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rc/v3_3_3
OpenSubdiv/opensubdiv/osd/mtlPatchCommon.metal
David G Yu 6e02082bd7 Metal patch shader changes for degenerate normals 
Updated Metal patch shaders to resolve degenerate normals.
This fix was ported from the GLSL patch shader source.

Also, added missing inf sharp test cases to mtlViewer.
2017-12-12 08:46:00 -08:00

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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.
//
//----------------------------------------------------------
// Patches.Common
//----------------------------------------------------------
#include <metal_stdlib>
#define offsetof_(X, Y) &(((device X*)nullptr)->Y)
#define OSD_IS_ADAPTIVE (OSD_PATCH_REGULAR || OSD_PATCH_GREGORY_BASIS || OSD_PATCH_GREGORY || OSD_PATCH_GREGORY_BOUNDARY)
#ifndef OSD_MAX_TESS_LEVEL
#define OSD_MAX_TESS_LEVEL 64
#endif
#ifndef OSD_NUM_ELEMENTS
#define OSD_NUM_ELEMENTS 3
#endif
static_assert(sizeof(OsdInputVertexType) > 0, "OsdInputVertexType must be defined and have a float3 position member");
#if OSD_IS_ADAPTIVE
#if OSD_PATCH_GREGORY_BASIS
constant constexpr unsigned IndexLookupStride = 5;
#else
constant constexpr unsigned IndexLookupStride = 1;
#endif
#define PATCHES_PER_THREADGROUP ((THREADS_PER_THREADGROUP * CONTROL_POINTS_PER_THREAD) / CONTROL_POINTS_PER_PATCH)
#define REAL_THREADGROUP_DIVISOR (CONTROL_POINTS_PER_PATCH / CONTROL_POINTS_PER_THREAD)
static_assert(REAL_THREADGROUP_DIVISOR % 2 == 0, "REAL_THREADGROUP_DIVISOR must be a power of 2");
static_assert(!OSD_ENABLE_SCREENSPACE_TESSELLATION || !USE_PTVS_FACTORS, "USE_PTVS_FACTORS cannot be enabled if OSD_ENABLE_SCREENSPACE_TESSELLATION is enabled");
static_assert(OSD_ENABLE_SCREENSPACE_TESSELLATION && (OSD_FRACTIONAL_ODD_SPACING || OSD_FRACTIONAL_EVEN_SPACING) || !OSD_ENABLE_SCREENSPACE_TESSELLATION, "OSD_ENABLE_SCREENSPACE_TESSELLATION requires OSD_FRACTIONAL_ODD_SPACING or OSD_FRACTIONAL_EVEN_SPACING");
#endif
//Adjustments to the UV reparameterization can be defined here.
#ifndef OSD_UV_CORRECTION
#define OSD_UV_CORRECTION
#endif
using namespace metal;
// ----------------------------------------------------------------------------
// 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.
//
using OsdPatchParamBufferType = packed_int3;
struct OsdPerVertexGregory {
float3 P;
short3 clipFlag;
int valence;
float3 e0;
float3 e1;
#if OSD_PATCH_GREGORY_BOUNDARY
int zerothNeighbor;
float3 org;
#endif
float3 r[OSD_MAX_VALENCE];
};
struct OsdPerPatchVertexGregory {
packed_float3 P;
packed_float3 Ep;
packed_float3 Em;
packed_float3 Fp;
packed_float3 Fm;
};
//----------------------------------------------------------
// HLSL->Metal Compatibility
//----------------------------------------------------------
float4 mul(float4x4 a, float4 b)
{
return a * b;
}
float3 mul(float4x4 a, float3 b)
{
float3x3 m(a[0].xyz, a[1].xyz, a[2].xyz);
return m * b;
}
//----------------------------------------------------------
// Patches.Common
//----------------------------------------------------------
// 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
struct HullVertex {
float4 position;
#if OSD_ENABLE_PATCH_CULL
short3 clipFlag;
#endif
float3 GetPosition() threadgroup
{
return position.xyz;
}
void SetPosition(float3 v) threadgroup
{
position.xyz = v;
}
};
// XXXdyu all downstream data can be handled by client code
struct OsdPatchVertex {
float3 position;
float3 normal;
float3 tangent;
float3 bitangent;
float4 patchCoord; //u, v, faceLevel, faceId
#if OSD_COMPUTE_NORMAL_DERIVATIVES
float3 Nu;
float3 Nv;
#endif
#if OSD_PATCH_ENABLE_SINGLE_CREASE
float2 vSegments;
#endif
};
struct OsdPerPatchTessFactors {
float4 tessOuterLo;
float4 tessOuterHi;
