// // 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 // For now, fractional spacing is supported only with screen space tessellation #ifndef OSD_ENABLE_SCREENSPACE_TESSELLATION #undef OSD_FRACTIONAL_EVEN_SPACING #undef OSD_FRACTIONAL_ODD_SPACING #endif #if defined OSD_FRACTIONAL_EVEN_SPACING #define OSD_SPACING fractional_even_spacing #elif defined OSD_FRACTIONAL_ODD_SPACING #define OSD_SPACING fractional_odd_spacing #else #define OSD_SPACING equal_spacing #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; } 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); } // ---------------------------------------------------------------------------- // 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); if ((boundaryMask & 1) != 0) { cpt[0] = 2*cpt[4] - cpt[8]; cpt[1] = 2*cpt[5] - cpt[9]; cpt[2] = 2*cpt[6] - cpt[10]; cpt[3] = 2*cpt[7] - cpt[11]; } if ((boundaryMask & 2) != 0) { cpt[3] = 2*cpt[2] - cpt[1]; cpt[7] = 2*cpt[6] - cpt[5]; cpt[11] = 2*cpt[10] - cpt[9]; cpt[15] = 2*cpt[14] - cpt[13]; } if ((boundaryMask & 4) != 0) { cpt[12] = 2*cpt[8] - cpt[4]; cpt[13] = 2*cpt[9] - cpt[5]; cpt[14] = 2*cpt[10] - cpt[6]; cpt[15] = 2*cpt[11] - cpt[7]; } if ((boundaryMask & 8) != 0) { cpt[0] = 2*cpt[1] - cpt[2]; cpt[4] = 2*cpt[5] - cpt[6]; cpt[8] = 2*cpt[9] - cpt[10]; cpt[12] = 2*cpt[13] - cpt[14]; } } // ---------------------------------------------------------------------------- // Tessellation // ---------------------------------------------------------------------------- // // Organization of B-spline and Bezier control points. // // Each patch is defined by 16 control points (labeled 0-15). // // The patch will be evaluated across the domain from (0,0) at // the lower-left to (1,1) at the upper-right. When computing // adaptive tessellation metrics, we consider refined vertex-vertex // and edge-vertex points along the transition edges of the patch // (labeled vv* and ev* respectively). // // The two segments of each transition edge are labeled Lo and Hi, // with the Lo segment occurring before the Hi segment along the // transition edge's domain parameterization. These Lo and Hi segment // tessellation levels determine how domain evaluation coordinates // are remapped along transition edges. The Hi segment value will // be zero for a non-transition edge. // // (0,1) (1,1) // // vv3 ev23 vv2 // | Lo3 | Hi3 | // --O-----------O-----+-----O-----------O-- // | 12 | 13 14 | 15 | // | | | | // | | | | // Hi0 | | | | Hi2 // | | | | // O-----------O-----------O-----------O // | 8 | 9 10 | 11 | // | | | | // ev03 --+ | | +-- ev12 // | | | | // | 4 | 5 6 | 7 | // O-----------O-----------O-----------O // | | | | // Lo0 | | | | Lo2 // | | | | // | | | | // | 0 | 1 2 | 3 | // --O-----------O-----+-----O-----------O-- // | Lo1 | Hi1 | // vv0 ev01 vv1 // // (0,0) (1,0) // #define OSD_MAX_TESS_LEVEL gl_MaxTessGenLevel float OsdComputePostProjectionSphereExtent(vec3 center, float diameter) { vec4 p = OsdProjectionMatrix() * vec4(center, 1.0); return abs(diameter * OsdProjectionMatrix()[1][1] / p.w); } float OsdComputeTessLevel(vec3 