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OpenSubdiv/opensubdiv/osd/glslPatchCommon.glsl
barry 1cdbb7246a Minor improvement to degenerate normals in GLSL Bezier triangle: 
- negate derivative terms when evaluating points on edge where u + v = 1
2019-02-11 18:05:08 -08:00

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//
// Copyright 2013 Pixar
//
// Licensed under the Apache License, Version 2.0 (the "Apache License")
// with the following modification; you may not use this file except in
// compliance with the Apache License and the following modification to it:
// Section 6. Trademarks. is deleted and replaced with:
//
// 6. Trademarks. This License does not grant permission to use the trade
// names, trademarks, service marks, or product names of the Licensor
// and its affiliates, except as required to comply with Section 4(c) of
// the License and to reproduce the content of the NOTICE file.
//
// You may obtain a copy of the Apache License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the Apache License with the above modification is
// distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
// KIND, either express or implied. See the Apache License for the specific
// language governing permissions and limitations under the Apache License.
//
//
// typical shader composition ordering (see glDrawRegistry:_CompileShader)
//
//
// - glsl version string (#version 430)
//
// - common defines (#define OSD_ENABLE_PATCH_CULL, ...)
// - source defines (#define VERTEX_SHADER, ...)
//
// - osd headers (glslPatchCommon: varying structs,
// glslPtexCommon: ptex functions)
// - client header (Osd*Matrix(), displacement callback, ...)
//
// - osd shader source (glslPatchBSpline, glslPatchGregory, ...)
// or
// client shader source (vertex/geometry/fragment shader)
//
//----------------------------------------------------------
// Patches.Common
//----------------------------------------------------------
// XXXdyu all handling of varying data can be managed by client code
#ifndef OSD_USER_VARYING_DECLARE
#define OSD_USER_VARYING_DECLARE
// type var;
#endif
#ifndef OSD_USER_VARYING_ATTRIBUTE_DECLARE
#define OSD_USER_VARYING_ATTRIBUTE_DECLARE
// layout(location = loc) in type var;
#endif
#ifndef OSD_USER_VARYING_PER_VERTEX
#define OSD_USER_VARYING_PER_VERTEX()
// output.var = var;
#endif
#ifndef OSD_USER_VARYING_PER_CONTROL_POINT
#define OSD_USER_VARYING_PER_CONTROL_POINT(ID_OUT, ID_IN)
// output[ID_OUT].var = input[ID_IN].var
#endif
#ifndef OSD_USER_VARYING_PER_EVAL_POINT
#define OSD_USER_VARYING_PER_EVAL_POINT(UV, a, b, c, d)
// output.var =
// mix(mix(input[a].var, input[b].var, UV.x),
// mix(input[c].var, input[d].var, UV.x), UV.y)
#endif
#ifndef OSD_USER_VARYING_PER_EVAL_POINT_TRIANGLE
#define OSD_USER_VARYING_PER_EVAL_POINT_TRIANGLE(UV, a, b, c)
// output.var =
// input[a].var * (1.0f-UV.x-UV.y) +
// input[b].var * UV.x +
// input[c].var * UV.y;
#endif
#if __VERSION__ < 420
#define centroid
#endif
struct ControlVertex {
vec4 position;
#ifdef OSD_ENABLE_PATCH_CULL
ivec3 clipFlag;
#endif
};
// XXXdyu all downstream data can be handled by client code
struct OutputVertex {
vec4 position;
vec3 normal;
vec3 tangent;
vec3 bitangent;
centroid vec4 patchCoord; // u, v, faceLevel, faceId
centroid vec2 tessCoord; // tesscoord.st
#if defined OSD_COMPUTE_NORMAL_DERIVATIVES
vec3 Nu;
vec3 Nv;
#endif
};
// osd shaders need following functions defined
mat4 OsdModelViewMatrix();
mat4 OsdProjectionMatrix();
mat4 OsdModelViewProjectionMatrix();
float OsdTessLevel();
int OsdGregoryQuadOffsetBase();
int OsdPrimitiveIdBase();
int OsdBaseVertex();
#ifndef OSD_DISPLACEMENT_CALLBACK
#define OSD_DISPLACEMENT_CALLBACK
#endif
// ----------------------------------------------------------------------------
// Patch Parameters
// ----------------------------------------------------------------------------
//
// Each patch has a corresponding patchParam. This is a set of three values
// specifying additional information about the patch:
//
// faceId -- topological face identifier (e.g. Ptex FaceId)
// bitfield -- refinement-level, non-quad, boundary, transition, uv-offset
// sharpness -- crease sharpness for single-crease patches
//
// These are stored in OsdPatchParamBuffer indexed by the value returned
// from OsdGetPatchIndex() which is a function of the current PrimitiveID
// along with an optional client provided offset.
