440 lines
23 KiB
Plaintext
440 lines
23 KiB
Plaintext
// Copyright (c) 2015-2016 The Khronos Group Inc.
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// Copyright notice at https://www.khronos.org/registry/speccopyright.html
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[[tessellation]]
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= Tessellation
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Tessellation involves three pipeline stages. First, a
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<<shaders-tessellation-control,tessellation control shader>> transforms
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control points of a patch and can: produce per-patch data. Second, a
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fixed-function tessellator generates multiple primitives corresponding to a
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tessellation of the patch in (u,v) or (u,v,w) parameter space. Third, a
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<<shaders-tessellation-evaluation,tessellation evaluation shader>>
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transforms the vertices of the tessellated patch, for example to compute
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their positions and attributes as part of the tessellated surface. The
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tessellator is enabled when the pipeline contains both a tessellation
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control shader and a tessellation evaluation shader.
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== Tessellator
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If a pipeline includes both tessellation shaders (control and evaluation),
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the tessellator consumes each input patch (after vertex shading) and
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produces a new set of independent primitives (points, lines, or triangles).
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These primitives are logically produced by subdividing a geometric primitive
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(rectangle or triangle) according to the per-patch tessellation levels
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written by the tessellation control shader. This subdivision is performed in
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an implementation-dependent manner. If no tessellation shaders are present
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in the pipeline, the tessellator is disabled and incoming primitives are
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passed through without modification.
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The type of subdivision performed by the tessellator is
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specified by an code:OpExecutionMode instruction in the tessellation
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evaluation or tessellation control shader using one of execution modes
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code:Triangles, code:Quads, and code:IsoLines. Other
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tessellation-related execution modes can: also be specified in either the
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tessellation control or tessellation evaluation shaders, and if they are
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specified in both then the modes must: be the same.
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Tessellation execution modes include:
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* code:Triangles, code:Quads, and code:IsoLines. These control the type of
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subdivision and topology of the output primitives. One mode must: be set
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in at least one of the tessellation shader stages.
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* code:VertexOrderCw and code:VertexOrderCcw. These control the
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orientation of triangles generated by the tessellator. One mode must: be
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set in at least one of the tessellation shader stages.
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* code:PointMode. Controls generation of points rather than triangles or
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lines. This functionality defaults to disabled, and is enabled if either
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shader stage includes the execution mode.
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* code:SpacingEqual, code:SpacingFractionalEven, and
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code:SpacingFractionalOdd. Controls the spacing of segments on the edges
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of tessellated primitives. One mode must: be set in at least one of the
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tessellation shader stages.
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* code:OutputVertices. Controls the size of the output patch of the
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tessellation control shader. One value must: be set in at least one of
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the tessellation shader stages.
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For triangles, the tessellator subdivides a triangle primitive into
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smaller triangles. For quads, the tessellator subdivides a rectangle
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primitive into smaller triangles. For isolines, the tessellator
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subdivides a rectangle primitive into a collection of line segments arranged
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in strips stretching across the rectangle in the latexmath:[$u$] dimension
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(i.e. the coordinates in code:TessCoord are of the form (0,x) through (1,x)
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for all tessellation evaluation shader invocations that share a line).
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Each vertex produced by the tessellator has an associated (u,v,w) or (u,v)
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position in a normalized parameter space, with parameter values in the range
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latexmath:[$[0,1\]$], as illustrated in figure
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<<img-tessellation-topology>>.
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[[img-tessellation-topology,Domain parameterization for tessellation primitive modes]]
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.Domain parameterization for tessellation primitive modes
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image:images/tessparam.{svgpdf}["Domain parameterization for tessellation primitive modes",{fullimagewidth}]
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For triangles, the vertex's position is a barycentric coordinate (u,v,w),
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where u + v + w = 1.0, and indicates the relative influence of the three
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vertices of the triangle on the position of the vertex. For quads and
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isolines, the position is a (u,v) coordinate indicating the relative
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horizontal and vertical position of the vertex relative to the subdivided
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rectangle. The subdivision process is explained in more detail in subsequent
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sections.
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== Tessellator Patch Discard
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A patch is discarded by the tessellator if any
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relevant outer tessellation level is less than or equal to zero.
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Patches will also be discarded if any relevant outer tessellation level
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corresponds to a floating-point NaN (not a number) in implementations
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supporting NaN.
