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OpenSubdiv/opensubdiv/osd/mtlPatchCommon.metal
David G Yu c2ed7d5cf0 Reorganized legacy patch drawing shader source 
Relocated from PatchCommon to PatchLegacy several aspects of the
shader source which can cause problems with typical use cases.
Specifically, things like resource bindings, input assembler and
interstage declarations are best left to client code.

These are not removed, just relocated and remain available for
backward compatibility. Updated the GLSL, HLSL, and MSL source.
2023-09-12 19:21:51 -07:00

1252 lines
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Metal
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#line 0 "osd/mtlPatchCommon.metal"
//
// Copyright 2015 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.
//
#include <metal_stdlib>
using namespace metal;
// The following callback functions are used when evaluating tessellation
// rates and when using legacy patch drawing.
float4x4 OsdModelViewMatrix();
float4x4 OsdProjectionMatrix();
float OsdTessLevel();
// ----------------------------------------------------------------------------
// 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
//
int OsdGetPatchFaceId(int3 patchParam)
{
return (patchParam.x & 0xfffffff);
}
int OsdGetPatchFaceLevel(int3 patchParam)
{
return (1 << ((patchParam.y & 0xf) - ((patchParam.y >> 4) & 1)));
}
int OsdGetPatchRefinementLevel(int3 patchParam)
{
return (patchParam.y & 0xf);
}
int OsdGetPatchBoundaryMask(int3 patchParam)
{
return ((patchParam.y >> 7) & 0x1f);
}
int OsdGetPatchTransitionMask(int3 patchParam)
{
return ((patchParam.x >> 28) & 0xf);
}
int2 OsdGetPatchFaceUV(int3 patchParam)
{
int u = (patchParam.y >> 22) & 0x3ff;
int v = (patchParam.y >> 12) & 0x3ff;
return int2(u,v);
}
bool OsdGetPatchIsRegular(int3 patchParam)
{
return ((patchParam.y >> 5) & 0x1) != 0;
}
bool OsdGetPatchIsTriangleRotated(int3 patchParam)
{
int2 uv = OsdGetPatchFaceUV(patchParam);
return (uv.x + uv.y) >= OsdGetPatchFaceLevel(patchParam);
}
float OsdGetPatchSharpness(int3 patchParam)
{
return as_type<float>(patchParam.z);
}
float OsdGetPatchSingleCreaseSegmentParameter(int3 patchParam, float2 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;
}
int4 OsdGetPatchCoord(int3 patchParam)
{
int faceId = OsdGetPatchFaceId(patchParam);
int faceLevel = OsdGetPatchFaceLevel(patchParam);
int2 faceUV = OsdGetPatchFaceUV(patchParam);
return int4(faceUV.x, faceUV.y, faceLevel, faceId);
}
float4 OsdInterpolatePatchCoord(float2 localUV, int3 patchParam)
{
int4 perPrimPatchCoord = OsdGetPatchCoord(patchParam);
int faceId = perPrimPatchCoord.w;
int faceLevel = perPrimPatchCoord.z;
float2 faceUV = float2(perPrimPatchCoord.x, perPrimPatchCoord.y);
float2 uv = localUV/faceLevel + faceUV/faceLevel;
// add 0.5 to integer values for more robust interpolation
return float4(uv.x, uv.y, faceLevel+0.5, faceId+0.5);
}
float4 OsdInterpolatePatchCoordTriangle(float2 localUV, int3 patchParam)
{
float4 result = OsdInterpolatePatchCoord(localUV, patchParam);
if (OsdGetPatchIsTriangleRotated(patchParam)) {
result.xy = float2(1.0f, 1.0f) - result.xy;
}
return result;
}