//
uniform isamplerBuffer OsdPatchParamBuffer;
int OsdGetPatchIndex(int primitiveId)
{
return (primitiveId + OsdPrimitiveIdBase());
}
ivec3 OsdGetPatchParam(int patchIndex)
{
return texelFetch(OsdPatchParamBuffer, patchIndex).xyz;
}
int OsdGetPatchFaceId(ivec3 patchParam)
{
return (patchParam.x & 0xfffffff);
}
int OsdGetPatchFaceLevel(ivec3 patchParam)
{
return (1 << ((patchParam.y & 0xf) - ((patchParam.y >> 4) & 1)));
}
int OsdGetPatchRefinementLevel(ivec3 patchParam)
{
return (patchParam.y & 0xf);
}
int OsdGetPatchBoundaryMask(ivec3 patchParam)
{
return ((patchParam.y >> 7) & 0x1f);
}
int OsdGetPatchTransitionMask(ivec3 patchParam)
{
return ((patchParam.x >> 28) & 0xf);
}
ivec2 OsdGetPatchFaceUV(ivec3 patchParam)
{
int u = (patchParam.y >> 22) & 0x3ff;
int v = (patchParam.y >> 12) & 0x3ff;
return ivec2(u,v);
}
bool OsdGetPatchIsRegular(ivec3 patchParam)
{
return ((patchParam.y >> 5) & 0x1) != 0;
}
bool OsdGetPatchIsTriangleRotated(ivec3 patchParam)
{
ivec2 uv = OsdGetPatchFaceUV(patchParam);
return (uv.x + uv.y) >= OsdGetPatchFaceLevel(patchParam);
}
float OsdGetPatchSharpness(ivec3 patchParam)
{
return intBitsToFloat(patchParam.z);
}
float OsdGetPatchSingleCreaseSegmentParameter(ivec3 patchParam, vec2 uv)
{
int boundaryMask = OsdGetPatchBoundaryMask(patchParam);
float s = 0;
if ((boundaryMask & 1) != 0) {
s = 1 - uv.y;
} else if ((boundaryMask & 2) != 0) {
s = uv.x;
} else if ((boundaryMask & 4) != 0) {
s = uv.y;
} else if ((boundaryMask & 8) != 0) {
s = 1 - uv.x;
}
return s;
}
ivec4 OsdGetPatchCoord(ivec3 patchParam)
{
int faceId = OsdGetPatchFaceId(patchParam);
int faceLevel = OsdGetPatchFaceLevel(patchParam);
ivec2 faceUV = OsdGetPatchFaceUV(patchParam);
return ivec4(faceUV.x, faceUV.y, faceLevel, faceId);
}
vec4 OsdInterpolatePatchCoord(vec2 localUV, ivec3 patchParam)
{
ivec4 perPrimPatchCoord = OsdGetPatchCoord(patchParam);
int faceId = perPrimPatchCoord.w;
int faceLevel = perPrimPatchCoord.z;
vec2 faceUV = vec2(perPrimPatchCoord.x, perPrimPatchCoord.y);
vec2 uv = localUV/faceLevel + faceUV/faceLevel;
// add 0.5 to integer values for more robust interpolation
return vec4(uv.x, uv.y, faceLevel+0.5f, faceId+0.5f);
}
vec4 OsdInterpolatePatchCoordTriangle(vec2 localUV, ivec3 patchParam)
{
vec4 result = OsdInterpolatePatchCoord(localUV, patchParam);
if (OsdGetPatchIsTriangleRotated(patchParam)) {
result.xy = vec2(1.0f) - result.xy;
}
return result;
}
// ----------------------------------------------------------------------------
// patch culling
// ----------------------------------------------------------------------------
#ifdef OSD_ENABLE_PATCH_CULL
#define OSD_PATCH_CULL_COMPUTE_CLIPFLAGS(P) \
vec4 clipPos = OsdModelViewProjectionMatrix() * P; \
bvec3 clip0 = lessThan(clipPos.xyz, vec3(clipPos.w)); \
bvec3 clip1 = greaterThan(clipPos.xyz, -vec3(clipPos.w)); \
outpt.v.clipFlag = ivec3(clip0) + 2*ivec3(clip1); \
#define OSD_PATCH_CULL(N) \
ivec3 clipFlag = ivec3(0); \
for(int i = 0; i < N; ++i) { \
clipFlag |= inpt[i].v.clipFlag; \
} \
if (clipFlag != ivec3(3) ) { \
gl_TessLevelInner[0] = 0; \
gl_TessLevelInner[1] = 0; \
gl_TessLevelOuter[0] = 0; \
gl_TessLevelOuter[1] = 0; \
gl_TessLevelOuter[2] = 0; \
gl_TessLevelOuter[3] = 0; \
return; \
}
#else
#define OSD_PATCH_CULL_COMPUTE_CLIPFLAGS(P)
#define OSD_PATCH_CULL(N)
#endif
// ----------------------------------------------------------------------------
void
OsdUnivar4x4(in float u, out float B[4], out float D[4])
{
float t = u;
float s = 1.0f - u;
float A0 = s * s;
float A1 = 2 * s * t;
float A2 = t * t;
B[0] = s * A0;
B[1] = t * A0 + s * A1;
B[2] = t * A1 + s * A2;
B[3] = t * A2;
D[0] = - A0;
D[1] = A0 - A1;
D[2] = A1 - A2;
D[3] = A2;
}
void
OsdUnivar4x4(in float u, out float B[4], out float D[4], out float C[4])
{
float t = u;
float s = 1.0f - u;
float A0 = s * s;
float A1 = 2 * s * t;
float A2 = t * t;
B[0] = s * A0;
B[1] = t * A0 + s * A1;
B[2] = t * A1 + s * A2;
B[3] = t * A2;
D[0] = - A0;
D[1] = A0 - A1;
D[2] = A1 - A2;
D[3] = A2;
A0 = - s;
A1 = s - t;
A2 = t;
C[0] = - A0;
C[1] = A0 - A1;
C[2] = A1 - A2;
C[3] = A2;
}
// ----------------------------------------------------------------------------
struct OsdPerPatchVertexBezier {
ivec3 patchParam;
vec3 P;
#if defined OSD_PATCH_ENABLE_SINGLE_CREASE
vec3 P1;
vec3 P2;
vec2 vSegments;
#endif
};
vec3
OsdEvalBezier(vec3 cp[16], vec2 uv)
{
vec3 BUCP[4] = vec3[4](vec3(0), vec3(0), vec3(0), vec3(0));
float B[4], D[4];
OsdUnivar4x4(uv.x, B, D);
for (int i=0; i<4; ++i) {
for (int j=0; j<4; ++j) {
vec3 A = cp[4*i + j];
BUCP[i] += A * B[j];
}
}
vec3 P = vec3(0);
OsdUnivar4x4(uv.y, B, D);
for (int k=0; k<4; ++k) {
P += B[k] * BUCP[k];
}
return P;
}
// When OSD_PATCH_ENABLE_SINGLE_CREASE is defined,
// this function evaluates single-crease patch, which is segmented into
// 3 parts in the v-direction.