p0, vec3 p1) { // Adaptive factor can be any computation that depends only on arg values. // Project the diameter of the edge's bounding sphere instead of using the // length of the projected edge itself to avoid problems near silhouettes. p0 = (OsdModelViewMatrix() * vec4(p0, 1.0)).xyz; p1 = (OsdModelViewMatrix() * vec4(p1, 1.0)).xyz; vec3 center = (p0 + p1) / 2.0; float diameter = distance(p0, p1); float projLength = OsdComputePostProjectionSphereExtent(center, diameter); float tessLevel = max(1.0, OsdTessLevel() * projLength); // We restrict adaptive tessellation levels to half of the device // supported maximum because transition edges are split into two // halves and the sum of the two corresponding levels must not exceed // the device maximum. We impose this limit even for non-transition // edges because a non-transition edge must be able to match up with // one half of the transition edge of an adjacent transition patch. return min(tessLevel, OSD_MAX_TESS_LEVEL / 2); } void OsdGetTessLevelsUniform(ivec3 patchParam, out vec4 tessOuterLo, out vec4 tessOuterHi) { // Uniform factors are simple powers of two for each level. // The maximum here can be increased if we know the maximum // refinement level of the mesh: // min(OSD_MAX_TESS_LEVEL, pow(2, MaximumRefinementLevel-1) int refinementLevel = OsdGetPatchRefinementLevel(patchParam); float tessLevel = min(OsdTessLevel(), OSD_MAX_TESS_LEVEL) / pow(2, refinementLevel-1); // tessLevels of transition edge should be clamped to 2. int transitionMask = OsdGetPatchTransitionMask(patchParam); vec4 tessLevelMin = vec4(1) + vec4(((transitionMask & 8) >> 3), ((transitionMask & 1) >> 0), ((transitionMask & 2) >> 1), ((transitionMask & 4) >> 2)); tessOuterLo = max(vec4(tessLevel), tessLevelMin); tessOuterHi = vec4(0); } void OsdGetTessLevelsRefinedPoints(vec3 cp[16], ivec3 patchParam, out vec4 tessOuterLo, out vec4 tessOuterHi) { // Each edge of a transition patch is adjacent to one or two patches // at the next refined level of subdivision. We compute the corresponding // vertex-vertex and edge-vertex refined points along the edges of the // patch using Catmull-Clark subdivision stencil weights. // For simplicity, we let the optimizer discard unused computation. vec3 vv0 = (cp[0] + cp[2] + cp[8] + cp[10]) * 0.015625 + (cp[1] + cp[4] + cp[6] + cp[9]) * 0.09375 + cp[5] * 0.5625; vec3 ev01 = (cp[1] + cp[2] + cp[9] + cp[10]) * 0.0625 + (cp[5] + cp[6]) * 0.375; vec3 vv1 = (cp[1] + cp[3] + cp[9] + cp[11]) * 0.015625 + (cp[2] + cp[5] + cp[7] + cp[10]) * 0.09375 + cp[6] * 0.5625; vec3 ev12 = (cp[5] + cp[7] + cp[9] + cp[11]) * 0.0625 + (cp[6] + cp[10]) * 0.375; vec3 vv2 = (cp[5] + cp[7] + cp[13] + cp[15]) * 0.015625 + (cp[6] + cp[9] + cp[11] + cp[14]) * 0.09375 + cp[10] * 0.5625; vec3 ev23 = (cp[5] + cp[6] + cp[13] + cp[14]) * 0.0625 + (cp[9] + cp[10]) * 0.375; vec3 vv3 = (cp[4] + cp[6] + cp[12] + cp[14]) * 0.015625 + (cp[5] + cp[8] + cp[10] + cp[13]) * 0.09375 + cp[9] * 0.5625; vec3 ev03 = (cp[4] + cp[6] + cp[8] + cp[10]) * 0.0625 + (cp[5] + cp[9]) * 0.375; tessOuterLo = vec4(0); tessOuterHi = vec4(0); int transitionMask = OsdGetPatchTransitionMask(patchParam); if ((transitionMask & 8) != 0) { tessOuterLo[0] = OsdComputeTessLevel(vv0, ev03); tessOuterHi[0] = OsdComputeTessLevel(vv3, ev03); } else { tessOuterLo[0] = OsdComputeTessLevel(cp[5], cp[9]); } if ((transitionMask & 1) != 0) { tessOuterLo[1] = OsdComputeTessLevel(vv0, ev01); tessOuterHi[1] = OsdComputeTessLevel(vv1, ev01); } else { tessOuterLo[1] = OsdComputeTessLevel(cp[5], cp[6]); } if ((transitionMask & 2) != 0) { tessOuterLo[2] = OsdComputeTessLevel(vv1, ev12); tessOuterHi[2] = OsdComputeTessLevel(vv2, ev12); } else { tessOuterLo[2] = OsdComputeTessLevel(cp[6], cp[10]); } if ((transitionMask & 4) != 0) { tessOuterLo[3] = OsdComputeTessLevel(vv3, ev23); tessOuterHi[3] = OsdComputeTessLevel(vv2, ev23); } else { tessOuterLo[3] = OsdComputeTessLevel(cp[9], cp[10]); } } void OsdGetTessLevelsLimitPoints(OsdPerPatchVertexBezier cpBezier[16], ivec3 patchParam, out vec4 tessOuterLo, out vec4 tessOuterHi) { // Each edge of a transition patch is adjacent to one or two patches // at the next refined level of subdivision. When the patch control // points have been converted to the Bezier basis, the control points // at the four corners are on the limit surface (since a Bezier patch // interpolates its corner control points). We can compute an adaptive // tessellation level for transition edges on the limit surface by // evaluating a limit position at the mid point of each transition edge. tessOuterLo = vec4(0); tessOuterHi = vec4(0); int transitionMask = OsdGetPatchTransitionMask(patchParam); #if defined OSD_PATCH_ENABLE_SINGLE_CREASE // PERFOMANCE: we just need to pick the correct corner points from P, P1, P2 vec3 p0 = OsdEvalBezier(cpBezier, patchParam, vec2(0.0, 0.0)); vec3 p3 = OsdEvalBezier(cpBezier, patchParam, vec2(1.0, 0.0)); vec3 p12 = OsdEvalBezier(cpBezier, patchParam, vec2(0.0, 1.0)); vec3 p15 = OsdEvalBezier(cpBezier, patchParam, vec2(1.0, 1.0)); if ((transitionMask & 8) != 0) { vec3 ev03 = OsdEvalBezier(cpBezier, patchParam, vec2(0.0, 0.5)); tessOuterLo[0] = OsdComputeTessLevel(p0, ev03); tessOuterHi[0] = OsdComputeTessLevel(p12, ev03); } else { tessOuterLo[0] = OsdComputeTessLevel(p0, p12); } if ((transitionMask & 1) != 0) { vec3 ev01 = OsdEvalBezier(cpBezier, patchParam, vec2(0.5, 0.0)); tessOuterLo[1] = OsdComputeTessLevel(p0, ev01); tessOuterHi[1] = OsdComputeTessLevel(p3, ev01); } else { tessOuterLo[1] = OsdComputeTessLevel(p0, p3); } if ((transitionMask & 2) != 0) { vec3 ev12 = OsdEvalBezier(cpBezier, patchParam, vec2(1.0, 0.5)); tessOuterLo[2] = OsdComputeTessLevel(p3, ev12); tessOuterHi[2] = OsdComputeTessLevel(p15, ev12); } else { tessOuterLo[2] = OsdComputeTessLevel(p3, p15); } if ((transitionMask & 4) != 0) { vec3 ev23 = OsdEvalBezier(cpBezier, patchParam, vec2(0.5, 1.0)); tessOuterLo[3] = OsdComputeTessLevel(p12, ev23); tessOuterHi[3] = OsdComputeTessLevel(p15, ev23); } else { tessOuterLo[3] = OsdComputeTessLevel(p12, p15); } #else if ((transitionMask & 8) != 0) { vec3 ev03 = OsdEvalBezier(cpBezier, patchParam, vec2(0.0, 