// ----------------------------------------------------------------------------
void
OsdUnivar4x4(float u, thread float* B)
{
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;
}
void
OsdUnivar4x4(float u, thread float* B, thread float* D)
{
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(float u, thread float* B, thread float* D, thread float* C)
{
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 {
packed_float3 P;
#if OSD_PATCH_ENABLE_SINGLE_CREASE
packed_float3 P1;
packed_float3 P2;
#if !USE_PTVS_SHARPNESS
float2 vSegments;
#endif
#endif
};
float3
OsdEvalBezier(float3 cp[16], float2 uv)
{
float3 BUCP[4] = {float3(0,0,0),float3(0,0,0),float3(0,0,0),float3(0,0,0)};
float B[4], D[4];
OsdUnivar4x4(uv.x, B, D);
for (int i=0; i<4; ++i) {
for (int j=0; j<4; ++j) {
float3 A = cp[4*i + j];
BUCP[i] += A * B[j];
}
}
float3 P = float3(0,0,0);
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) |
// +------------------+-------------------+------------------+
//
float3
OsdEvalBezier(device OsdPerPatchVertexBezier* cp, int3 patchParam, float2 uv)
{
float3 BUCP[4] = {float3(0,0,0),float3(0,0,0),float3(0,0,0),float3(0,0,0)};
float B[4], D[4];
float s = OsdGetPatchSingleCreaseSegmentParameter(patchParam, uv);
OsdUnivar4x4(uv.x, B, D);
#if OSD_PATCH_ENABLE_SINGLE_CREASE
#if USE_PTVS_SHARPNESS
float sharpness = OsdGetPatchSharpness(patchParam);
float Sf = floor(sharpness);
float Sc = ceil(sharpness);
float s0 = 1 - exp2(-Sf);
float s1 = 1 - exp2(-Sc);
float2 vSegments(s0, s1);
#else
float2 vSegments = cp[0].vSegments;
#endif // USE_PTVS_SHARPNESS
//By doing the offset calculation ahead of time it can be kept out of the actual indexing lookup.
if(s <= vSegments.x)
cp = (device OsdPerPatchVertexBezier*)(((device float*)cp) + 0);
else if( s <= vSegments.y)
cp = (device OsdPerPatchVertexBezier*)(((device float*)cp) + 3);
else
cp = (device OsdPerPatchVertexBezier*)(((device float*)cp) + 6);
BUCP[0] += cp[0].P * B[0];
BUCP[0] += cp[1].P * B[1];
BUCP[0] += cp[2].P * B[2];
BUCP[0] += cp[3].P * B[3];
BUCP[1] += cp[4].P * B[0];
BUCP[1] += cp[5].P * B[1];
BUCP[1] += cp[6].P * B[2];
BUCP[1] += cp[7].P * B[3];
BUCP[2] += cp[8].P * B[0];
BUCP[2] += cp[9].P * B[1];
BUCP[2] += cp[10].P * B[2];
BUCP[2] += cp[11].P * B[3];
BUCP[3] += cp[12].P * B[0];
BUCP[3] += cp[13].P * B[1];
BUCP[3] += cp[14].P * B[2];
BUCP[3] += cp[15].P * B[3];
#else // single crease
for (int i=0; i<4; ++i) {
for (int j=0; j<4; ++j) {
float3 A = cp[4*i + j].P;
BUCP[i] += A * B[j];
}
}
#endif // single crease
OsdUnivar4x4(uv.y, B);
float3 P = B[0] * BUCP[0];
for (int k=1; k<4; ++k) {
P += B[k] * BUCP[k];
}
return P;
}
// ----------------------------------------------------------------------------
// Boundary Interpolation
// ----------------------------------------------------------------------------
template<typename VertexType>
void
OsdComputeBSplineBoundaryPoints(threadgroup VertexType* cpt, int3 patchParam)
{
//APPL TODO - multithread this
int boundaryMask = OsdGetPatchBoundaryMask(patchParam);
// Don't extrapolate corner points until all boundary points in place
if ((boundaryMask & 1) != 0) {
cpt[1].SetPosition(2*cpt[5].GetPosition() - cpt[9].GetPosition());