//
// v=0 vSegment.x vSegment.y v=1
// +------------------+-------------------+------------------+
// | cp 0 | cp 1 | cp 2 |
// | (infinite sharp) | (floor sharpness) | (ceil sharpness) |
// +------------------+-------------------+------------------+
//
vec3
OsdEvalBezier(OsdPerPatchVertexBezier cp[16], ivec3 patchParam, vec2 uv)
{
vec3 BUCP[4] = vec3[4](vec3(0), vec3(0), vec3(0), vec3(0));
float B[4], D[4];
float s = OsdGetPatchSingleCreaseSegmentParameter(patchParam, uv);
OsdUnivar4x4(uv.x, B, D);
#if defined OSD_PATCH_ENABLE_SINGLE_CREASE
vec2 vSegments = cp[0].vSegments;
if (s <= vSegments.x) {
for (int i=0; i<4; ++i) {
for (int j=0; j<4; ++j) {
vec3 A = cp[4*i + j].P;
BUCP[i] += A * B[j];
}
}
} else if (s <= vSegments.y) {
for (int i=0; i<4; ++i) {
for (int j=0; j<4; ++j) {
vec3 A = cp[4*i + j].P1;
BUCP[i] += A * B[j];
}
}
} else {
for (int i=0; i<4; ++i) {
for (int j=0; j<4; ++j) {
vec3 A = cp[4*i + j].P2;
BUCP[i] += A * B[j];
}
}
}
#else
for (int i=0; i<4; ++i) {
for (int j=0; j<4; ++j) {
vec3 A = cp[4*i + j].P;
BUCP[i] += A * B[j];
}
}
#endif
vec3 P = vec3(0);
OsdUnivar4x4(uv.y, B, D);
for (int k=0; k<4; ++k) {
P += B[k] * BUCP[k];
}
return P;
}
// ----------------------------------------------------------------------------
// Boundary Interpolation
// ----------------------------------------------------------------------------
void
OsdComputeBSplineBoundaryPoints(inout vec3 cpt[16], ivec3 patchParam)
{
int boundaryMask = OsdGetPatchBoundaryMask(patchParam);
// Don't extrpolate corner points until all boundary points in place
if ((boundaryMask & 1) != 0) {
cpt[1] = 2*cpt[5] - cpt[9];
cpt[2] = 2*cpt[6] - cpt[10];
}
if ((boundaryMask & 2) != 0) {
cpt[7] = 2*cpt[6] - cpt[5];
cpt[11] = 2*cpt[10] - cpt[9];
}
if ((boundaryMask & 4) != 0) {
cpt[13] = 2*cpt[9] - cpt[5];
cpt[14] = 2*cpt[10] - cpt[6];
}
if ((boundaryMask & 8) != 0) {
cpt[4] = 2*cpt[5] - cpt[6];
cpt[8] = 2*cpt[9] - cpt[10];
}
// Now safe to extrapolate corner points:
if ((boundaryMask & 1) != 0) {
cpt[0] = 2*cpt[4] - cpt[8];
cpt[3] = 2*cpt[7] - cpt[11];
}
if ((boundaryMask & 2) != 0) {
cpt[3] = 2*cpt[2] - cpt[1];
cpt[15] = 2*cpt[14] - cpt[13];
}
if ((boundaryMask & 4) != 0) {
cpt[12] = 2*cpt[8] - cpt[4];
cpt[15] = 2*cpt[11] - cpt[7];
}
if ((boundaryMask & 8) != 0) {
cpt[0] = 2*cpt[1] - cpt[2];
cpt[12] = 2*cpt[13] - cpt[14];
}
}
void
OsdComputeBoxSplineTriangleBoundaryPoints(inout vec3 cpt[12], ivec3 patchParam)
{
int boundaryMask = OsdGetPatchBoundaryMask(patchParam);
if (boundaryMask == 0) return;
int upperBits = (boundaryMask >> 3) & 0x3;
int lowerBits = boundaryMask & 7;
int eBits = lowerBits;
int vBits = 0;
if (upperBits == 1) {
vBits = eBits;
eBits = 0;
} else if (upperBits == 2) {
// Opposite vertex bit is edge bit rotated one to the right:
vBits = ((eBits & 1) << 2) | (eBits >> 1);
}
bool edge0IsBoundary = (eBits & 1) != 0;
bool edge1IsBoundary = (eBits & 2) != 0;
bool edge2IsBoundary = (eBits & 4) != 0;
if (edge0IsBoundary) {
if (edge2IsBoundary) {
cpt[0] = cpt[4] + (cpt[4] - cpt[8]);
} else {
cpt[0] = cpt[4] + (cpt[3] - cpt[7]);
}
cpt[1] = cpt[4] + cpt[5] - cpt[8];
if (edge1IsBoundary) {
cpt[2] = cpt[5] + (cpt[5] - cpt[8]);
} else {
cpt[2] = cpt[5] + (cpt[6] - cpt[9]);
}
}
if (edge1IsBoundary) {
if (edge0IsBoundary) {
cpt[6] = cpt[5] + (cpt[5] - cpt[4]);
} else {
cpt[6] = cpt[5] + (cpt[2] - cpt[1]);
}
cpt[9] = cpt[5] + cpt[8] - cpt[4];
if (edge2IsBoundary) {
cpt[11] = cpt[8] + (cpt[8] - cpt[4]);
} else {
cpt[11] = cpt[8] + (cpt[10] - cpt[7]);
}
}
if (edge2IsBoundary) {
if (edge1IsBoundary) {
cpt[10] = cpt[8] + (cpt[8] - cpt[5]);
} else {
cpt[10] = cpt[8] + (cpt[11] - cpt[9]);
}
cpt[7] = cpt[8] + cpt[4] - cpt[5];
if (edge0IsBoundary) {
cpt[3] = cpt[4] + (cpt[4] - cpt[5]);
} else {
cpt[3] = cpt[4] + (cpt[0] - cpt[1]);
}
}
if ((vBits & 1) != 0) {
cpt[3] = cpt[4] + cpt[7] - cpt[8];
cpt[0] = cpt[4] + cpt[1] - cpt[5];
}
if ((vBits & 2) != 0) {
cpt[2] = cpt[5] + cpt[1] - cpt[4];