0.5)); tessOuterLo[0] = OsdComputeTessLevel(cpBezier[0].P, ev03); tessOuterHi[0] = OsdComputeTessLevel(cpBezier[12].P, ev03); } else { tessOuterLo[0] = OsdComputeTessLevel(cpBezier[0].P, cpBezier[12].P); } if ((transitionMask & 1) != 0) { vec3 ev01 = OsdEvalBezier(cpBezier, patchParam, vec2(0.5, 0.0)); tessOuterLo[1] = OsdComputeTessLevel(cpBezier[0].P, ev01); tessOuterHi[1] = OsdComputeTessLevel(cpBezier[3].P, ev01); } else { tessOuterLo[1] = OsdComputeTessLevel(cpBezier[0].P, cpBezier[3].P); } if ((transitionMask & 2) != 0) { vec3 ev12 = OsdEvalBezier(cpBezier, patchParam, vec2(1.0, 0.5)); tessOuterLo[2] = OsdComputeTessLevel(cpBezier[3].P, ev12); tessOuterHi[2] = OsdComputeTessLevel(cpBezier[15].P, ev12); } else { tessOuterLo[2] = OsdComputeTessLevel(cpBezier[3].P, cpBezier[15].P); } if ((transitionMask & 4) != 0) { vec3 ev23 = OsdEvalBezier(cpBezier, patchParam, vec2(0.5, 1.0)); tessOuterLo[3] = OsdComputeTessLevel(cpBezier[12].P, ev23); tessOuterHi[3] = OsdComputeTessLevel(cpBezier[15].P, ev23); } else { tessOuterLo[3] = OsdComputeTessLevel(cpBezier[12].P, cpBezier[15].P); } #endif } // Round up to the nearest even integer float OsdRoundUpEven(float x) { return 2*ceil(x/2); } // Round up to the nearest odd integer float OsdRoundUpOdd(float x) { return 2*ceil((x+1)/2)-1; } // Compute outer and inner tessellation levels taking into account the // current tessellation spacing mode. void OsdComputeTessLevels(inout vec4 tessOuterLo, inout vec4 tessOuterHi, out vec4 tessLevelOuter, out vec2 tessLevelInner) { // Outer levels are the sum of the Lo and Hi segments where the Hi // segments will have lengths of zero for non-transition edges. #if defined OSD_FRACTIONAL_EVEN_SPACING // Combine fractional outer transition edge levels before rounding. vec4 combinedOuter = tessOuterLo + tessOuterHi; // Round the segments of transition edges separately. We will recover the // fractional parameterization of transition edges after tessellation. tessLevelOuter = combinedOuter; if (tessOuterHi[0] > 0) { tessLevelOuter[0] = OsdRoundUpEven(tessOuterLo[0]) + OsdRoundUpEven(tessOuterHi[0]); } if (tessOuterHi[1] > 0) { tessLevelOuter[1] = OsdRoundUpEven(tessOuterLo[1]) + OsdRoundUpEven(tessOuterHi[1]); } if (tessOuterHi[2] > 0) { tessLevelOuter[2] = OsdRoundUpEven(tessOuterLo[2]) + OsdRoundUpEven(tessOuterHi[2]); } if (tessOuterHi[3] > 0) { tessLevelOuter[3] = OsdRoundUpEven(tessOuterLo[3]) + OsdRoundUpEven(tessOuterHi[3]); } #elif defined OSD_FRACTIONAL_ODD_SPACING // Combine fractional outer transition edge levels before rounding. vec4 combinedOuter = tessOuterLo + tessOuterHi; // Round the segments of transition edges separately. We will recover the // fractional parameterization of transition edges after tessellation. // // The sum of the two outer odd segment lengths will be an even number // which the tessellator will increase by +1 so that there will be a // total odd number of segments. We clamp the combinedOuter tess levels // (used to compute the inner tess levels) so that the outer transition // edges will be sampled without degenerate