cpt[2].SetPosition(2*cpt[6].GetPosition() - cpt[10].GetPosition());
}
if ((boundaryMask & 2) != 0) {
cpt[7].SetPosition(2*cpt[6].GetPosition() - cpt[5].GetPosition());
cpt[11].SetPosition(2*cpt[10].GetPosition() - cpt[9].GetPosition());
}
if ((boundaryMask & 4) != 0) {
cpt[13].SetPosition(2*cpt[9].GetPosition() - cpt[5].GetPosition());
cpt[14].SetPosition(2*cpt[10].GetPosition() - cpt[6].GetPosition());
}
if ((boundaryMask & 8) != 0) {
cpt[4].SetPosition(2*cpt[5].GetPosition() - cpt[6].GetPosition());
cpt[8].SetPosition(2*cpt[9].GetPosition() - cpt[10].GetPosition());
}
// Now safe to extrapolate corner points:
if ((boundaryMask & 1) != 0) {
cpt[0].SetPosition(2*cpt[4].GetPosition() - cpt[8].GetPosition());
cpt[3].SetPosition(2*cpt[7].GetPosition() - cpt[11].GetPosition());
}
if ((boundaryMask & 2) != 0) {
cpt[3].SetPosition(2*cpt[2].GetPosition() - cpt[1].GetPosition());
cpt[15].SetPosition(2*cpt[14].GetPosition() - cpt[13].GetPosition());
}
if ((boundaryMask & 4) != 0) {
cpt[12].SetPosition(2*cpt[8].GetPosition() - cpt[4].GetPosition());
cpt[15].SetPosition(2*cpt[11].GetPosition() - cpt[7].GetPosition());
}
if ((boundaryMask & 8) != 0) {
cpt[0].SetPosition(2*cpt[1].GetPosition() - cpt[2].GetPosition());
cpt[12].SetPosition(2*cpt[13].GetPosition() - cpt[14].GetPosition());
}
}
template<typename VertexType>
void
OsdComputeBoxSplineTriangleBoundaryPoints(thread VertexType* cpt, int3 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].SetPosition(cpt[4].GetPosition() + (cpt[4].GetPosition() - cpt[8].GetPosition()));
} else {
cpt[0].SetPosition(cpt[4].GetPosition() + (cpt[3].GetPosition() - cpt[7].GetPosition()));
}
cpt[1].SetPosition(cpt[4].GetPosition() + cpt[5].GetPosition() - cpt[8].GetPosition());
if (edge1IsBoundary) {
cpt[2].SetPosition(cpt[5].GetPosition() + (cpt[5].GetPosition() - cpt[8].GetPosition()));
} else {
cpt[2].SetPosition(cpt[5].GetPosition() + (cpt[6].GetPosition() - cpt[9].GetPosition()));
}
}
if (edge1IsBoundary) {
if (edge0IsBoundary) {
cpt[6].SetPosition(cpt[5].GetPosition() + (cpt[5].GetPosition() - cpt[4].GetPosition()));
} else {
cpt[6].SetPosition(cpt[5].GetPosition() + (cpt[2].GetPosition() - cpt[1].GetPosition()));
}
cpt[9].SetPosition(cpt[5].GetPosition() + cpt[8].GetPosition() - cpt[4].GetPosition());
if (edge2IsBoundary) {
cpt[11].SetPosition(cpt[8].GetPosition() + (cpt[8].GetPosition() - cpt[4].GetPosition()));
} else {
cpt[11].SetPosition(cpt[8].GetPosition() + (cpt[10].GetPosition() - cpt[7].GetPosition()));
}
}
if (edge2IsBoundary) {
if (edge1IsBoundary) {
cpt[10].SetPosition(cpt[8].GetPosition() + (cpt[8].GetPosition() - cpt[5].GetPosition()));
} else {
cpt[10].SetPosition(cpt[8].GetPosition() + (cpt[11].GetPosition() - cpt[9].GetPosition()));
}
cpt[7].SetPosition(cpt[8].GetPosition() + cpt[4].GetPosition() - cpt[5].GetPosition());
if (edge0IsBoundary) {
cpt[3].SetPosition(cpt[4].GetPosition() + (cpt[4].GetPosition() - cpt[5].GetPosition()));
} else {
cpt[3].SetPosition(cpt[4].GetPosition() + (cpt[0].GetPosition() - cpt[1].GetPosition()));
}
}
if ((vBits & 1) != 0) {
cpt[3].SetPosition(cpt[4].GetPosition() + cpt[7].GetPosition() - cpt[8].GetPosition());