cpt[6] = cpt[5] + cpt[9] - cpt[8];
}
if ((vBits & 4) != 0) {
cpt[11] = cpt[8] + cpt[9] - cpt[5];
cpt[10] = cpt[8] + cpt[7] - cpt[4];
}
}
// ----------------------------------------------------------------------------
// BSpline
// ----------------------------------------------------------------------------
// compute single-crease patch matrix
mat4
OsdComputeMs(float sharpness)
{
float s = pow(2.0f, sharpness);
float s2 = s*s;
float s3 = s2*s;
mat4 m = mat4(
0, s + 1 + 3*s2 - s3, 7*s - 2 - 6*s2 + 2*s3, (1-s)*(s-1)*(s-1),
0, (1+s)*(1+s), 6*s - 2 - 2*s2, (s-1)*(s-1),
0, 1+s, 6*s - 2, 1-s,
0, 1, 6*s - 2, 1);
m /= (s*6.0);
m[0][0] = 1.0/6.0;
return m;
}
// flip matrix orientation
mat4
OsdFlipMatrix(mat4 m)
{
return mat4(m[3][3], m[3][2], m[3][1], m[3][0],
m[2][3], m[2][2], m[2][1], m[2][0],
m[1][3], m[1][2], m[1][1], m[1][0],
m[0][3], m[0][2], m[0][1], m[0][0]);
}
// Regular BSpline to Bezier
uniform mat4 Q = mat4(
1.f/6.f, 4.f/6.f, 1.f/6.f, 0.f,
0.f, 4.f/6.f, 2.f/6.f, 0.f,
0.f, 2.f/6.f, 4.f/6.f, 0.f,
0.f, 1.f/6.f, 4.f/6.f, 1.f/6.f
);
// Infinitely Sharp (boundary)
uniform mat4 Mi = mat4(
1.f/6.f, 4.f/6.f, 1.f/6.f, 0.f,
0.f, 4.f/6.f, 2.f/6.f, 0.f,
0.f, 2.f/6.f, 4.f/6.f, 0.f,
0.f, 0.f, 1.f, 0.f
);
// convert BSpline cv to Bezier cv
void
OsdComputePerPatchVertexBSpline(ivec3 patchParam, int ID, vec3 cv[16],
out OsdPerPatchVertexBezier result)
{
result.patchParam = patchParam;
int i = ID%4;
int j = ID/4;
#if defined OSD_PATCH_ENABLE_SINGLE_CREASE
vec3 P = vec3(0); // 0 to 1-2^(-Sf)
vec3 P1 = vec3(0); // 1-2^(-Sf) to 1-2^(-Sc)
vec3 P2 = vec3(0); // 1-2^(-Sc) to 1
float sharpness = OsdGetPatchSharpness(patchParam);
if (sharpness > 0) {
float Sf = floor(sharpness);
float Sc = ceil(sharpness);
float Sr = fract(sharpness);
mat4 Mf = OsdComputeMs(Sf);
mat4 Mc = OsdComputeMs(Sc);
mat4 Mj = (1-Sr) * Mf + Sr * Mi;
mat4 Ms = (1-Sr) * Mf + Sr * Mc;
float s0 = 1 - pow(2, -floor(sharpness));
float s1 = 1 - pow(2, -ceil(sharpness));
result.vSegments = vec2(s0, s1);
mat4 MUi = Q, MUj = Q, MUs = Q;
mat4 MVi = Q, MVj = Q, MVs = Q;
int boundaryMask = OsdGetPatchBoundaryMask(patchParam);
if ((boundaryMask & 1) != 0) {
MVi = OsdFlipMatrix(Mi);
MVj = OsdFlipMatrix(Mj);
MVs = OsdFlipMatrix(Ms);
}
if ((boundaryMask & 2) != 0) {
MUi = Mi;
MUj = Mj;
MUs = Ms;
}
if ((boundaryMask & 4) != 0) {
MVi = Mi;
MVj = Mj;
MVs = Ms;
}
if ((boundaryMask & 8) != 0) {
MUi = OsdFlipMatrix(Mi);
MUj = OsdFlipMatrix(Mj);
MUs = OsdFlipMatrix(Ms);
}
vec3 Hi[4], Hj[4], Hs[4];
for (int l=0; l<4; ++l) {
Hi[l] = Hj[l] = Hs[l] = vec3(0);
for (int k=0; k<4; ++k) {
Hi[l] += MUi[i][k] * cv[l*4 + k];
Hj[l] += MUj[i][k] * cv[l*4 + k];
Hs[l] += MUs[i][k] * cv[l*4 + k];
}
}
for (int k=0; k<4; ++k) {
P += MVi[j][k]*Hi[k];
P1 += MVj[j][k]*Hj[k];
P2 += MVs[j][k]*Hs[k];
}
result.P = P;
result.P1 = P1;
result.P2 = P2;
} else {
result.vSegments = vec2(0);
OsdComputeBSplineBoundaryPoints(cv, patchParam);
vec3 Hi[4];
for (int l=0; l<4; ++l) {
Hi[l] = vec3(0);
for (int k=0; k<4; ++k) {
Hi[l] += Q[i][k] * cv[l*4 + k];
}
}
for (int k=0; k<4; ++k) {
P += Q[j][k]*Hi[k];
}
result.P = P;
result.P1 = P;
result.P2 = P;
}
#else
OsdComputeBSplineBoundaryPoints(cv, patchParam);
vec3 H[4];
for (int l=0; l<4; ++l) {
H[l] = vec3(0);
for (int k=0; k<4; ++k) {
H[l] += Q[i][k] * cv[l*4 + k];
}
}
{
result.P = vec3(0);
for (int k=0; k<4; ++k) {
result.P += Q[j][k]*H[k];
}
}
#endif
}
void
OsdEvalPatchBezier(ivec3 patchParam, vec2 UV,
OsdPerPatchVertexBezier cv[16],
out vec3 P, out vec3 dPu, out vec3 dPv,
out vec3 N, out vec3 dNu, out vec3 dNv)
{
//
// Use the recursive nature of the basis functions to compute a 2x2 set
// of intermediate points (via repeated linear interpolation). These
// points define a bilinear surface tangent to the desired surface at P
// and so containing dPu and dPv. The cost of computing P, dPu and dPv
// this way is comparable to that of typical tensor product evaluation
// (if not faster).
