// // Copyright 2013-2019 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. // // ---------------------------------------------------------------------------- // Legacy Gregory // ---------------------------------------------------------------------------- #if defined(OSD_PATCH_GREGORY) || defined(OSD_PATCH_GREGORY_BOUNDARY) #define M_PI 3.14159265359f // precomputed catmark coefficient table up to valence 29 static float OsdCatmarkCoefficient[30] = { 0, 0, 0, 0.812816, 0.500000, 0.363644, 0.287514, 0.238688, 0.204544, 0.179229, 0.159657, 0.144042, 0.131276, 0.120632, 0.111614, 0.103872, 0.09715, 0.0912559, 0.0860444, 0.0814022, 0.0772401, 0.0734867, 0.0700842, 0.0669851, 0.0641504, 0.0615475, 0.0591488, 0.0569311, 0.0548745, 0.0529621 }; float OsdComputeCatmarkCoefficient(int valence) { #if OSD_MAX_VALENCE < 30 return OsdCatmarkCoefficient[valence]; #else if (valence < 30) { return OsdCatmarkCoefficient[valence]; } else { float t = 2.0f * float(M_PI) / float(valence); return 1.0f / (valence * (cos(t) + 5.0f + sqrt((cos(t) + 9) * (cos(t) + 1)))/16.0f); } #endif } float cosfn(int n, int j) { return cos((2.0f * M_PI * j)/float(n)); } float sinfn(int n, int j) { return sin((2.0f * M_PI * j)/float(n)); } #if !defined OSD_MAX_VALENCE || OSD_MAX_VALENCE < 1 #undef OSD_MAX_VALENCE #define OSD_MAX_VALENCE 4 #endif struct OsdPerVertexGregory { float3 P : POSITION0; int3 clipFlag : CLIPFLAG; int valence : BLENDINDICE0; float3 e0 : POSITION1; float3 e1 : POSITION2; #ifdef OSD_PATCH_GREGORY_BOUNDARY int zerothNeighbor : BLENDINDICE1; float3 org : POSITION3; #endif float3 r[OSD_MAX_VALENCE] : POSITION4; }; struct OsdPerPatchVertexGregory { int3 patchParam: PATCHPARAM; float3 P : POSITION0; float3 Ep : POSITION1; float3 Em : POSITION2; float3 Fp : POSITION3; float3 Fm : POSITION4; }; #ifndef OSD_NUM_ELEMENTS #define OSD_NUM_ELEMENTS 3 #endif Buffer<float> OsdVertexBuffer : register( t2 ); Buffer<int> OsdValenceBuffer : register( t3 ); float3 OsdReadVertex(int vertexIndex) { int index = int(OSD_NUM_ELEMENTS * (vertexIndex /*+ OsdBaseVertex()*/)); return float3(OsdVertexBuffer[index], OsdVertexBuffer[index+1], OsdVertexBuffer[index+2]); } int OsdReadVertexValence(int vertexID) { int index = int(vertexID * (2 * OSD_MAX_VALENCE + 1)); return OsdValenceBuffer[index]; } int OsdReadVertexIndex(int vertexID, int valenceVertex) { int index = int(vertexID * (2 * OSD_MAX_VALENCE + 1) + 1 + valenceVertex); return OsdValenceBuffer[index]; } Buffer<int> OsdQuadOffsetBuffer : register( t4 ); int OsdReadQuadOffset(int primitiveID, int offsetVertex) { int index = int(4*primitiveID+OsdGregoryQuadOffsetBase() + offsetVertex); return