};
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
};
struct OsdPerPatchVertexGregoryBasis {
packed_float3 P;
};
#if OSD_PATCH_REGULAR
using PatchVertexType = HullVertex;
using PerPatchVertexType = OsdPerPatchVertexBezier;
#elif OSD_PATCH_GREGORY || OSD_PATCH_GREGORY_BOUNDARY
using PatchVertexType = OsdPerVertexGregory;
using PerPatchVertexType = OsdPerPatchVertexGregory;
#elif OSD_PATCH_GREGORY_BASIS
using PatchVertexType = HullVertex;
using PerPatchVertexType = OsdPerPatchVertexGregoryBasis;
#else
using PatchVertexType = OsdInputVertexType;
using PerPatchVertexType = OsdInputVertexType;
#endif
//Shared buffers used by OSD that are common to all kernels
struct OsdPatchParamBufferSet
{
const device OsdInputVertexType* vertexBuffer [[buffer(VERTEX_BUFFER_INDEX)]];
const device unsigned* indexBuffer [[buffer(CONTROL_INDICES_BUFFER_INDEX)]];
const device OsdPatchParamBufferType* patchParamBuffer [[buffer(OSD_PATCHPARAM_BUFFER_INDEX)]];
device PerPatchVertexType* perPatchVertexBuffer [[buffer(OSD_PERPATCHVERTEXBEZIER_BUFFER_INDEX)]];
#if !USE_PTVS_FACTORS
device OsdPerPatchTessFactors* patchTessBuffer [[buffer(OSD_PERPATCHTESSFACTORS_BUFFER_INDEX)]];
#endif
#if OSD_PATCH_GREGORY || OSD_PATCH_GREGORY_BOUNDARY
const device int* quadOffsetBuffer [[buffer(OSD_QUADOFFSET_BUFFER_INDEX)]];
const device int* valenceBuffer [[buffer(OSD_VALENCE_BUFFER_INDEX)]];
#endif
const constant unsigned& kernelExecutionLimit [[buffer(OSD_KERNELLIMIT_BUFFER_INDEX)]];
};
//Shared buffers used by OSD that are common to all PTVS implementations
struct OsdVertexBufferSet
{
const device OsdInputVertexType* vertexBuffer [[buffer(VERTEX_BUFFER_INDEX)]];
const device unsigned* indexBuffer [[buffer(CONTROL_INDICES_BUFFER_INDEX)]];
const device OsdPatchParamBufferType* patchParamBuffer [[buffer(OSD_PATCHPARAM_BUFFER_INDEX)]];
device PerPatchVertexType* perPatchVertexBuffer [[buffer(OSD_PERPATCHVERTEXBEZIER_BUFFER_INDEX)]];
#if !USE_PTVS_FACTORS
device OsdPerPatchTessFactors* patchTessBuffer [[buffer(OSD_PERPATCHTESSFACTORS_BUFFER_INDEX)]];
#endif
};
// ----------------------------------------------------------------------------
// Patch Parameters Accessors
// ----------------------------------------------------------------------------
int3 OsdGetPatchParam(int patchIndex, const device OsdPatchParamBufferType* osdPatchParamBuffer)
{
#if OSD_PATCH_ENABLE_SINGLE_CREASE
return int3(osdPatchParamBuffer[patchIndex]);
#else
auto p = osdPatchParamBuffer[patchIndex];
return int3(p[0], p[1], 0);
#endif
}
int OsdGetPatchIndex(int primitiveId)
{
return primitiveId;
}
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 >> 8) & 0xf);
}
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;
}
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;
}
// ----------------------------------------------------------------------------
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;
}
// ----------------------------------------------------------------------------
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;
}
bool OsdCullPerPatchVertex(
threadgroup PatchVertexType* patch,
float4x4 ModelViewMatrix
)
{
#if OSD_ENABLE_BACKPATCH_CULL && OSD_PATCH_REGULAR
auto v0 = float3(ModelViewMatrix * patch[5].position);
auto v3 = float3(ModelViewMatrix * patch[6].position);
auto v12 = float3(ModelViewMatrix * patch[9].position);
auto n = normalize(cross(v3 - v0, v12 - v0));
v0 = normalize(v0 + v3 + v12);
if(dot(v0, n) > 0.6f)
{
return false;
}
#endif
#if OSD_ENABLE_PATCH_CULL
short3 clipFlag = short3(0,0,0);
for(int i = 0; i < CONTROL_POINTS_PER_PATCH; ++i) {
clipFlag |= patch[i].clipFlag;
}
if (any(clipFlag != short3(3,3,3))) {
return false;
}
#endif
return true;
}