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No new primitives are generated and the tessellation evaluation shader is
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not executed for patches that are discarded. For code:Quads, all four outer
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levels are relevant. For code:Triangles and code:IsoLines, only the first
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three or two outer levels, respectively, are relevant. Negative inner levels
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will not cause a patch to be discarded; they will be clamped as described
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below.
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[[tessellation-tessellator-spacing]]
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== Tessellator Spacing
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Each of the tessellation levels is used to determine the number and
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spacing of segments used to subdivide a corresponding edge. The method
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used to derive the number and spacing of segments is specified by an
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code:OpExecutionMode in the tessellation control or tessellation evaluation
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shader using one of the identifiers code:SpacingEqual,
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code:SpacingFractionalEven, or code:SpacingFractionalOdd.
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If code:SpacingEqual is used, the floating-point tessellation level is first
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clamped to latexmath:[$[1,\mathit{maxLevel}\]$], where
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latexmath:[$\mathit{maxLevel}$] is the implementation-dependent maximum
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tessellation level
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(sname:VkPhysicalDeviceLimits::pname:maxTessellationGenerationLevel). The
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result is rounded up to the nearest integer latexmath:[$n$], and the
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corresponding edge is divided into latexmath:[$n$] segments of equal length
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in (u,v) space.
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If code:SpacingFractionalEven is used, the tessellation level is first
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clamped to latexmath:[$[2,\mathit{maxLevel}\]$] and then rounded up to the
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nearest even integer latexmath:[$n$]. If code:SpacingFractionalOdd is used,
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the tessellation level is clamped to latexmath:[$[1,\mathit{maxLevel}-1\]$]
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and then rounded up to the nearest odd integer latexmath:[$n$]. If
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latexmath:[$n$] is one, the edge will not be subdivided. Otherwise, the
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corresponding edge will be divided into latexmath:[$n-2$] segments of equal
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length, and two additional segments of equal length that are typically
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shorter than the other segments. The length of the two additional segments
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relative to the others will decrease monotonically with
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latexmath:[$n-f$], where latexmath:[$f$] is the clamped floating-point
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tessellation level. When latexmath:[$n-f$] is zero, the additional segments
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will have equal length to the other segments. As latexmath:[$n-f$]
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approaches 2.0, the relative length of the additional segments approaches
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zero. The two additional segments should: be placed symmetrically on
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opposite sides of the subdivided edge. The relative location of these two
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segments is implementation-dependent, but must: be identical for any pair of
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subdivided edges with identical values of latexmath:[$f$].
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When the tessellator produces triangles (in the code:Triangles or
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code:Quads modes), the orientation of all triangles is specified with
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an code:OpExecutionMode of code:VertexOrderCw or code:VertexOrderCcw in the
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tessellation control or tessellation evaluation shaders. If the order is
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code:VertexOrderCw, the vertices of all generated triangles will have
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clockwise ordering in (u,v) or (u,v,w) space. If the order is
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code:VertexOrderCcw, the vertices will have counter-clockwise ordering.
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The vertices of a triangle have counter-clockwise ordering if
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[latexmath]
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++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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\[
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a = u_0 v_1 - u_1 v_0 + u_1 v_2 - u_2 v_1 + u_2 v_0 - u_0 v_2
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\]
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++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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is positive, and clockwise ordering if latexmath:[$a$] is negative.
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latexmath:[$u_i$] and latexmath:[$v_i$] are the latexmath:[$u$] and
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latexmath:[$v$] coordinates in normalized parameter space of the
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latexmath:[$i$]th vertex of the triangle.
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[NOTE]
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.Note
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====
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The value latexmath:[$a$] is proportional (with a positive factor) to the
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signed area of the triangle.
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In code:Triangles mode, even though the vertex coordinates have a
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latexmath:[$w$] value, it does not participate directly in the computation
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of latexmath:[$a$], being an affine combination of latexmath:[$u$] and
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latexmath:[$v$].
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====
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For all primitive modes, the tessellator is capable of generating points
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instead of lines or triangles. If the tessellation control or tessellation
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evaluation shader specifies the code:OpExecutionMode code:PointMode, the
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primitive generator will generate one point for each distinct vertex
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produced by tessellation. Otherwise, the tessellator will produce a
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collection of line segments or triangles according to the primitive mode.
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When tessellating triangles or quads in point mode with fractional odd
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spacing, the tessellator may: produce _interior vertices_ that are
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positioned on the edge of the patch if an inner tessellation level is less
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than or equal to one. Such vertices are considered distinct from vertices
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produced by subdividing the outer edge of the patch, even if there are pairs
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of vertices with identical coordinates.
