FACING_BIT_KHR`

was previously
annotated as
`VK_GEOMETRY_INSTANCE_TRIANGLE_FRONT_COUNTERCLOCKWISE_BIT_KHR`

because
of this.

If the ray was traced with a pipeline trace
ray instruction, the `HitKindKHR`

built-in is set to
`HitKindFrontFacingTriangleKHR`

if the intersection is with front-facing
geometry, and `HitKindBackFacingTriangleKHR`

if the intersection is with
back-facing geometry, for shader stages considering this intersection.

If the ray was traced with `OpRayQueryProceedKHR`

,
`OpRayQueryGetIntersectionFrontFaceKHR`

will return true for intersection
candidates with front faces, or false for back faces.

### Culling

If `CullBackFacingTrianglesKHR`

was included in the `Ray Flags`

parameter
of the ray trace instruction, and the intersection is determined as with the
back face of a triangle primitive, the intersection is dropped, and no
further processing of this intersection occurs.

If `CullFrontFacingTrianglesKHR`

was included in the `Ray Flags`

parameter of the ray trace instruction, and the intersection is determined
as with the front face of a triangle primitive, the intersection is dropped,
and no further processing of this intersection occurs.

This culling is disabled if
`VK_GEOMETRY_INSTANCE_TRIANGLE_FACING_CULL_DISABLE_BIT_KHR`

was included
in VkAccelerationStructureInstanceKHR::`flags`

for the instance
which the intersected geometry belongs to.

Intersection candidates that have not intersected with any face (a == 0) are unconditionally culled, irrespective of ray flags and geometry instance flags.

The `CullBackFacingTrianglesKHR`

and `CullFrontFacingTrianglesKHR`

`Ray Flags`

are mutually exclusive.

### Ray Opacity Culling

Each geometry in the acceleration structure may be considered either opaque or not. Opaque geometries continue through traversal as normal, whereas non-opaque geometries need to be either confirmed or discarded by shader code. Intersection candidates can also be culled based on their opacity.

### Determination

Each individual intersection candidate is initially determined as opaque if
`VK_GEOMETRY_OPAQUE_BIT_KHR`

was included in the
VkAccelerationStructureGeometryKHR::`flags`

when the geometry it
intersected with was built, otherwise it is considered non-opaque.

If the geometry includes an opacity micromap, the opacity of the intersection at this point is instead derived as described in Ray Opacity Micromap.

If the intersection candidate was generated by an intersection shader, the intersection is initially considered to have opacity matching the AABB candidate that it was generated from.

However, this opacity can be overridden when it is built into an instance.
Setting `VK_GEOMETRY_INSTANCE_FORCE_OPAQUE_BIT_KHR`

in
VkAccelerationStructureInstanceKHR::`flags`

will force all
geometries in the instance to be considered opaque.
Similarly, setting `VK_GEOMETRY_INSTANCE_FORCE_NO_OPAQUE_BIT_KHR`

will
force all geometries in the instance to be considered non-opaque.

This can again be overridden by including `OpaqueKHR`

or `NoOpaqueKHR`

in the `Ray Flags`

parameter when tracing a ray.
`OpaqueKHR`

forces all geometries to behave as if they are opaque,
regardless of their build parameters.
Similarly, `NoOpaqueKHR`

forces all geometries to behave as if they are
non-opaque.

If the ray was traced with `OpRayQueryProceedKHR`

, to determine the
opacity of AABB intersection candidates,
`OpRayQueryGetIntersectionCandidateAABBOpaqueKHR`

can be used.
This instruction will return `true`

for opaque intersection candidates,
and `false`

for non-opaque intersection candidates.

### Culling

If `CullOpaqueKHR`

is included in the `Ray Flags`

parameter when tracing
a ray, an intersection with a geometry that is considered opaque is dropped,
and no further processing occurs.

If `CullNoOpaqueKHR`

is included in the `Ray Flags`

parameter when
tracing a ray, an intersection with a geometry that is considered non-opaque
is dropped, and no further processing occurs.

The `OpaqueKHR`

, `NoOpaqueKHR`

, `CullOpaqueKHR`

, and
`CullNoOpaqueKHR`

`Ray Flags`

are mutually exclusive.

### Ray Opacity Micromap

A `VK_GEOMETRY_TYPE_TRIANGLES_KHR`

geometry in the acceleration
structure may have an opacity micromap associated with it to give
finer-grained opacity information.