// 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);
if ((boundaryMask & 1) != 0) {
cpt[0].SetPosition(2*cpt[4].GetPosition() - cpt[8].GetPosition());
cpt[1].SetPosition(2*cpt[5].GetPosition() - cpt[9].GetPosition());
cpt[2].SetPosition(2*cpt[6].GetPosition() - cpt[10].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[7].SetPosition(2*cpt[6].GetPosition() - cpt[5].GetPosition());
cpt[11].SetPosition(2*cpt[10].GetPosition() - cpt[9].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[13].SetPosition(2*cpt[9].GetPosition() - cpt[5].GetPosition());
cpt[14].SetPosition(2*cpt[10].GetPosition() - cpt[6].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[4].SetPosition(2*cpt[5].GetPosition() - cpt[6].GetPosition());
cpt[8].SetPosition(2*cpt[9].GetPosition() - cpt[10].GetPosition());
cpt[12].SetPosition(2*cpt[13].GetPosition() - cpt[14].GetPosition());
}
}
template<typename VertexType>
void
OsdComputeBSplineBoundaryPoints(thread VertexType* cpt, int3 patchParam)
{
int boundaryMask = OsdGetPatchBoundaryMask(patchParam);
if ((boundaryMask & 1) != 0) {
cpt[0].SetPosition(2*cpt[4].GetPosition() - cpt[8].GetPosition());
cpt[1].SetPosition(2*cpt[5].GetPosition() - cpt[9].GetPosition());
cpt[2].SetPosition(2*cpt[6].GetPosition() - cpt[10].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[7].SetPosition(2*cpt[6].GetPosition() - cpt[5].GetPosition());
cpt[11].SetPosition(2*cpt[10].GetPosition() - cpt[9].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[13].SetPosition(2*cpt[9].GetPosition() - cpt[5].GetPosition());
cpt[14].SetPosition(2*cpt[10].GetPosition() - cpt[6].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[4].SetPosition(2*cpt[5].GetPosition() - cpt[6].GetPosition());
cpt[8].SetPosition(2*cpt[9].GetPosition() - cpt[10].GetPosition());
cpt[12].SetPosition(2*cpt[13].GetPosition() - cpt[14].GetPosition());
}
}
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);
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);
}
// ----------------------------------------------------------------------------
// 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 occuring 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)
//
float OsdComputePostProjectionSphereExtent(const float4x4 OsdProjectionMatrix, float3 center, float diameter)
{
//float4 p = OsdProjectionMatrix * float4(center, 1.0);
float w = OsdProjectionMatrix[0][3] * center.x + OsdProjectionMatrix[1][3] * center.y + OsdProjectionMatrix[2][3] * center.z + OsdProjectionMatrix[3][3];
return abs(diameter * OsdProjectionMatrix[1][1] / w);
}
// 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(thread float4& tessOuterLo, thread float4& tessOuterHi,
thread float4& tessLevelOuter, thread float2& 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 OSD_FRACTIONAL_EVEN_SPACING
// Combine fractional outer transition edge levels before rounding.
float4 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 OSD_FRACTIONAL_ODD_SPACING
// Combine fractional outer transition edge levels before rounding.
float4 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(float4(3,3,3,3), combinedOuter);
}
if (tessOuterHi[1] > 0) {
tessLevelOuter[1] =
OsdRoundUpOdd(tessOuterLo[1]) + OsdRoundUpOdd(tessOuterHi[1]);
combinedOuter = max(float4(3,3,3,3), combinedOuter);
}
if (tessOuterHi[2] > 0) {
tessLevelOuter[2] =
OsdRoundUpOdd(tessOuterLo[2]) + OsdRoundUpOdd(tessOuterHi[2]);
combinedOuter = max(float4(3,3,3,3), combinedOuter);
}
if (tessOuterHi[3] > 0) {
tessLevelOuter[3] =
OsdRoundUpOdd(tessOuterLo[3]) + OsdRoundUpOdd(tessOuterHi[3]);
combinedOuter = max(float4(3,3,3,3), combinedOuter);
}
#else //OSD_FRACTIONAL_ODD_SPACING
// Round equally spaced transition edge levels before combining.