cpt[0].SetPosition(cpt[4].GetPosition() + cpt[1].GetPosition() - cpt[5].GetPosition());
}
if ((vBits & 2) != 0) {
cpt[2].SetPosition(cpt[5].GetPosition() + cpt[1].GetPosition() - cpt[4].GetPosition());
cpt[6].SetPosition(cpt[5].GetPosition() + cpt[9].GetPosition() - cpt[8].GetPosition());
}
if ((vBits & 4) != 0) {
cpt[11].SetPosition(cpt[8].GetPosition() + cpt[9].GetPosition() - cpt[5].GetPosition());
cpt[10].SetPosition(cpt[8].GetPosition() + cpt[7].GetPosition() - cpt[4].GetPosition());
}
}
// ----------------------------------------------------------------------------
// BSpline
// ----------------------------------------------------------------------------
// compute single-crease patch matrix
float4x4
OsdComputeMs(float sharpness)
{
float s = exp2(sharpness);
float s2 = s*s;
float s3 = s2*s;
float4x4 m(
float4(0, s + 1 + 3*s2 - s3, 7*s - 2 - 6*s2 + 2*s3, (1-s)*(s-1)*(s-1)),
float4(0, (1+s)*(1+s), 6*s - 2 - 2*s2, (s-1)*(s-1)),
float4(0, 1+s, 6*s - 2, 1-s),
float4(0, 1, 6*s - 2, 1));
m[0] /= (s*6.0);
m[1] /= (s*6.0);
m[2] /= (s*6.0);
m[3] /= (s*6.0);
m[0][0] = 1.0/6.0;
return m;
}
float4x4
OsdComputeMs2(float sharpness, float factor)
{
float s = exp2(sharpness);
float s2 = s*s;
float s3 = s2*s;
float sx6 = s*6.0;
float sx6m2 = sx6 - 2;
float sfrac1 = 1-s;
float ssub1 = s-1;
float ssub1_2 = ssub1 * ssub1;
float div6 = 1.0/6.0;
float4x4 m(
float4(0, s + 1 + 3*s2 - s3, 7*s - 2 - 6*s2 + 2*s3, sfrac1 * ssub1_2),
float4(0, 1 + 2*s + s2, sx6m2 - 2*s2, ssub1_2),
float4(0, 1+s, sx6m2, sfrac1),
float4(0, 1, sx6m2, 1));
m *= factor * (1/sx6);
m[0][0] = div6 * factor;
return m;
}
// flip matrix orientation
void OsdFlipMatrix(threadgroup float * src, threadgroup float * dst)
{
for (int i = 0; i < 16; i++) dst[i] = src[15-i];
}
float4x4 OsdFlipMatrix(float4x4 m)
{
return float4x4(float4(m[3][3], m[3][2], m[3][1], m[3][0]),
float4(m[2][3], m[2][2], m[2][1], m[2][0]),
float4(m[1][3], m[1][2], m[1][1], m[1][0]),
float4(m[0][3], m[0][2], m[0][1], m[0][0]));
}
// Regular BSpline to Bezier
constant float4x4 Q(
float4(1.f/6.f, 4.f/6.f, 1.f/6.f, 0.f),
float4(0.f, 4.f/6.f, 2.f/6.f, 0.f),
float4(0.f, 2.f/6.f, 4.f/6.f, 0.f),
float4(0.f, 1.f/6.f, 4.f/6.f, 1.f/6.f)
);
// Infinitely Sharp (boundary)
constant float4x4 Mi(
float4(1.f/6.f, 4.f/6.f, 1.f/6.f, 0.f),
float4(0.f, 4.f/6.f, 2.f/6.f, 0.f),
float4(0.f, 2.f/6.f, 4.f/6.f, 0.f),
float4(0.f, 0.f, 1.f, 0.f)
);
// convert BSpline cv to Bezier cv
template<typename VertexType> //VertexType should be some type that implements float3 VertexType::GetPosition()
void
OsdComputePerPatchVertexBSpline(
int3 patchParam, unsigned ID,
threadgroup VertexType* cv,
device OsdPerPatchVertexBezier& result)
{
int i = ID%4;
int j = ID/4;
#if OSD_PATCH_ENABLE_SINGLE_CREASE
float3 P = float3(0,0,0); // 0 to 1-2^(-Sf)
float3 P1 = float3(0,0,0); // 1-2^(-Sf) to 1-2^(-Sc)
float3 P2 = float3(0,0,0); // 1-2^(-Sc) to 1
float sharpness = OsdGetPatchSharpness(patchParam);
int boundaryMask = OsdGetPatchBoundaryMask(patchParam);
if (sharpness > 0 && (boundaryMask & 15))
{
float Sf = floor(sharpness);
float Sc = ceil(sharpness);
float Sr = fract(sharpness);
float4x4 Mj = OsdComputeMs2(Sf, 1-Sr);
float4x4 Ms = Mj;
Mj += (Sr * Mi);