If the intersection candidate is with a geometry with an associated opacity
micromap and `VK_GEOMETRY_INSTANCE_DISABLE_OPACITY_MICROMAPS_EXT`

is not
set in its instance then the micromap is used to determine geometry opacity
instead of the `VK_GEOMETRY_OPAQUE_BIT_KHR`

flag in the geometry.

The opacity information in the micromap object is accessed using the candidate intersection u and v coordinates. The integer u and v are computed from ⌊u⌋ + ⌊v⌋, clamping ⌊u⌋ as needed to keep the sum less than or equal to 1 << subdivisionlevel. These values are mapped into a linear index with a space filling curve which is defined recursively by traversing into the sub-triangle nearest vertex 0, then the middle triangle with ordering flipped, then nearest vertex 1 then nearest vertex 2.

This encoding is spatially coherent, purely hierarchical, and allows a bit-parallel conversion between barycentric address and index values.

See the appendix for reference code implementing this mapping.

The result of the opacity micromap lookup and operations is to treat the
intersection as opaque, non-opaque, or ignored.
The interpretation of the values depends on
`VK_GEOMETRY_INSTANCE_FORCE_OPACITY_MICROMAP_2_STATE_EXT`

in the
instance of the candidate intersection or
`ForceOpacityMicromap2StateEXT`

ray flags on the ray.
If either is set, the opacity micromap information is interpreted in 2 state
override mode.
If the result of the micromap lookup is to treat the intersection candidate
as ignored, no further processing of that candidate is done.

If the associated opacity micromap has format
`VK_OPACITY_MICROMAP_FORMAT_2_STATE_EXT`

, each element of the micromap
is represented by a single bit at the index derived above.

If the associated opacity micromap has format
`VK_OPACITY_MICROMAP_FORMAT_4_STATE_EXT`

, each element is represented by
a two bit value at the index derived above.

4 State value | 2 State value | Special index value | 2 State override | Result |
---|---|---|---|---|

0 | 0 | Y | Ignored | |

0 | 0 | N | Ignored | |

1 | 1 | Y | Opaque | |

1 | 1 | N | Opaque | |

2 | Y | Ignored | ||

2 | N | Non-opaque | ||

3 | Y | Opaque | ||

3 | N | Non-opaque |

## Ray Intersection Confirmation

Depending on the opacity of intersected geometry and whether it is a triangle or an AABB, candidate intersections are further processed to determine the eventual hit result. Candidates generated from AABB intersections run through the same confirmation process as triangle hits.

### AABB Intersection Candidates

For an intersection candidate with an AABB geometry generated by Ray Intersection Candidate Determination, shader code is executed to determine whether any hits should be reported to the traversal infrastructure; no further processing of this intersection candidate occurs. The occurrence of an AABB intersection candidate does not guarantee the ray intersects the primitive bounds. To avoid propagating false intersections the application should verify the intersection candidate before reporting any hits.

If the ray was traced with a pipeline trace
ray instruction, an intersection shader is
invoked from the Shader Binding Table according to the
specified indexing for the
intersected geometry.
If this shader calls `OpReportIntersectionKHR`

, a new intersection
candidate is generated as described
below.
If the intersection shader is `VK_SHADER_UNUSED_KHR`

(which is only
allowed for a zero shader group) then no further processing of the
intersection candidate occurs.

Each new candidate generated as a result of this processing is a generated
intersection candidate that intersects the AABB geometry, with a t
value equal to the `Hit`

parameter of the `OpReportIntersectionKHR`

instruction.
The new generated candidate is then independently run through
Ray Intersection Confirmation as a
generated
intersection.

If the ray was traced with `OpRayQueryProceedKHR`

, control is returned to
the shader which executed `OpRayQueryProceedKHR`

, returning `true`

.
The resulting ray query has a candidate intersection type of
`RayQueryCandidateIntersectionAABBKHR`

.
`OpRayQueryGenerateIntersectionKHR`

can be called to commit a new
intersection candidate with committed intersection type of
`RayQueryCommittedIntersectionGeneratedKHR`

.
Further ray query processing can be continued by executing
`OpRayQueryProceedKHR`

with the same ray query, or intersection can be
terminated with `OpRayQueryTerminateKHR`

.
Unlike rays traced with a pipeline trace
ray instruction, candidates generated in this way skip generated
intersection candidate confirmation; applications should make this
determination before generating the intersection.