tessOuterLo = round(tessOuterLo);
tessOuterHi = round(tessOuterHi);
float4 combinedOuter = tessOuterLo + tessOuterHi;
tessLevelOuter = combinedOuter;
#endif //OSD_FRACTIONAL_ODD_SPACING
// 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;
}
float OsdComputeTessLevel(const float OsdTessLevel, const float4x4 OsdProjectionMatrix, const float4x4 OsdModelViewMatrix, float3 p0, float3 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.
float3 center = (p0 + p1) / 2.0;
float diameter = distance(p0, p1);
float projLength = OsdComputePostProjectionSphereExtent(OsdProjectionMatrix, 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
// halfs 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, (float)(OSD_MAX_TESS_LEVEL / 2));
}
void
OsdGetTessLevelsUniform(const float OsdTessLevel, int3 patchParam,
thread float4& tessOuterLo, thread float4& 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, ((float)OSD_MAX_TESS_LEVEL / 2)) /
pow(2, refinementLevel - 1.0f);
// float tessLevel = min(OsdTessLevel, (float)OSD_MAX_TESS_LEVEL);
// if(refinementLevel != 0)
// tessLevel /= (1 << (refinementLevel - 1));
// else
// {
// tessLevel /= pow(2.0, (0 - 1));
// tessLevel /= pow(2.0, (refinementLevel - 1));
// }
// tessLevels of transition edge should be clamped to 2.
int transitionMask = OsdGetPatchTransitionMask(patchParam);
float4 tessLevelMin = float4(1)
+ float4(((transitionMask & 8) >> 3),
((transitionMask & 1) >> 0),
((transitionMask & 2) >> 1),
((transitionMask & 4) >> 2));
// tessLevelMin = (tessLevelMin - 1.0) * 2.0f + 1.0;
// tessLevelMin = float4(OsdTessLevel);
tessOuterLo = max(float4(tessLevel,tessLevel,tessLevel,tessLevel),
tessLevelMin);
tessOuterHi = float4(0,0,0,0);
// tessOuterLo.x = refinementLevel;
}
void
OsdGetTessLevelsRefinedPoints(const float OsdTessLevel,
const float4x4 OsdProjectionMatrix, const float4x4 OsdModelViewMatrix,
float3 cp[16], int3 patchParam,
thread float4& tessOuterLo, thread float4& 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.
float3 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;
float3 ev01 = (cp[1] + cp[2] + cp[9] + cp[10]) * 0.0625 +
(cp[5] + cp[6]) * 0.375;
float3 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;
float3 ev12 = (cp[5] + cp[7] + cp[9] + cp[11]) * 0.0625 +
(cp[6] + cp[10]) * 0.375;
float3 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;
float3 ev23 = (cp[5] + cp[6] + cp[13] + cp[14]) * 0.0625 +
(cp[9] + cp[10]) * 0.375;
float3 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;
float3 ev03 = (cp[4] + cp[6] + cp[8] + cp[10]) * 0.0625 +
(cp[5] + cp[9]) * 0.375;
tessOuterLo = float4(0,0,0,0);
tessOuterHi = float4(0,0,0,0);
int transitionMask = OsdGetPatchTransitionMask(patchParam);
if ((transitionMask & 8) != 0) {
tessOuterLo[0] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix, vv0, ev03);
tessOuterHi[0] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix, vv3, ev03);
} else {
tessOuterLo[0] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix, cp[5], cp[9]);
}
if ((transitionMask & 1) != 0) {
tessOuterLo[1] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix, vv0, ev01);
tessOuterHi[1] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix, vv1, ev01);
} else {
tessOuterLo[1] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix, cp[5], cp[6]);
}
if ((transitionMask & 2) != 0) {
tessOuterLo[2] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix, vv1, ev12);
tessOuterHi[2] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix, vv2, ev12);
} else {
tessOuterLo[2] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix, cp[6], cp[10]);
}
if ((transitionMask & 4) != 0) {
tessOuterLo[3] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix, vv3, ev23);