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The points, lines, or triangles produced by the tessellator
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are passed to subsequent pipeline stages in an
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implementation-dependent order.
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[[tessellation-triangle-tessellation]]
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== Triangle Tessellation
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If the tessellation primitive mode is code:Triangles, an equilateral
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triangle is subdivided into a collection of triangles covering the area of
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the original triangle. First, the original triangle is subdivided into a
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collection of concentric equilateral triangles. The edges of each of these
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triangles are subdivided, and the area between each triangle pair is filled
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by triangles produced by joining the vertices on the subdivided edges. The
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number of concentric triangles and the number of subdivisions along each
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triangle except the outermost is derived from the first inner tessellation
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level. The edges of the outermost triangle are subdivided independently,
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using the first, second, and third outer tessellation levels to control the
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number of subdivisions of the latexmath:[$u=0$] (left), latexmath:[$v=0$]
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(bottom), and latexmath:[$w=0$] (right) edges, respectively. The second
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inner tessellation level and the fourth outer tessellation level have no
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effect in this mode.
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If the first inner tessellation level and all three outer tessellation
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levels are exactly one after clamping and rounding, only a single triangle
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with (u,v,w) coordinates of (0,0,1), (1,0,0), and (0,1,0) is generated.
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If the inner tessellation level is one and any of the outer tessellation
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levels is greater than one, the inner tessellation level is treated as
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though it were originally specified as latexmath:[$1+\epsilon$] and will
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result in a two- or three-segment subdivision depending on the tessellation
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spacing. When used with fractional odd spacing, the three-segment
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subdivision may: produce _inner vertices_ positioned on the edge of the
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triangle.
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If any tessellation level is greater than one, tessellation begins by
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producing a set of concentric inner triangles and subdividing their edges.
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First, the three outer edges are temporarily subdivided using the clamped
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and rounded first inner tessellation level and the specified tessellation
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spacing, generating latexmath:[$n$] segments. For the outermost inner
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triangle, the inner triangle is degenerate -- a single point at the center
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of the triangle -- if latexmath:[$n$] is two. Otherwise, for each corner of
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the outer triangle, an inner triangle corner is produced at the intersection
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of two lines extended perpendicular to the corner's two adjacent edges
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running through the vertex of the subdivided outer edge nearest that corner.
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If latexmath:[$n$] is three, the edges of the inner triangle are not
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subdivided and is the final triangle in the set of concentric triangles.
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Otherwise, each edge of the inner triangle is divided into latexmath:[$n-2$]
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segments, with the latexmath:[$n-1$] vertices of this subdivision produced
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by intersecting the inner edge with lines perpendicular to the edge running
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through the latexmath:[$n-1$] innermost vertices of the subdivision of the
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outer edge. Once the outermost inner triangle is subdivided, the previous
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subdivision process repeats itself, using the generated triangle as an outer
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triangle. This subdivision process is illustrated in <<img-innertri,Inner
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Triangle Tessellation>>.
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[[img-innertri,Inner Triangle Tessellation]]
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.Inner Triangle Tessellation
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image:images/innertri.{svgpdf}["Inner Triangle Tessellation",{fullimagewidth}]
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// TODO: Add caption:
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// Inner triangle tessellation with inner tessellation
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// levels of (a) five and (b) four, respectively (not to scale). Solid
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// black circles depict vertices along the edges of the concentric
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// triangles. The edges of inner triangles are subdivided by intersecting
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// the edge with segments perpendicular to the edge passing through each
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// inner vertex of the subdivided outer edge. Dotted lines depict edges
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// connecting corresponding vertices on the inner and outer triangle
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// edges.
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Once all the concentric triangles are produced and their edges are
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subdivided, the area between each pair of adjacent inner triangles is
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filled completely with a set of non-overlapping triangles. In this
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subdivision, two of the three vertices of each triangle are taken from
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adjacent vertices on a subdivided edge of one triangle; the third is one
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of the vertices on the corresponding edge of the other triangle. If the
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innermost triangle is degenerate (i.e., a point), the triangle containing
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it is subdivided into six triangles by connecting each of the six vertices
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on that triangle with the center point. If the innermost triangle is not
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degenerate, that triangle is added to the set of generated triangles
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as-is.