triangles. tessLevelOuter = combinedOuter; if (tessOuterHi[0] > 0) { tessLevelOuter[0] = OsdRoundUpOdd(tessOuterLo[0]) + OsdRoundUpOdd(tessOuterHi[0]); combinedOuter = max(vec4(3), combinedOuter); } if (tessOuterHi[1] > 0) { tessLevelOuter[1] = OsdRoundUpOdd(tessOuterLo[1]) + OsdRoundUpOdd(tessOuterHi[1]); combinedOuter = max(vec4(3), combinedOuter); } if (tessOuterHi[2] > 0) { tessLevelOuter[2] = OsdRoundUpOdd(tessOuterLo[2]) + OsdRoundUpOdd(tessOuterHi[2]); combinedOuter = max(vec4(3), combinedOuter); } if (tessOuterHi[3] > 0) { tessLevelOuter[3] = OsdRoundUpOdd(tessOuterLo[3]) + OsdRoundUpOdd(tessOuterHi[3]); combinedOuter = max(vec4(3), combinedOuter); } #else // Round equally spaced transition edge levels before combining. tessOuterLo = round(tessOuterLo); tessOuterHi = round(tessOuterHi); vec4 combinedOuter = tessOuterLo + tessOuterHi; tessLevelOuter = combinedOuter; #endif // Inner levels are the averages the corresponding outer levels. tessLevelInner[0] = (combinedOuter[1] + combinedOuter[3]) * 0.5; tessLevelInner[1] = (combinedOuter[0] + combinedOuter[2]) * 0.5; } void OsdGetTessLevelsUniform(ivec3 patchParam, out vec4 tessLevelOuter, out vec2 tessLevelInner, out vec4 tessOuterLo, out vec4 tessOuterHi) { // uniform tessellation OsdGetTessLevelsUniform(patchParam, tessOuterLo, tessOuterHi); OsdComputeTessLevels(tessOuterLo, tessOuterHi, tessLevelOuter, tessLevelInner); } void OsdGetTessLevelsAdaptiveRefinedPoints(vec3 cpRefined[16], ivec3 patchParam, out vec4 tessLevelOuter, out vec2 tessLevelInner, out vec4 tessOuterLo, out vec4 tessOuterHi) { OsdGetTessLevelsRefinedPoints(cpRefined, patchParam, tessOuterLo, tessOuterHi); OsdComputeTessLevels(tessOuterLo, tessOuterHi, tessLevelOuter, tessLevelInner); } void OsdGetTessLevelsAdaptiveLimitPoints(OsdPerPatchVertexBezier cpBezier[16], ivec3 patchParam, out vec4 tessLevelOuter, out vec2 tessLevelInner, out vec4 tessOuterLo, out vec4 tessOuterHi) { OsdGetTessLevelsLimitPoints(cpBezier, patchParam, tessOuterLo, tessOuterHi); OsdComputeTessLevels(tessOuterLo, tessOuterHi, tessLevelOuter, tessLevelInner); } void OsdGetTessLevels(vec3 cp0, vec3 cp1, vec3 cp2, vec3 cp3, ivec3 patchParam, out vec4 tessLevelOuter, out vec2 tessLevelInner) { vec4 tessOuterLo = vec4(0); vec4 tessOuterHi = vec4(0); #if defined OSD_ENABLE_SCREENSPACE_TESSELLATION tessOuterLo[0] = OsdComputeTessLevel(cp0, cp1); tessOuterLo[1] = OsdComputeTessLevel(cp0, cp3); tessOuterLo[2] = OsdComputeTessLevel(cp2, cp3); tessOuterLo[3] = OsdComputeTessLevel(cp1, cp2); tessOuterHi = vec4(0); #else OsdGetTessLevelsUniform(patchParam, tessOuterLo, tessOuterHi); #endif OsdComputeTessLevels(tessOuterLo, tessOuterHi, tessLevelOuter, tessLevelInner); } #if defined OSD_FRACTIONAL_EVEN_SPACING || defined OSD_FRACTIONAL_ODD_SPACING float OsdGetTessFractionalSplit(float t, float level, float levelUp) { // Fractional tessellation of an edge will produce n segments where n // is the tessellation level of the edge (level) rounded up to the // nearest even or odd integer (levelUp). There will be n-2 segments of // equal length (dx1) and