tessOuterHi[3] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix, vv2, ev23);
} else {
tessOuterLo[3] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix, cp[9], cp[10]);
}
}
float3 miniMul(float4x4 a, float3 b)
{
float3 r;
r.x = a[0][0] * b[0] + a[1][0] * b[1] + a[2][0] * b[2] + a[3][0];
r.y = a[0][1] * b[0] + a[1][1] * b[1] + a[2][1] * b[2] + a[3][1];
r.z = a[0][2] * b[0] + a[1][2] * b[1] + a[2][2] * b[2] + a[3][2];
return r;
}
void
OsdGetTessLevelsLimitPoints(const float OsdTessLevel, const float4x4 OsdProjectionMatrix, const float4x4 OsdModelViewMatrix,
device OsdPerPatchVertexBezier* cpBezier,
int3 patchParam, thread float4& tessOuterLo, thread float4& 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 = float4(0,0,0,0);
tessOuterHi = float4(0,0,0,0);
int transitionMask = OsdGetPatchTransitionMask(patchParam);
#if OSD_PATCH_ENABLE_SINGLE_CREASE
// PERFOMANCE: we just need to pick the correct corner points from P, P1, P2
float3 p0 = OsdEvalBezier(cpBezier, patchParam, float2(0.0, 0.0));
float3 p3 = OsdEvalBezier(cpBezier, patchParam, float2(1.0, 0.0));
float3 p12 = OsdEvalBezier(cpBezier, patchParam, float2(0.0, 1.0));
float3 p15 = OsdEvalBezier(cpBezier, patchParam, float2(1.0, 1.0));
p0 = miniMul(OsdModelViewMatrix, p0);
p3 = miniMul(OsdModelViewMatrix, p3);
p12 = miniMul(OsdModelViewMatrix, p12);
p15 = miniMul(OsdModelViewMatrix, p15);
thread float3 * tPt;
float3 ev;
if ((transitionMask & 8) != 0) { // EVO3
ev = OsdEvalBezier(cpBezier, patchParam, float2(0.0, 0.5));
ev = miniMul(OsdModelViewMatrix, ev);
tPt = &ev;
tessOuterHi[0] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix,p12, ev);
} else {
tPt = &p12;
}
tessOuterLo[0] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix,p0, *tPt);
if ((transitionMask & 1) != 0) { // EV01
ev = OsdEvalBezier(cpBezier, patchParam, float2(0.5, 0.0));
ev = miniMul(OsdModelViewMatrix, ev);
tPt = &ev;
tessOuterHi[1] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix,p3, ev);
} else {
tPt = &p3;
}
tessOuterLo[1] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix,p0, *tPt);
if ((transitionMask & 2) != 0) { // EV12
ev = OsdEvalBezier(cpBezier, patchParam, float2(1.0, 0.5));
ev = miniMul(OsdModelViewMatrix, ev);
tPt = &ev;
tessOuterHi[2] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix,p15, ev);
} else {
tPt = &p15;
}
tessOuterLo[2] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix,p3, *tPt);
if ((transitionMask & 4) != 0) { // EV23
ev = OsdEvalBezier(cpBezier, patchParam, float2(0.5, 1.0));
ev = miniMul(OsdModelViewMatrix, ev);
tPt = &ev;
tessOuterHi[3] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix,p15, ev);
} else {
tPt = &p15;
}
tessOuterLo[3] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix,p12, *tPt);
#else // OSD_PATCH_ENABLE_SINGLE_CREASE
float3 p0 = OsdEvalBezier(cpBezier, patchParam, float2(0.0, 0.5));
float3 p3 = OsdEvalBezier(cpBezier, patchParam, float2(0.5, 0.0));
float3 p12 = OsdEvalBezier(cpBezier, patchParam, float2(1.0, 0.5));
float3 p15 = OsdEvalBezier(cpBezier, patchParam, float2(0.5, 1.0));
p0 = miniMul(OsdModelViewMatrix, p0);
p3 = miniMul(OsdModelViewMatrix, p3);
p12 = miniMul(OsdModelViewMatrix, p12);
p15 = miniMul(OsdModelViewMatrix, p15);
float3 c00 = miniMul(OsdModelViewMatrix, cpBezier[0].P);
float3 c12 = miniMul(OsdModelViewMatrix, cpBezier[12].P);
float3 c03 = miniMul(OsdModelViewMatrix, cpBezier[3].P);
float3 c15 = miniMul(OsdModelViewMatrix, cpBezier[15].P);
if ((transitionMask & 8) != 0) {
tessOuterLo[0] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix,c00, p0);
tessOuterHi[0] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix,c12, p0);
} else {
tessOuterLo[0] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix,c00, c12);
}
if ((transitionMask & 1) != 0) {