//
// If N = dPu X dPv degenerates, it often results from an edge of the
// 2x2 bilinear hull collapsing or two adjacent edges colinear. In both
// cases, the expected non-planar quad degenerates into a triangle, and
// the tangent plane of that triangle provides the desired normal N.
//
// Reduce 4x4 points to 2x4 -- two levels of linear interpolation in U
// and so 3 original rows contributing to each of the 2 resulting rows:
float u = UV.x;
float uinv = 1.0f - u;
float u0 = uinv * uinv;
float u1 = u * uinv * 2.0f;
float u2 = u * u;
vec3 LROW[4], RROW[4];
#ifndef OSD_PATCH_ENABLE_SINGLE_CREASE
LROW[0] = u0 * cv[ 0].P + u1 * cv[ 1].P + u2 * cv[ 2].P;
LROW[1] = u0 * cv[ 4].P + u1 * cv[ 5].P + u2 * cv[ 6].P;
LROW[2] = u0 * cv[ 8].P + u1 * cv[ 9].P + u2 * cv[10].P;
LROW[3] = u0 * cv[12].P + u1 * cv[13].P + u2 * cv[14].P;
RROW[0] = u0 * cv[ 1].P + u1 * cv[ 2].P + u2 * cv[ 3].P;
RROW[1] = u0 * cv[ 5].P + u1 * cv[ 6].P + u2 * cv[ 7].P;
RROW[2] = u0 * cv[ 9].P + u1 * cv[10].P + u2 * cv[11].P;
RROW[3] = u0 * cv[13].P + u1 * cv[14].P + u2 * cv[15].P;
#else
vec2 vSegments = cv[0].vSegments;
float s = OsdGetPatchSingleCreaseSegmentParameter(patchParam, UV);
for (int i = 0; i < 4; ++i) {
int j = i*4;
if (s <= vSegments.x) {
LROW[i] = u0 * cv[ j ].P + u1 * cv[j+1].P + u2 * cv[j+2].P;
RROW[i] = u0 * cv[j+1].P + u1 * cv[j+2].P + u2 * cv[j+3].P;
} else if (s <= vSegments.y) {
LROW[i] = u0 * cv[ j ].P1 + u1 * cv[j+1].P1 + u2 * cv[j+2].P1;
RROW[i] = u0 * cv[j+1].P1 + u1 * cv[j+2].P1 + u2 * cv[j+3].P1;
} else {
LROW[i] = u0 * cv[ j ].P2 + u1 * cv[j+1].P2 + u2 * cv[j+2].P2;
RROW[i] = u0 * cv[j+1].P2 + u1 * cv[j+2].P2 + u2 * cv[j+3].P2;
}
}
#endif
// Reduce 2x4 points to 2x2 -- two levels of linear interpolation in V
// and so 3 original pairs contributing to each of the 2 resulting:
float v = UV.y;
float vinv = 1.0f - v;
float v0 = vinv * vinv;
float v1 = v * vinv * 2.0f;
float v2 = v * v;
vec3 LPAIR[2], RPAIR[2];
LPAIR[0] = v0 * LROW[0] + v1 * LROW[1] + v2 * LROW[2];
RPAIR[0] = v0 * RROW[0] + v1 * RROW[1] + v2 * RROW[2];
LPAIR[1] = v0 * LROW[1] + v1 * LROW[2] + v2 * LROW[3];
RPAIR[1] = v0 * RROW[1] + v1 * RROW[2] + v2 * RROW[3];
// Interpolate points on the edges of the 2x2 bilinear hull from which
// both position and partials are trivially determined:
vec3 DU0 = vinv * LPAIR[0] + v * LPAIR[1];
vec3 DU1 = vinv * RPAIR[0] + v * RPAIR[1];
vec3 DV0 = uinv * LPAIR[0] + u * RPAIR[0];
vec3 DV1 = uinv * LPAIR[1] + u * RPAIR[1];
int level = OsdGetPatchFaceLevel(patchParam);
dPu = (DU1 - DU0) * 3 * level;
dPv = (DV1 - DV0) * 3 * level;
P = u * DU1 + uinv * DU0;
// Compute the normal and test for degeneracy:
//
// We need a geometric measure of the size of the patch for a suitable
// tolerance. Magnitudes of the partials are generally proportional to
// that size -- the sum of the partials is readily available, cheap to
// compute, and has proved effective in most cases (though not perfect).
// The size of the bounding box of the patch, or some approximation to
// it, would be better but more costly to compute.
//
float proportionalNormalTolerance = 0.00001f;
float nEpsilon = (length(dPu) + length(dPv)) * proportionalNormalTolerance;
N = cross(dPu, dPv);
float nLength = length(N);
if (nLength > nEpsilon) {
N = N / nLength;
} else {
vec3 diagCross = cross(RPAIR[1] - LPAIR[0], LPAIR[1] - RPAIR[0]);
float diagCrossLength = length(diagCross);
if (diagCrossLength > nEpsilon) {
N = diagCross / diagCrossLength;
}
}
#ifndef OSD_COMPUTE_NORMAL_DERIVATIVES
dNu = vec3(0);
dNv = vec3(0);
#else
//
// Compute 2nd order partials of P(u,v) in order to compute 1st order partials
// for the un-normalized n(u,v) = dPu X dPv, then project into the tangent
// plane of normalized N. With resulting dNu and dNv we can make another
// attempt to resolve a still-degenerate normal.