Ms += OsdComputeMs2(Sc, Sr);
#if USE_PTVS_SHARPNESS
#else
float s0 = 1 - exp2(-Sf);
float s1 = 1 - exp2(-Sc);
result.vSegments = float2(s0, s1);
#endif
bool isBoundary[2];
isBoundary[0] = (((boundaryMask & 8) != 0) || ((boundaryMask & 2) != 0)) ? true : false;
isBoundary[1] = (((boundaryMask & 4) != 0) || ((boundaryMask & 1) != 0)) ? true : false;
bool needsFlip[2];
needsFlip[0] = (boundaryMask & 8) ? true : false;
needsFlip[1] = (boundaryMask & 1) ? true : false;
float3 Hi[4], Hj[4], Hs[4];
if (isBoundary[0])
{
int t[4] = {0,1,2,3};
int ti = i, step = 1, start = 0;
if (needsFlip[0]) {
t[0] = 3; t[1] = 2; t[2] = 1; t[3] = 0;
ti = 3-i;
start = 3; step = -1;
}
for (int l=0; l<4; ++l) {
Hi[l] = Hj[l] = Hs[l] = float3(0,0,0);
for (int k=0, tk = start; k<4; ++k, tk+=step) {
float3 p = cv[l*4 + k].GetPosition();
Hi[l] += Mi[ti][tk] * p;
Hj[l] += Mj[ti][tk] * p;
Hs[l] += Ms[ti][tk] * p;
}
}
}
else
{
for (int l=0; l<4; ++l) {
Hi[l] = Hj[l] = Hs[l] = float3(0,0,0);
for (int k=0; k<4; ++k) {
float3 p = cv[l*4 + k].GetPosition();
float3 val = Q[i][k] * p;
Hi[l] += val;
Hj[l] += val;
Hs[l] += val;
}
}
}
{
int t[4] = {0,1,2,3};
int tj = j, step = 1, start = 0;
if (needsFlip[1]) {
t[0] = 3; t[1] = 2; t[2] = 1; t[3] = 0;
tj = 3-j;
start = 3; step = -1;
}
for (int k=0, tk = start; k<4; ++k, tk+=step) {
if (isBoundary[1])
{
P += Mi[tj][tk]*Hi[k];
P1 += Mj[tj][tk]*Hj[k];
P2 += Ms[tj][tk]*Hs[k];
}
else
{
P += Q[j][k]*Hi[k];
P1 += Q[j][k]*Hj[k];
P2 += Q[j][k]*Hs[k];
}
}
}
result.P = P;
result.P1 = P1;
result.P2 = P2;
} else {
#if USE_PTVS_SHARPNESS
#else
result.vSegments = float2(0, 0);
#endif
OsdComputeBSplineBoundaryPoints(cv, patchParam);
float3 Hi[4];
for (int l=0; l<4; ++l) {
Hi[l] = float3(0,0,0);
for (int k=0; k<4; ++k) {
Hi[l] += Q[i][k] * cv[l*4 + k].GetPosition();
}
}
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);
float3 H[4];
for (int l=0; l<4; ++l) {
H[l] = float3(0,0,0);
for(int k=0; k<4; ++k) {
H[l] += Q[i][k] * (cv + l*4 + k)->GetPosition();
}
}
{
result.P = float3(0,0,0);
for (int k=0; k<4; ++k){
result.P += Q[j][k]*H[k];
}
}
#endif
}
template<typename PerPatchVertexBezier>
void
OsdEvalPatchBezier(int3 patchParam, float2 UV,
PerPatchVertexBezier cv,
thread float3& P, thread float3& dPu, thread float3& dPv,
thread float3& N, thread float3& dNu, thread float3& dNv,
thread float2& vSegments)
{
//
// 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;
float3 LROW[4], RROW[4];
#if OSD_PATCH_ENABLE_SINGLE_CREASE
#if USE_PTVS_SHARPNESS
float sharpness = OsdGetPatchSharpness(patchParam);
float Sf = floor(sharpness);
float Sc = ceil(sharpness);
float s0 = 1 - exp2(-Sf);
float s1 = 1 - exp2(-Sc);
vSegments = float2(s0, s1);
#else // USE_PTVS_SHARPNESS
vSegments = cv[0].vSegments;
#endif // USE_PTVS_SHARPNESS
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;
}
}
#else
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;
#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;
float3 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:
float3 DU0 = vinv * LPAIR[0] + v * LPAIR[1];
float3 DU1 = vinv * RPAIR[0] + v * RPAIR[1];
float3 DV0 = uinv * LPAIR[0] + u * RPAIR[0];
float3 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 {