tessOuterLo[1] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix,c00, p3);
tessOuterHi[1] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix,c03, p3);
} else {
tessOuterLo[1] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix,c00, c03);
}
if ((transitionMask & 2) != 0) {
tessOuterLo[2] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix,c03, p12);
tessOuterHi[2] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix,c15, p12);
} else {
tessOuterLo[2] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix,c03, c15);
}
if ((transitionMask & 4) != 0) {
tessOuterLo[3] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix,c12, p15);
tessOuterHi[3] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix,c15, p15);
} else {
tessOuterLo[3] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix,c12, c15);
}
#endif
}
void
OsdGetTessLevelsUniform(const float OsdTessLevel, int3 patchParam,
thread float4& tessLevelOuter, thread float2& tessLevelInner,
thread float4& tessOuterLo, thread float4& tessOuterHi)
{
OsdGetTessLevelsUniform(OsdTessLevel, patchParam, tessOuterLo, tessOuterHi);
OsdComputeTessLevels(tessOuterLo, tessOuterHi, tessLevelOuter, tessLevelInner);
}
void
OsdGetTessLevelsAdaptiveRefinedPoints(const float OsdTessLevel, const float4x4 OsdProjectionMatrix, const float4x4 OsdModelViewMatrix,
float3 cpRefined[16], int3 patchParam,
thread float4& tessLevelOuter, thread float2& tessLevelInner,
thread float4& tessOuterLo, thread float4& tessOuterHi)
{
OsdGetTessLevelsRefinedPoints(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix, cpRefined, patchParam, tessOuterLo, tessOuterHi);
OsdComputeTessLevels(tessOuterLo, tessOuterHi,
tessLevelOuter, tessLevelInner);
}
void
OsdGetTessLevelsAdaptiveLimitPoints(const float OsdTessLevel, const float4x4 OsdProjectionMatrix, const float4x4 OsdModelViewMatrix,
device OsdPerPatchVertexBezier* cpBezier,
int3 patchParam,
thread float4& tessLevelOuter, thread float2& tessLevelInner,
thread float4& tessOuterLo, thread float4& tessOuterHi)
{
OsdGetTessLevelsLimitPoints(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix, cpBezier, patchParam, tessOuterLo, tessOuterHi);
OsdComputeTessLevels(tessOuterLo, tessOuterHi,
tessLevelOuter, tessLevelInner);
}
void
OsdGetTessLevels(const float OsdTessLevel, const float4x4 OsdProjectionMatrix, const float4x4 OsdModelViewMatrix,
float3 cp0, float3 cp1, float3 cp2, float3 cp3,
int3 patchParam,
thread float4& tessLevelOuter, thread float2& tessLevelInner)
{
float4 tessOuterLo = float4(0,0,0,0);
float4 tessOuterHi = float4(0,0,0,0);
cp0 = mul(OsdModelViewMatrix, float4(cp0, 1.0)).xyz;
cp1 = mul(OsdModelViewMatrix, float4(cp1, 1.0)).xyz;
cp2 = mul(OsdModelViewMatrix, float4(cp2, 1.0)).xyz;
cp3 = mul(OsdModelViewMatrix, float4(cp3, 1.0)).xyz;
#if OSD_ENABLE_SCREENSPACE_TESSELLATION
tessOuterLo[0] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix, cp0, cp1);
tessOuterLo[1] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix, cp0, cp3);
tessOuterLo[2] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix, cp2, cp3);
tessOuterLo[3] = OsdComputeTessLevel(OsdTessLevel, OsdProjectionMatrix, OsdModelViewMatrix, cp1, cp2);
tessOuterHi = float4(0,0,0,0);
#else //OSD_ENABLE_SCREENSPACE_TESSELLATION
OsdGetTessLevelsUniform(OsdTessLevel, patchParam, tessOuterLo, tessOuterHi);
#endif //OSD_ENABLE_SCREENSPACE_TESSELLATION
OsdComputeTessLevels(tessOuterLo, tessOuterHi,
tessLevelOuter, tessLevelInner);
}
#if OSD_FRACTIONAL_EVEN_SPACING || 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 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 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 //OSD_FRACTIONAL_ODD_SPACING
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 //OSD_FRACTIONAL_EVEN_SPACING || OSD_FRACTIONAL_ODD_SPACING
