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OpenSubdiv/opensubdiv/osd/glslPatchCommon.glsl
David G Yu f881c49a5b Minor revisions to some Osd deprecation notes 
Several of the methods in osd/patchBasisCommon.h were
never intended as public API, and several have been
deprecated in favor of the newer OsdEvaluatePatchBasis()
and OsdEvaluatePatchBasisNormalized() methods. These
obsolete methods have now all be marked as deprecated.

Also, fixed a minor spelling typo in glslPatchBasisCommon.glsl
2019-06-10 15:29:03 -07:00

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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 extrapolate 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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