two additional segments of equal length (dx0) // that are typically shorter than the other segments. The two additional // segments should be placed symmetrically on opposite sides of the // edge (offset). #if defined OSD_FRACTIONAL_EVEN_SPACING if (level <= 2) return t; float base = pow(2.0,floor(log2(levelUp))); float offset = 1.0/(int(2*base-levelUp)/2 & int(base/2-1)); #elif defined OSD_FRACTIONAL_ODD_SPACING if (level <= 1) return t; float base = pow(2.0,floor(log2(levelUp))); float offset = 1.0/(((int(2*base-levelUp)/2+1) & int(base/2-1))+1); #endif float dx0 = (1.0 - (levelUp-level)/2) / levelUp; float dx1 = (1.0 - 2.0*dx0) / (levelUp - 2.0*ceil(dx0)); if (t < 0.5) { float x = levelUp/2 - round(t*levelUp); return 0.5 - (x*dx1 + int(x*offset > 1) * (dx0 - dx1)); } else if (t > 0.5) { float x = round(t*levelUp) - levelUp/2; return 0.5 + (x*dx1 + int(x*offset > 1) * (dx0 - dx1)); } else { return t; } } #endif float OsdGetTessTransitionSplit(float t, float lo, float hi) { #if defined OSD_FRACTIONAL_EVEN_SPACING float loRoundUp = OsdRoundUpEven(lo); float hiRoundUp = OsdRoundUpEven(hi); // Convert the parametric t into a segment index along the combined edge. float ti = round(t * (loRoundUp + hiRoundUp)); if (ti <= loRoundUp) { float t0 = ti / loRoundUp; return OsdGetTessFractionalSplit(t0, lo, loRoundUp) * 0.5; } else { float t1 = (ti - loRoundUp) / hiRoundUp; return OsdGetTessFractionalSplit(t1, hi, hiRoundUp) * 0.5 + 0.5; } #elif defined OSD_FRACTIONAL_ODD_SPACING float loRoundUp = OsdRoundUpOdd(lo); float hiRoundUp = OsdRoundUpOdd(hi); // Convert the parametric t into a segment index along the combined edge. // The +1 below is to account for the extra segment produced by the // tessellator since the sum of two odd tess levels will be rounded // up by one to the next odd integer tess level. float ti = round(t * (loRoundUp + hiRoundUp + 1)); if (ti <= loRoundUp) { float t0 = ti / loRoundUp; return OsdGetTessFractionalSplit(t0, lo, loRoundUp) * 0.5; } else if (ti > (loRoundUp+1)) { float t1 = (ti - (loRoundUp+1)) / hiRoundUp; return OsdGetTessFractionalSplit(t1, hi, hiRoundUp) * 0.5 + 0.5; } else { return 0.5; } #else // Convert the parametric t into a segment index along the combined edge. float ti = round(t * (lo + hi)); if (ti <= lo) { return (ti / lo) * 0.5; } else { return ((ti - lo) / hi) * 0.5 + 0.5; } #endif } vec2 OsdGetTessParameterization(vec2 uv, vec4 tessOuterLo, vec4 tessOuterHi) { vec2 UV = uv; if (UV.x == 0 && tessOuterHi[0] > 0) { UV.y = OsdGetTessTransitionSplit(UV.y, tessOuterLo[0], tessOuterHi[0]); } else if (UV.y == 0 && tessOuterHi[1] > 0) { UV.x = OsdGetTessTransitionSplit(UV.x, tessOuterLo[1], tessOuterHi[1]); } else if (UV.x == 1 && tessOuterHi[2] > 0) { UV.y = OsdGetTessTransitionSplit(UV.y, tessOuterLo[2], tessOuterHi[2]); } else if (UV.y == 1 && tessOuterHi[3] > 0) { UV.x = OsdGetTessTransitionSplit(UV.x, tessOuterLo[3], tessOuterHi[3]); } return UV; } // ---------------------------------------------------------------------------- // 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); }