float
OsdGetTessTransitionSplit(float t, float lo, float hi )
{
#if 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 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 = (t * (loRoundUp + hiRoundUp + 1));
OSD_UV_CORRECTION
ti = round(ti);
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 //OSD_FRACTIONAL_ODD_SPACING
// 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 //OSD_FRACTIONAL_ODD_SPACING
}
float2
OsdGetTessParameterization(float2 uv, float4 tessOuterLo, float4 tessOuterHi)
{
float2 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;
}
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);
}
// ----------------------------------------------------------------------------
// GregoryBasis
// ----------------------------------------------------------------------------
void
OsdComputePerPatchVertexGregoryBasis(int3 patchParam, int ID, float3 cv,
device OsdPerPatchVertexGregoryBasis& result)
{
result.P = cv;
}
// 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)
);
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;
}
// ----------------------------------------------------------------------------
// BSpline
// ----------------------------------------------------------------------------
// 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
}
// 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;
}
// flip matrix orientation
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]));
}
void OsdFlipMatrix(threadgroup float * src, threadgroup float * dst)
{
for (int i = 0; i < 16; i++) dst[i] = src[15-i];
}
// ----------------------------------------------------------------------------
// Legacy Gregory
// ----------------------------------------------------------------------------
#if OSD_PATCH_GREGORY || OSD_PATCH_GREGORY_BOUNDARY
#if OSD_MAX_VALENCE<=10
constant float ef[7] = {
0.813008, 0.500000, 0.363636, 0.287505,
0.238692, 0.204549, 0.179211
};
#else
constant float ef[27] = {
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
};
#endif
float cosfn(int n, int j) {
return cospi((2.0f * j)/float(n));
}
float sinfn(int n, int j) {
return sinpi((2.0f * j)/float(n));
}
#ifndef OSD_MAX_VALENCE
#define OSD_MAX_VALENCE 4
#endif
template<typename OsdVertexBuffer>
float3 OsdReadVertex(int vertexIndex, OsdVertexBuffer osdVertexBuffer)
{
int index = (vertexIndex /*+ OsdBaseVertex()*/);
return osdVertexBuffer[index].position;
}
template<typename OsdValenceBuffer>
int OsdReadVertexValence(int vertexID, OsdValenceBuffer osdValenceBuffer)
{
int index = int(vertexID * (2 * OSD_MAX_VALENCE + 1));
return osdValenceBuffer[index];
}
template<typename OsdValenceBuffer>
int OsdReadVertexIndex(int vertexID, int valenceVertex, OsdValenceBuffer osdValenceBuffer)
{
int index = int(vertexID * (2 * OSD_MAX_VALENCE + 1) + 1 + valenceVertex);
return osdValenceBuffer[index];
}
template<typename OsdQuadOffsetBuffer>
int OsdReadQuadOffset(int primitiveID, int offsetVertex, OsdQuadOffsetBuffer osdQuadOffsetBuffer)
{
int index = int(4*primitiveID + offsetVertex);
return osdQuadOffsetBuffer[index];
}
void OsdComputePerVertexGregory(unsigned vID, float3 P, threadgroup OsdPerVertexGregory& v, OsdPatchParamBufferSet osdBuffers)
{
v.clipFlag = short3(0,0,0);
int ivalence = OsdReadVertexValence(vID, osdBuffers.valenceBuffer);
v.valence = ivalence;
int valence = abs(ivalence);
float3 f[OSD_MAX_VALENCE];
float3 pos = P;
float3 opos = float3(0,0,0);
#if 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, osdBuffers.valenceBuffer);
#if OSD_PATCH_GREGORY_BOUNDARY
bool isBoundaryNeighbor = false;
int valenceNeighbor = OsdReadVertexValence(idx_neighbor, osdBuffers.valenceBuffer);
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, osdBuffers.vertexBuffer);