OsdQuadOffsetBuffer[index]; } void OsdComputePerVertexGregory(int vID, float3 P, out OsdPerVertexGregory v) { v.clipFlag = int3(0,0,0); int ivalence = OsdReadVertexValence(vID); v.valence = ivalence; int valence = abs(ivalence); float3 f[OSD_MAX_VALENCE]; float3 pos = P; float3 opos = float3(0,0,0); #ifdef OSD_PATCH_GREGORY_BOUNDARY v.org = pos; int boundaryEdgeNeighbors[2]; int currNeighbor = 0; int ibefore = 0; int zerothNeighbor = 0; #endif for (int i=0; i<valence; ++i) { int im = (i+valence-1)%valence; int ip = (i+1)%valence; int idx_neighbor = OsdReadVertexIndex(vID, 2*i); #ifdef OSD_PATCH_GREGORY_BOUNDARY bool isBoundaryNeighbor = false; int valenceNeighbor = OsdReadVertexValence(idx_neighbor); if (valenceNeighbor < 0) { isBoundaryNeighbor = true; if (currNeighbor<2) { boundaryEdgeNeighbors[currNeighbor] = idx_neighbor; } currNeighbor++; if (currNeighbor == 1) { ibefore = i; zerothNeighbor = i; } else { if (i-ibefore == 1) { int tmp = boundaryEdgeNeighbors[0]; boundaryEdgeNeighbors[0] = boundaryEdgeNeighbors[1]; boundaryEdgeNeighbors[1] = tmp; zerothNeighbor = i; } } } #endif float3 neighbor = OsdReadVertex(idx_neighbor); int idx_diagonal = OsdReadVertexIndex(vID, 2*i + 1); float3 diagonal = OsdReadVertex(idx_diagonal); int idx_neighbor_p = OsdReadVertexIndex(vID, 2*ip); float3 neighbor_p = OsdReadVertex(idx_neighbor_p); int idx_neighbor_m = OsdReadVertexIndex(vID, 2*im); float3 neighbor_m = OsdReadVertex(idx_neighbor_m); int idx_diagonal_m = OsdReadVertexIndex(vID, 2*im + 1); float3 diagonal_m = OsdReadVertex(idx_diagonal_m); f[i] = (pos * float(valence) + (neighbor_p + neighbor)*2.0f + diagonal) / (float(valence)+5.0f); opos += f[i]; v.r[i] = (neighbor_p-neighbor_m)/3.0f + (diagonal - diagonal_m)/6.0f; } opos /= valence; v.P = float4(opos, 1.0f).xyz; float3 e; v.e0 = float3(0,0,0); v.e1 = float3(0,0,0); for(int iv=0; iv<valence; ++iv) { int im = (iv + valence -1) % valence; e = 0.5f * (f[iv] + f[im]); v.e0 += cosfn(valence, iv)*e; v.e1 += sinfn(valence, iv)*e; } float ef = OsdComputeCatmarkCoefficient(valence); v.e0 *= ef; v.e1 *= ef; #ifdef OSD_PATCH_GREGORY_BOUNDARY v.zerothNeighbor = zerothNeighbor; if (currNeighbor == 1) { boundaryEdgeNeighbors[1] = boundaryEdgeNeighbors[0]; } if (ivalence < 0) { if (valence > 2) { v.P = (OsdReadVertex(boundaryEdgeNeighbors[0]) + OsdReadVertex(boundaryEdgeNeighbors[1]) + 4.0f * pos)/6.0f; } else { v.P = pos; } v.e0 = (OsdReadVertex(boundaryEdgeNeighbors[0]) - OsdReadVertex(boundaryEdgeNeighbors[1]))/6.0; float k = float(float(valence) - 1.0f); //k is the number of faces float c = cos(M_PI/k); float s = sin(M_PI/k); float gamma = -(4.0f*s)/(3.0f*k+c); float alpha_0k = -((1.0f+2.0f*c)*sqrt(1.0f+c))/((3.0f*k+c)*sqrt(1.0f-c)); float beta_0 = s/(3.0f*k + c); int idx_diagonal = OsdReadVertexIndex(vID, 2*zerothNeighbor + 1); float3 diagonal = OsdReadVertex(idx_diagonal); v.e1 = gamma * pos + alpha_0k * OsdReadVertex(boundaryEdgeNeighbors[0]) + alpha_0k * OsdReadVertex(boundaryEdgeNeighbors[1]) + beta_0 * diagonal; for (int x=1; x<valence - 1; ++x) { int curri = ((x + zerothNeighbor)%valence); float alpha = (4.0f*sin((M_PI * float(x))/k))/(3.0f*k+c); float beta = (sin((M_PI * float(x))/k) + sin((M_PI * float(x+1))/k))/(3.0f*k+c); int idx_neighbor = OsdReadVertexIndex(vID, 2*curri); float3 neighbor = OsdReadVertex(idx_neighbor); idx_diagonal = OsdReadVertexIndex(vID, 2*curri + 1); diagonal = OsdReadVertex(idx_diagonal); v.e1 += alpha * neighbor + beta * diagonal; } v.e1 /= 3.0f; } #endif } void OsdComputePerPatchVertexGregory(int3 patchParam, int ID, int primitiveID, in OsdPerVertexGregory v[4], out OsdPerPatchVertexGregory result) { result.patchParam = patchParam; result.P = v[ID].P; int i = ID; int ip = (i+1)%4; int im = (i+3)%4; int valence = abs(v[i].valence); int n = valence; int start = OsdReadQuadOffset(primitiveID, i) & 0xff; int prev = (OsdReadQuadOffset(primitiveID, i) >> 8) & 0xff; int start_m = OsdReadQuadOffset(primitiveID, im) & 0xff; int prev_p = (OsdReadQuadOffset(primitiveID, ip) >> 8) & 0xff; int np = abs(v[ip].valence); int nm = abs(v[im].valence); // Control Vertices based on : // "Approximating Subdivision Surfaces with Gregory Patches // for Hardware Tessellation" // Loop, Schaefer, Ni, Castano (ACM ToG Siggraph Asia 2009) // // P3 e3- e2+ P2 // O--------O--------O--------O // | | | | // | | | | // | | f3- | f2+ | // | O O | // e3+ O------O O------O e2- // | f3+ f2- | // | | // | | // | f0- f1+ | // e0- O------O O------O e1+ // | O O | // | | f0+ | f1- | // | | | | // | | | | // O--------O--------O--------O // P0 e0+ e1- P1 // #ifdef OSD_PATCH_GREGORY_BOUNDARY float3 Em_ip; if (v[ip].valence < -2) { int j = (np + prev_p - v[ip].zerothNeighbor) % np; Em_ip = v[ip].P + cos((M_PI*j)/float(np-1))*v[ip].e0 + sin((M_PI*j)/float(np-1))*v[ip].e1; } else { Em_ip = v[ip].P + v[ip].e0*cosfn(np, prev_p) + v[ip].e1*sinfn(np, prev_p); } float3 Ep_im; if (v[im].valence < -2) { int j = (nm + start_m - v[im].zerothNeighbor) % nm; Ep_im = v[im].P + cos((M_PI*j)/float(nm-1))*v[im].e0 + sin((M_PI*j)/float(nm-1))*v[im].e1; } else { Ep_im = v[im].P + v[im].e0*cosfn(nm, start_m) + v[im].e1*sinfn(nm, start_m); } if (v[i].valence < 0) { n = (n-1)*2; } if (v[im].valence < 0) { nm = (nm-1)*2; } if (v[ip].valence < 0) { np = (np-1)*2; } if (v[i].valence > 2) { result.Ep = v[i].P + (v[i].e0*cosfn(n, start) + v[i].e1*sinfn(n, start)); result.Em = v[i].P + (v[i].e0*cosfn(n, prev) + v[i].e1*sinfn(n, prev)); float s1=3-2*cosfn(n,1)-cosfn(np,1); float s2=2*cosfn(n,1); result.Fp = (cosfn(np,1)*v[i].P + s1*result.Ep + s2*Em_ip + v[i].r[start])/3.0f; s1 = 3.0f-2.0f*cos(2.0f*M_PI/float(n))-cos(2.0f*M_PI/float(nm)); result.Fm = (cosfn(nm,1)*v[i].P + s1*result.Em + s2*Ep_im - v[i].r[prev])/3.0f; } else if (v[i].valence < -2) { int j = (valence + start - v[i].zerothNeighbor) % valence; result.Ep = v[i].P + cos((M_PI*j)/float(valence-1))*v[i].e0 + sin((M_PI*j)/float(valence-1))*v[i].e1; j = (valence + prev - v[i].zerothNeighbor) % valence; result.Em = v[i].P + cos((M_PI*j)/float(valence-1))*v[i].e0 + sin((M_PI*j)/float(valence-1))*v[i].e1; float3 Rp = ((-2.0f * v[i].org - 1.0f * v[im].org) + (2.0f * v[ip].org + 1.0f * v[(i+2)%4].org))/3.0f; float3 Rm = ((-2.0f * v[i].org - 1.0f * v[ip].org) + (2.0f * v[im].org + 1.0f * v[(i+2)%4].org))/3.0f; float s1 = 3-2*cosfn(n,1)-cosfn(np,1); float s2 = 2*cosfn(n,1); result.Fp = (cosfn(np,1)*v[i].P + s1*result.Ep + s2*Em_ip + v[i].r[start])/3.0f; s1 = 3.0f-2.0f*cos(2.0f*M_PI/float(n))-cos(2.0f*M_PI/float(nm)); result.Fm = (cosfn(nm,1)*v[i].P + s1*result.Em + s2*Ep_im - v[i].r[prev])/3.0f; if (v[im].valence < 0) { s1 = 3-2*cosfn(n,1)-cosfn(np,1); result.Fp = result.Fm = (cosfn(np,1)*v[i].P + s1*result.Ep + s2*Em_ip + v[i].r[start])/3.0f; } else if (v[ip].valence < 0) { s1 = 3.0f-2.0f*cos(2.0f*M_PI/n)-cos(2.0f*M_PI/nm); result.Fm = result.Fp = (cosfn(nm,1)*v[i].P + s1*result.Em + s2*Ep_im - v[i].r[prev])/3.0f; } } else if (v[i].valence == -2) { result.Ep = (2.0f * v[i].org + v[ip].org)/3.0f; result.Em = (2.0f * v[i].org + v[im].org)/3.0f; result.Fp = result.Fm = (4.0f * v[i].org + v[(i+2)%n].org + 2.0f * v[ip].org + 2.0f * v[im].org)/9.0f; } #else // not OSD_PATCH_GREGORY_BOUNDARY result.Ep = v[i].P + v[i].e0 * cosfn(n, start) + v[i].e1*sinfn(n, start); result.Em = v[i].P + v[i].e0 * cosfn(n, prev ) + v[i].e1*sinfn(n, prev ); float3 Em_ip = v[ip].P + v[ip].e0*cosfn(np, prev_p) + v[ip].e1*sinfn(np, prev_p); float3 Ep_im = v[im].P + v[im].e0*cosfn(nm, start_m) + v[im].e1*sinfn(nm, start_m); float s1 = 3-2*cosfn(n,1)-cosfn(np,1); float s2 = 2*cosfn(n,1); result.Fp = (cosfn(np,1)*v[i].P + s1*result.Ep + s2*Em_ip + v[i].r[start])/3.0f; s1 = 3.0f-2.0f*cos(2.0f*M_PI/float(n))-cos(2.0f*M_PI/float(nm)); result.Fm = (cosfn(nm,1)*v[i].P + s1*result.Em +s2*Ep_im - v[i].r[prev])/3.0f; #endif } #endif // OSD_PATCH_GREGORY || OSD_PATCH_GREGORY_BOUNDARY