This operation may be executed multiple times for the same intersection candidate.

### Triangle and Generated Intersection Candidates

For triangle and generated intersection candidates, additional shader code may be executed based on the intersection’s opacity.

If the intersection is opaque, the candidate is immediately confirmed as a valid hit and passes to the next stage of processing.

For non-opaque intersection candidates, shader code is executed to determine whether a hit occurred or not.

If the ray was traced with a pipeline trace
ray instruction, an any-hit shader is invoked from
the Shader Binding Table according to the specified indexing.
If this shader calls `OpIgnoreIntersectionKHR`

, the candidate is dropped
and no further processing of the candidate occurs.
If the any-hit shader identified is
`VK_SHADER_UNUSED_KHR`

, the candidate is immediately confirmed as a
valid hit and passes to the next stage of processing.

If the ray was traced with `OpRayQueryProceedKHR`

, control is returned to
the shader which executed `OpRayQueryProceedKHR`

, returning `true`

.
As only triangle candidates participate in this operation with ray queries,
the resulting candidate intersection type is always
`RayQueryCandidateIntersectionTriangleKHR`

.
`OpRayQueryConfirmIntersectionKHR`

can be called on the ray query to
confirm the candidate as a hit with committed intersection type of
`RayQueryCommittedIntersectionTriangleKHR`

.
Further ray query processing can be continued by executing
`OpRayQueryProceedKHR`

with the same ray query, or intersection can be
terminated with `OpRayQueryTerminateKHR`

.
If `OpRayQueryConfirmIntersectionKHR`

has not been executed, the
candidate is dropped and no further processing of the candidate occurs.

This operation may be executed multiple times for the same intersection
candidate unless `VK_GEOMETRY_NO_DUPLICATE_ANY_HIT_INVOCATION_BIT_KHR`

was specified for the intersected geometry.

## Ray Closest Hit Determination

Unless the ray was traced with the `TerminateOnFirstHitKHR`

ray flag, the
implementation must track the closest confirmed hit until all geometries
have been tested and either confirmed or dropped.

After an intersection candidate is confirmed, its t value is compared
to t_{max} to determine which intersection is closer, where t is
the parametric distance along the ray at which the intersection occurred.

- If t < t
_{max}, t_{max}is set to t and the candidate is set as the current closest hit. - If t > t
_{max}, the candidate is dropped and no further processing of that candidate occurs. - If t = t
_{max}, the candidate may be set as the current closest hit or dropped.

If `TerminateOnFirstHitKHR`

was included in the `Ray Flags`

used to trace
the ray, once the first hit is confirmed, the ray trace is terminated.

## Ray Result Determination

Once all candidates have finished processing the prior stages, or if the ray is forcibly terminated, the final result of the ray trace is determined.

If a closest hit result was identified by Ray Closest Hit Determination, a closest hit has occurred, otherwise the final result is a miss.

For rays traced with pipeline trace ray
instructions which can invoke a closest hit shader, if a closest hit result
was identified, a closest hit shader is invoked
from the Shader Binding Table according to the
specified indexing for the
intersected geometry.
Control returns to the shader that executed the
pipeline trace ray instruction once this
shader returns.
This shader is skipped if either the ray flags included
`SkipClosestHitShaderKHR`

, or if the closest hit
shader identified is `VK_SHADER_UNUSED_KHR`

.

For rays traced with a pipeline trace ray
instruction where no hit result was identified, the miss
shader identified by the `Miss Index`

parameter of the instruction is
invoked.
Control returns to the shader that executed the pipeline trace ray
instruction once this shader returns.
This shader is skipped if the miss shader identified is
`VK_SHADER_UNUSED_KHR`

.

If the ray was traced with `OpRayQueryProceedKHR`

, control is returned to
the shader which executed `OpRayQueryProceedKHR`

, returning `false`

.
If a closest hit was identified by Ray Closest Hit Determination, the
ray query will now have a committed intersection type of
`RayQueryCommittedIntersectionGeneratedKHR`

or
`RayQueryCommittedIntersectionTriangleKHR`

.
If no closest hit was identified, the committed intersection type will be
`RayQueryCommittedIntersectionNoneKHR`

.

No further processing of a ray query occurs after this result is determined.