int idx_diagonal = OsdReadVertexIndex(vID, 2*i + 1, osdBuffers.valenceBuffer);
float3 diagonal = OsdReadVertex(idx_diagonal, osdBuffers.vertexBuffer);
int idx_neighbor_p = OsdReadVertexIndex(vID, 2*ip, osdBuffers.valenceBuffer);
float3 neighbor_p = OsdReadVertex(idx_neighbor_p, osdBuffers.vertexBuffer);
int idx_neighbor_m = OsdReadVertexIndex(vID, 2*im, osdBuffers.valenceBuffer);
float3 neighbor_m = OsdReadVertex(idx_neighbor_m, osdBuffers.vertexBuffer);
int idx_diagonal_m = OsdReadVertexIndex(vID, 2*im + 1, osdBuffers.valenceBuffer);
float3 diagonal_m = OsdReadVertex(idx_diagonal_m, osdBuffers.vertexBuffer);
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 i=0; i<valence; ++i) {
int im = (i + valence -1) % valence;
e = 0.5f * (f[i] + f[im]);
v.e0 += cosfn(valence, i)*e;
v.e1 += sinfn(valence, i)*e;
}
v.e0 *= ef[valence - 3];
v.e1 *= ef[valence - 3];
#if 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], osdBuffers.vertexBuffer) +
OsdReadVertex(boundaryEdgeNeighbors[1], osdBuffers.vertexBuffer) +
4.0f * pos)/6.0f;
} else {
v.P = pos;
}
v.e0 = (OsdReadVertex(boundaryEdgeNeighbors[0], osdBuffers.vertexBuffer) -
OsdReadVertex(boundaryEdgeNeighbors[1], osdBuffers.vertexBuffer))/6.0;
float k = float(float(valence) - 1.0f); //k is the number of faces
float c = cospi(1.0/k);
float s = sinpi(1.0/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, osdBuffers.valenceBuffer);
float3 diagonal = OsdReadVertex(idx_diagonal, osdBuffers.vertexBuffer);
v.e1 = gamma * pos +
alpha_0k * OsdReadVertex(boundaryEdgeNeighbors[0], osdBuffers.vertexBuffer) +
alpha_0k * OsdReadVertex(boundaryEdgeNeighbors[1], osdBuffers.vertexBuffer) +
beta_0 * diagonal;
for (int x=1; x<valence - 1; ++x) {
int curri = ((x + zerothNeighbor)%valence);
float alpha = (4.0f*sinpi((float(x))/k))/(3.0f*k+c);
float beta = (sinpi((float(x))/k) + sinpi((float(x+1))/k))/(3.0f*k+c);
int idx_neighbor = OsdReadVertexIndex(vID, 2*curri, osdBuffers.valenceBuffer);
float3 neighbor = OsdReadVertex(idx_neighbor, osdBuffers.vertexBuffer);
idx_diagonal = OsdReadVertexIndex(vID, 2*curri + 1, osdBuffers.valenceBuffer);
diagonal = OsdReadVertex(idx_diagonal, osdBuffers.vertexBuffer);
v.e1 += alpha * neighbor + beta * diagonal;
}
v.e1 /= 3.0f;
}
#endif
}
void
OsdComputePerPatchVertexGregory(int3 patchParam, unsigned ID, unsigned primitiveID,
threadgroup OsdPerVertexGregory* v,
device OsdPerPatchVertexGregory& result,
OsdPatchParamBufferSet osdBuffers)
{
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, osdBuffers.quadOffsetBuffer) & 0xff;
int prev = (OsdReadQuadOffset(primitiveID, i, osdBuffers.quadOffsetBuffer) >> 8) & 0xff;
int start_m = OsdReadQuadOffset(primitiveID, im, osdBuffers.quadOffsetBuffer) & 0xff;
int prev_p = (OsdReadQuadOffset(primitiveID, ip, osdBuffers.quadOffsetBuffer) >> 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
//
#if 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 + cospi(j/float(np-1))*v[ip].e0 + sinpi(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 + cospi(j/float(nm-1))*v[im].e0 + sinpi(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*cospi(2.0f/float(n))-cospi(2.0f/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 + cospi(j/float(valence-1))*v[i].e0 + sinpi(j/float(valence-1))*v[i].e1;
j = (valence + prev - v[i].zerothNeighbor) % valence;
result.Em = v[i].P + cospi(j/float(valence-1))*v[i].e0 + sinpi(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*cospi(2.0f/float(n))-cospi(2.0f/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*cospi(2.0f/n)-cospi(2.0f/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*cospi(2.0f/float(n))-cospi(2.0f/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
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