float3 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 = float3(0,0,0);
dNv = float3(0,0,0);
#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);
float3 dUU = float3(0,0,0);
float3 dVV = float3(0,0,0);
float3 dUV = float3(0,0,0);
for (int i=0; i<4; ++i) {
for (int j=0; j<4; ++j) {
#if OSD_PATCH_ENABLE_SINGLE_CREASE
int k = 4*i + j;
float3 CV = (s <= vSegments.x) ? cv[k].P
: ((s <= vSegments.y) ? cv[k].P1
: cv[k].P2);
#else
float3 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 {
packed_float3 P;
};
void
OsdComputePerPatchVertexGregoryBasis(int3 patchParam, int ID, float3 cv,
device OsdPerPatchVertexGregoryBasis& result)
{
result.P = cv;
}
void
OsdEvalPatchGregory(int3 patchParam, float2 UV, thread float3* cv,
thread float3& P, thread float3& dPu, thread float3& dPv,
thread float3& N, thread float3& dNu, thread float3& 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];
float2 vSegments;
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, vSegments);
}
//
// 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.
//
template<typename VertexType>
void
OsdComputePerPatchVertexBoxSplineTriangle(
int3 patchParam, int ID,
threadgroup VertexType* cv,
device 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] = {
// 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 = float3(0);
int cvCoeffBase = 12 * ID;
for (int i = 0; i < 12; ++i) {
result.P += boxToBezierMatrix[cvCoeffBase + i] * cv[i].GetPosition();
}
result.P *= boxToBezierMatrixScale;
}
template<typename PerPatchVertexBezier>
void
OsdEvalPatchBezierTriangle(int3 patchParam, float2 UV,
PerPatchVertexBezier cv,
thread float3& P, thread float3& dPu, thread float3& dPv,
thread float3& N, thread float3& dNu, thread float3& 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;
float3 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;
float3 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;
float3 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;
float3 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;
float3 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;
float3 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;
float3 V0 = w * Q0 + u * Q1 + v * Q3;
float3 V1 = w * Q1 + u * Q2 + v * Q4;
float3 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;
float3 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;
float3 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;
float3 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;
float3 dUU = (Q0 - 2 * Q1 + Q2) * d2Scale;
float3 dVV = (Q0 - 2 * Q3 + Q5) * d2Scale;
float3 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 = float3(0);
dNv = float3(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;
float3 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;
float3 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;
float3 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(int3 patchParam, float2 UV, float3 cv[18],
thread float3& P, thread float3& dPu, thread float3& dPv,
thread float3& N, thread float3& dNu, thread float3& 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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