//
// We don't use the Weingarten equations here as they require N != 0 and also
// are a little less numerically stable/accurate in single precision.
//
float B0u[4], B1u[4], B2u[4];
float B0v[4], B1v[4], B2v[4];
OsdUnivar4x4(UV.x, B0u, B1u, B2u);
OsdUnivar4x4(UV.y, B0v, B1v, B2v);
vec3 dUU = vec3(0);
vec3 dVV = vec3(0);
vec3 dUV = vec3(0);
for (int i=0; i<4; ++i) {
for (int j=0; j<4; ++j) {
#ifdef OSD_PATCH_ENABLE_SINGLE_CREASE
int k = 4*i + j;
vec3 CV = (s <= vSegments.x) ? cv[k].P
: ((s <= vSegments.y) ? cv[k].P1
: cv[k].P2);
#else
vec3 CV = cv[4*i + j].P;
#endif
dUU += (B0v[i] * B2u[j]) * CV;
dVV += (B2v[i] * B0u[j]) * CV;
dUV += (B1v[i] * B1u[j]) * CV;
}
}
dUU *= 6 * level;
dVV *= 6 * level;
dUV *= 9 * level;
dNu = cross(dUU, dPv) + cross(dPu, dUV);
dNv = cross(dUV, dPv) + cross(dPu, dVV);
float nLengthInv = 1.0;
if (nLength > nEpsilon) {
nLengthInv = 1.0 / nLength;
} else {
// N may have been resolved above if degenerate, but if N was resolved
// we don't have an accurate length for its un-normalized value, and that
// length is needed to project the un-normalized dNu and dNv into the
// tangent plane of N.
//
// So compute N more accurately with available second derivatives, i.e.
// with a 1st order Taylor approximation to un-normalized N(u,v).
float DU = (UV.x == 1.0f) ? -1.0f : 1.0f;
float DV = (UV.y == 1.0f) ? -1.0f : 1.0f;
N = DU * dNu + DV * dNv;
nLength = length(N);
if (nLength > nEpsilon) {
nLengthInv = 1.0f / nLength;
N = N * nLengthInv;
}
}
// Project derivatives of non-unit normals into tangent plane of N:
dNu = (dNu - dot(dNu,N) * N) * nLengthInv;
dNv = (dNv - dot(dNv,N) * N) * nLengthInv;
#endif
}
// ----------------------------------------------------------------------------
// Gregory Basis
// ----------------------------------------------------------------------------
struct OsdPerPatchVertexGregoryBasis {
ivec3 patchParam;
vec3 P;
};
void
OsdComputePerPatchVertexGregoryBasis(ivec3 patchParam, int ID, vec3 cv,
out OsdPerPatchVertexGregoryBasis result)
{
result.patchParam = patchParam;
result.P = cv;
}
void
OsdEvalPatchGregory(ivec3 patchParam, vec2 UV, vec3 cv[20],
out vec3 P, out vec3 dPu, out vec3 dPv,
out vec3 N, out vec3 dNu, out vec3 dNv)
{
float u = UV.x, v = UV.y;
float U = 1-u, V = 1-v;
//(0,1) (1,1)
// P3 e3- e2+ P2
// 15------17-------11-------10
// | | | |
// | | | |
// | | f3- | f2+ |
// | 19 13 |
// e3+ 16-----18 14-----12 e2-
// | f3+ f2- |
// | |
// | |
// | f0- f1+ |
// e0- 2------4 8------6 e1+
// | 3 f0+ 9 |
// | | | f1- |
// | | | |
// | | | |
// 0--------1--------7--------5
// P0 e0+ e1- P1
//(0,0) (1,0)
float d11 = u+v;
float d12 = U+v;
float d21 = u+V;
float d22 = U+V;
OsdPerPatchVertexBezier bezcv[16];
bezcv[ 5].P = (d11 == 0.0) ? cv[3] : (u*cv[3] + v*cv[4])/d11;
bezcv[ 6].P = (d12 == 0.0) ? cv[8] : (U*cv[9] + v*cv[8])/d12;
bezcv[ 9].P = (d21 == 0.0) ? cv[18] : (u*cv[19] + V*cv[18])/d21;
bezcv[10].P = (d22 == 0.0) ? cv[13] : (U*cv[13] + V*cv[14])/d22;
bezcv[ 0].P = cv[0];
bezcv[ 1].P = cv[1];
bezcv[ 2].P = cv[7];
bezcv[ 3].P = cv[5];
bezcv[ 4].P = cv[2];
bezcv[ 7].P = cv[6];
bezcv[ 8].P = cv[16];
bezcv[11].P = cv[12];
bezcv[12].P = cv[15];
bezcv[13].P = cv[17];
bezcv[14].P = cv[11];
bezcv[15].P = cv[10];
OsdEvalPatchBezier(patchParam, UV, bezcv, P, dPu, dPv, N, dNu, dNv);
}
//
// Convert the 12 points of a regular patch resulting from Loop subdivision
// into a more accessible Bezier patch for both tessellation assessment and
// evaluation.
//
// Regular patch for Loop subdivision -- quartic triangular Box spline:
//
// 10 --- 11
// . . . .
// . . . .
// 7 --- 8 --- 9
// . . . . . .
// . . . . . .
// 3 --- 4 --- 5 --- 6
// . . . . . .
// . . . . . .
// 0 --- 1 --- 2
//
// The equivalant quartic Bezier triangle (15 points):
//
// 14
// . .
// . .
// 12 --- 13
// . . . .
// . . . .