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After the area corresponding to any inner triangles is filled, the
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tessellator generates triangles to cover the area between the outermost
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triangle and the outermost inner triangle. To do this, the temporary
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subdivision of the outer triangle edge above is discarded. Instead, the
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latexmath:[$u=0$], latexmath:[$v=0$], and latexmath:[$w=0$] edges are
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subdivided according to the first, second, and third outer tessellation
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levels, respectively, and the tessellation spacing. The original subdivision
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of the first inner triangle is retained. The area between the outer and
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first inner triangles is completely filled by non-overlapping triangles as
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described above. If the first (and only) inner triangle is degenerate, a set
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of triangles is produced by connecting each vertex on the outer triangle
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edges with the center point.
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After all triangles are generated, each vertex in the subdivided triangle
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is assigned a barycentric (u,v,w) coordinate based on its location
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relative to the three vertices of the outer triangle.
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The algorithm used to subdivide the triangular domain in (u,v,w) space into
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individual triangles is implementation-dependent. However, the set of
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triangles produced will completely cover the domain, and no portion of the
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domain will be covered by multiple triangles. The order in which the
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generated triangles passed to subsequent pipeline stages and the order of
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the vertices in those triangles are both implementation-dependent. However,
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when depicted in a manner similar to <<img-innertri,Inner Triangle
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Tessellation>>, the order of the vertices in the generated triangles will be
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either all clockwise or all counter-clockwise, according to the vertex order
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layout declaration.
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[[tessellation-quad-tessellation]]
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== Quad Tessellation
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If the tessellation primitive mode is code:Quads, a rectangle is subdivided
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into a collection of triangles covering the area of the original rectangle.
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First, the original rectangle is subdivided into a regular mesh of
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rectangles, where the number of rectangles along the latexmath:[$u=0$] and
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latexmath:[$u=1$] (vertical) and latexmath:[$v=0$] and latexmath:[$v=1$]
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(horizontal) edges are derived from the first and second inner tessellation
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levels, respectively. All rectangles, except those adjacent to one of the
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outer rectangle edges, are decomposed into triangle pairs. The outermost
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rectangle edges are subdivided independently, using the first, second,
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third, and fourth outer tessellation levels to control the number of
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subdivisions of the latexmath:[$u=0$] (left), latexmath:[$v=0$] (bottom),
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latexmath:[$u=1$] (right), and latexmath:[$v=1$] (top) edges, respectively.
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The area between the inner rectangles of the mesh and the outer rectangle
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edges are filled by triangles produced by joining the vertices on the
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subdivided outer edges to the vertices on the edge of the inner rectangle
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mesh.
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If both clamped inner tessellation levels and all four clamped outer
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tessellation levels are exactly one, only a single triangle pair covering
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the outer rectangle is generated. Otherwise, if either clamped inner
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tessellation level is one, that tessellation level is treated as though it
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were originally specified as latexmath:[$1+\epsilon$] and will result in a
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two- or three-segment subdivision depending on the tessellation spacing.
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When used with fractional odd spacing, the three-segment subdivision may:
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produce _inner vertices_ positioned on the edge of the rectangle.
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If any tessellation level is greater than one, tessellation begins by
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subdividing the latexmath:[$u=0$] and latexmath:[$u=1$] edges of the outer
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rectangle into latexmath:[$m$] segments using the clamped and rounded first
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inner tessellation level and the tessellation spacing. The latexmath:[$v=0$]
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and latexmath:[$v=1$] edges are subdivided into latexmath:[$n$] segments
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using the second inner tessellation level. Each vertex on the
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latexmath:[$u=0$] and latexmath:[$v=0$] edges are joined with the
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corresponding vertex on the latexmath:[$u=1$] and latexmath:[$v=1$] edges to
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produce a set of vertical and horizontal lines that divide the rectangle
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into a grid of smaller rectangles. The primitive generator emits a pair of
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non-overlapping triangles covering each such rectangle not adjacent to an
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edge of the outer rectangle. The boundary of the region covered by these
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triangles forms an inner rectangle, the edges of which are subdivided by the
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grid vertices that lie on the edge. If either latexmath:[$m$] or
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latexmath:[$n$] is two, the inner rectangle is degenerate, and one or both
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of the rectangle's _edges_ consist of a single point. This subdivision is
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illustrated in Figure <<img-innerquad,Inner Quad Tessellation>>.
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[[img-innerquad,Inner Quad Tessellation]]
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.Inner Quad Tessellation
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image:images/innerquad.{svgpdf}["Inner Quad Tessellation",{fullimagewidth}]
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// TODO: Add caption:
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// Inner quad tessellation with inner tessellation
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// levels of
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// (a) $(4,2)$ and (b) $(7,4)$, respectively. Gray regions on the
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// bottom figure
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// depict the 10 inner rectangles, each of which will be subdivided
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// into two triangles.