// 9 -- 10 --- 11
// . . . . . .
// . . . . . .
// 5 --- 6 --- 7 --- 8
// . . . . . . . .
// . . . . . . . .
// 0 --- 1 --- 2 --- 3 --- 4
//
// A hybrid cubic/quartic Bezier patch with cubic boundaries is a close
// approximation and would only use 12 control points, but we need a full
// quartic patch to maintain accuracy along boundary curves -- especially
// between subdivision levels.
//
void
OsdComputePerPatchVertexBoxSplineTriangle(ivec3 patchParam, int ID, vec3 cv[12],
out OsdPerPatchVertexBezier result)
{
//
// Conversion matrix from 12-point Box spline to 15-point quartic Bezier
// patch and its common scale factor:
//
const float boxToBezierMatrix[12*15] = float[12*15](
// L0 L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11
2, 2, 0, 2, 12, 2, 0, 2, 2, 0, 0, 0, // B0
1, 3, 0, 0, 12, 4, 0, 1, 3, 0, 0, 0, // B1
0, 4, 0, 0, 8, 8, 0, 0, 4, 0, 0, 0, // B2
0, 3, 1, 0, 4, 12, 0, 0, 3, 1, 0, 0, // B3
0, 2, 2, 0, 2, 12, 2, 0, 2, 2, 0, 0, // B4
0, 1, 0, 1, 12, 3, 0, 3, 4, 0, 0, 0, // B5
0, 1, 0, 0, 10, 6, 0, 1, 6, 0, 0, 0, // B6
0, 1, 0, 0, 6, 10, 0, 0, 6, 1, 0, 0, // B7
0, 1, 0, 0, 3, 12, 1, 0, 4, 3, 0, 0, // B8
0, 0, 0, 0, 8, 4, 0, 4, 8, 0, 0, 0, // B9
0, 0, 0, 0, 6, 6, 0, 1, 10, 1, 0, 0, // B10
0, 0, 0, 0, 4, 8, 0, 0, 8, 4, 0, 0, // B11
0, 0, 0, 0, 4, 3, 0, 3, 12, 1, 1, 0, // B12
0, 0, 0, 0, 3, 4, 0, 1, 12, 3, 0, 1, // B13
0, 0, 0, 0, 2, 2, 0, 2, 12, 2, 2, 2 // B14
);
const float boxToBezierMatrixScale = 1.0 / 24.0;
OsdComputeBoxSplineTriangleBoundaryPoints(cv, patchParam);
result.patchParam = patchParam;
result.P = vec3(0);
int cvCoeffBase = 12 * ID;
for (int i = 0; i < 12; ++i) {
result.P += boxToBezierMatrix[cvCoeffBase + i] * cv[i];
}
result.P *= boxToBezierMatrixScale;
}
void
OsdEvalPatchBezierTriangle(ivec3 patchParam, vec2 UV,
OsdPerPatchVertexBezier cv[15],
out vec3 P, out vec3 dPu, out vec3 dPv,
out vec3 N, out vec3 dNu, out vec3 dNv)
{
float u = UV.x;
float v = UV.y;
float w = 1.0 - u - v;
float uu = u * u;
float vv = v * v;
float ww = w * w;
#ifdef OSD_COMPUTE_NORMAL_DERIVATIVES
//
// When computing normal derivatives, we need 2nd derivatives, so compute
// an intermediate quadratic Bezier triangle from which 2nd derivatives
// can be easily computed, and which in turn yields the triangle that gives
// the position and 1st derivatives.
//
// Quadratic barycentric basis functions (in addition to those above):
float uv = u * v * 2.0;
float vw = v * w * 2.0;
float wu = w * u * 2.0;
vec3 Q0 = ww * cv[ 0].P + wu * cv[ 1].P + uu * cv[ 2].P +
uv * cv[ 6].P + vv * cv[ 9].P + vw * cv[ 5].P;
vec3 Q1 = ww * cv[ 1].P + wu * cv[ 2].P + uu * cv[ 3].P +
uv * cv[ 7].P + vv * cv[10].P + vw * cv[ 6].P;
vec3 Q2 = ww * cv[ 2].P + wu * cv[ 3].P + uu * cv[ 4].P +
uv * cv[ 8].P + vv * cv[11].P + vw * cv[ 7].P;
vec3 Q3 = ww * cv[ 5].P + wu * cv[ 6].P + uu * cv[ 7].P +
uv * cv[10].P + vv * cv[12].P + vw * cv[ 9].P;
vec3 Q4 = ww * cv[ 6].P + wu * cv[ 7].P + uu * cv[ 8].P +
uv * cv[11].P + vv * cv[13].P + vw * cv[10].P;
vec3 Q5 = ww * cv[ 9].P + wu * cv[10].P + uu * cv[11].P +
uv * cv[13].P + vv * cv[14].P + vw * cv[12].P;
vec3 V0 = w * Q0 + u * Q1 + v * Q3;
vec3 V1 = w * Q1 + u * Q2 + v * Q4;
vec3 V2 = w * Q3 + u * Q4 + v * Q5;
#else
//
// When 2nd derivatives are not required, factor the recursive evaluation
// of a point to directly provide the three points of the triangle at the
// last stage -- which then trivially provides both position and 1st
// derivatives. Each point of the triangle results from evaluating the
// corresponding cubic Bezier sub-triangle for each corner of the quartic:
//
// Cubic barycentric basis functions:
float uuu = uu * u;
float uuv = uu * v * 3.0;
float uvv = u * vv * 3.0;
float vvv = vv * v;
float vvw = vv * w * 3.0;
float vww = v * ww * 3.0;
float www = ww * w;
float wwu = ww * u * 3.0;
float wuu = w * uu * 3.0;
float uvw = u * v * w * 6.0;
vec3 V0 = www * cv[ 0].P + wwu * cv[ 1].P + wuu * cv[ 2].P
+ uuu * cv[ 3].P + uuv * cv[ 7].P + uvv * cv[10].P
+ vvv * cv[12].P + vvw * cv[ 9].P + vww * cv[ 5].P + uvw * cv[ 6].P;
vec3 V1 = www * cv[ 1].P + wwu * cv[ 2].P + wuu * cv[ 3].P
+ uuu * cv[ 4].P + uuv * cv[ 8].P + uvv * cv[11].P
+ vvv * cv[13].P + vvw * cv[10].P + vww * cv[ 6].P + uvw * cv[ 7].P;
vec3 V2 = www * cv[ 5].P + wwu * cv[ 6].P + wuu * cv[ 7].P
+ uuu * cv[ 8].P + uuv * cv[11].P + uvv * cv[13].P
+ vvv * cv[14].P + vvw * cv[12].P + vww * cv[ 9].P + uvw * cv[10].P;
#endif
//
// Compute P, du and dv all from the triangle formed from the three Vi:
//
P = w * V0 + u * V1 + v * V2;
int dSign = OsdGetPatchIsTriangleRotated(patchParam) ? -1 : 1;
int level = OsdGetPatchFaceLevel(patchParam);
float d1Scale = dSign * level * 4;
dPu = (V1 - V0) * d1Scale;
dPv = (V2 - V0) * d1Scale;
// Compute N and test for degeneracy:
//
// We need a geometric measure of the size of the patch for a suitable
// tolerance. Magnitudes of the partials are generally proportional to
// that size -- the sum of the partials is readily available, cheap to
// compute, and has proved effective in most cases (though not perfect).