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// Solid black circles depict vertices on the boundary of the outer and
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// inner rectangles,
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// where the inner rectangle on the top figure
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// is degenerate (a single line segment). Dotted lines depict the
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// horizontal and vertical edges connecting corresponding
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// vertices on the inner and outer rectangle edges.
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After the area corresponding to the inner rectangle is filled, the
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tessellator must: produce triangles to cover the area between the inner and
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outer rectangles. To do this, the subdivision of the outer rectangle edge
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above is discarded. Instead, the latexmath:[$u=0$], latexmath:[$v=0$],
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latexmath:[$u=1$], and latexmath:[$v=1$] edges are subdivided according to
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the first, second, third, and fourth outer tessellation levels,
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respectively, and the tessellation spacing. The original subdivision of the
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inner rectangle is retained. The area between the outer and inner rectangles
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is completely filled by non-overlapping triangles. Two of the three vertices
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of each triangle are adjacent vertices on a subdivided edge of one
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rectangle; the third is one of the vertices on the corresponding edge of the
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other triangle. If either edge of the innermost rectangle is degenerate, the
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area near the corresponding outer edges is filled by connecting each vertex
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on the outer edge with the single vertex making up the _inner edge_.
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The algorithm used to subdivide the rectangular domain in (u,v) space into
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individual triangles is implementation-dependent. However, the set of
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triangles produced will completely cover the domain, and no portion of the
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domain will be covered by multiple triangles. The order in which the
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generated triangles passed to subsequent pipeline stages and the order of
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the vertices in those triangles are both implementation-dependent.
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However, when depicted in a manner similar to <<img-innerquad,Inner Quad
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Tessellation>>, the order of the vertices in the generated triangles will be
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either all clockwise or all counter-clockwise, according to the vertex order
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layout declaration.
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[[tessellation-isoline-tessellation]]
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== Isoline Tessellation
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If the tessellation primitive mode is code:IsoLines, a set of independent
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horizontal line segments is drawn. The segments are arranged into
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connected strips called _isolines_, where the vertices of each isoline
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have a constant v coordinate and u coordinates covering the full range
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[0,1]. The number of isolines generated is derived from the first outer
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tessellation level; the number of segments in each isoline is derived from
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the second outer tessellation level. Both inner tessellation levels and
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the third and fourth outer tessellation levels have no effect in this
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mode.
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As with quad tessellation above, isoline tessellation begins with a
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rectangle. The latexmath:[$u=0$] and latexmath:[$u=1$] edges of the
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rectangle are subdivided according to the first outer tessellation level.
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For the purposes of this subdivision, the tessellation spacing mode is
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ignored and treated as equal_spacing. An isoline is drawn connecting each
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vertex on the latexmath:[$u=0$] rectangle edge to the corresponding vertex
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on the latexmath:[$u=1$] rectangle edge, except that no line is drawn
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between (0,1) and (1,1). If the number of isolines on the subdivided
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latexmath:[$u=0$] and latexmath:[$u=1$] edges is latexmath:[$n$], this
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process will result in latexmath:[$n$] equally spaced lines with constant v
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coordinates of 0, latexmath:[$\frac{1}{n}, \frac{2}{n}, \ldots,
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|
\frac{n-1}{n}$].
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Each of the latexmath:[$n$] isolines is then subdivided according to the
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|
second outer tessellation level and the tessellation spacing, resulting in
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latexmath:[$m$] line segments. Each segment of each line is emitted by the
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|
tessellator.
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|
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The order in which the generated line segments are passed to subsequent
|
|
pipeline stages and the order of the vertices in each generated line
|
|
segment are both implementation-dependent.
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== Tessellation Pipeline State
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The pname:pTessellationState member of slink:VkGraphicsPipelineCreateInfo is
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of type sname:VkPipelineTessellationStateCreateInfo:
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|
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include::../structs/VkPipelineTessellationStateCreateInfo.txt[]
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|
|
|
The members of the sname:VkPipelineTessellationStateCreateInfo structure are
|
|
as follows:
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* pname:sType is the type of this structure.
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* pname:pNext is `NULL` or a pointer to an extension-specific structure.
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|
* pname:flags is reserved for future use.
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|
* pname:patchControlPoints number of control points per patch.
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include::../validity/structs/VkPipelineTessellationStateCreateInfo.txt[]
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