// The size of the bounding box of the patch, or some approximation to
// it, would be better but more costly to compute.
//
float proportionalNormalTolerance = 0.00001f;
float nEpsilon = (length(dPu) + length(dPv)) * proportionalNormalTolerance;
N = cross(dPu, dPv);
float nLength = length(N);
#ifdef OSD_COMPUTE_NORMAL_DERIVATIVES
//
// Compute normal derivatives using 2nd order partials, then use the
// normal derivatives to resolve a degenerate normal:
//
float d2Scale = dSign * level * level * 12;
vec3 dUU = (Q0 - 2 * Q1 + Q2) * d2Scale;
vec3 dVV = (Q0 - 2 * Q3 + Q5) * d2Scale;
vec3 dUV = (Q0 - Q1 + Q4 - Q3) * d2Scale;
dNu = cross(dUU, dPv) + cross(dPu, dUV);
dNv = cross(dUV, dPv) + cross(dPu, dVV);
if (nLength < nEpsilon) {
// Use 1st order Taylor approximation of N(u,v) within patch interior:
if (w > 0.0) {
N = dNu + dNv;
} else if (u >= 1.0) {
N = -dNu + dNv;
} else if (v >= 1.0) {
N = dNu - dNv;
} else {
N = -dNu - dNv;
}
nLength = length(N);
if (nLength < nEpsilon) {
nLength = 1.0;
}
}
N = N / nLength;
// Project derivs of non-unit normal function onto tangent plane of N:
dNu = (dNu - dot(dNu,N) * N) / nLength;
dNv = (dNv - dot(dNv,N) * N) / nLength;
#else
dNu = vec3(0);
dNv = vec3(0);
//
// Resolve a degenerate normal using the interior triangle of the
// intermediate quadratic patch that results from recursive evaluation.
// This addresses common cases of degenerate or colinear boundaries
// without resorting to use of explicit 2nd derivatives:
//
if (nLength < nEpsilon) {
float uv = u * v * 2.0;
float vw = v * w * 2.0;
float wu = w * u * 2.0;
vec3 Q1 = ww * cv[ 1].P + wu * cv[ 2].P + uu * cv[ 3].P +
uv * cv[ 7].P + vv * cv[10].P + vw * cv[ 6].P;
vec3 Q3 = ww * cv[ 5].P + wu * cv[ 6].P + uu * cv[ 7].P +
uv * cv[10].P + vv * cv[12].P + vw * cv[ 9].P;
vec3 Q4 = ww * cv[ 6].P + wu * cv[ 7].P + uu * cv[ 8].P +
uv * cv[11].P + vv * cv[13].P + vw * cv[10].P;
N = cross((Q4 - Q1), (Q3 - Q1));
nLength = length(N);
if (nLength < nEpsilon) {
nLength = 1.0;
}
}
N = N / nLength;
#endif
}
void
OsdEvalPatchGregoryTriangle(ivec3 patchParam, vec2 UV, vec3 cv[18],
out vec3 P, out vec3 dPu, out vec3 dPv,
out vec3 N, out vec3 dNu, out vec3 dNv)
{
float u = UV.x;
float v = UV.y;
float w = 1.0 - u - v;
float duv = u + v;
float dvw = v + w;
float dwu = w + u;
OsdPerPatchVertexBezier bezcv[15];
bezcv[ 6].P = (duv == 0.0) ? cv[3] : ((u*cv[ 3] + v*cv[ 4]) / duv);
bezcv[ 7].P = (dvw == 0.0) ? cv[8] : ((v*cv[ 8] + w*cv[ 9]) / dvw);
bezcv[10].P = (dwu == 0.0) ? cv[13] : ((w*cv[13] + u*cv[14]) / dwu);
bezcv[ 0].P = cv[ 0];
bezcv[ 1].P = cv[ 1];
bezcv[ 2].P = cv[15];
bezcv[ 3].P = cv[ 7];
bezcv[ 4].P = cv[ 5];
bezcv[ 5].P = cv[ 2];
bezcv[ 8].P = cv[ 6];
bezcv[ 9].P = cv[17];
bezcv[11].P = cv[16];
bezcv[12].P = cv[11];
bezcv[13].P = cv[12];
bezcv[14].P = cv[10];
OsdEvalPatchBezierTriangle(patchParam, UV, bezcv, P, dPu, dPv, N, dNu, dNv);
}
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