OpenSubdiv/opensubdiv/far/gregoryBasis.cpp

708 lines
22 KiB
C++

//
// 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.
//
#include "../far/gregoryBasis.h"
#include "../far/topologyRefiner.h"
#include <cassert>
#include <cmath>
#include <cstring>
namespace OpenSubdiv {
namespace OPENSUBDIV_VERSION {
// Builds a table of local indices pairs for each vertex of the patch.
//
// o
// N0 |
// | ....
// | .... : Gregory patch
// o ------ o ------ o ....
// N1 V | .... M3
// | .......
// | .......
// o .......
// N2
//
// [...] [N2 - N3] [...]
//
// Each value pair is composed of 2 index values in range [0-4[ pointing
// to the 2 neighbor vertices of the vertex 'V' belonging to the Gregory patch.
// Neighbor ordering is valence CCW and must match the winding of the 1-ring
// vertices.
//
static void
getQuadOffsets(Vtr::Level const& level, Vtr::Index fIndex, Vtr::Index offsets[]) {
Far::ConstIndexArray fVerts = level.getFaceVertices(fIndex);
assert(fVerts.size()==4);
for (int i = 0; i < 4; ++i) {
Vtr::Index vIndex = fVerts[i];
Vtr::ConstIndexArray vFaces = level.getVertexFaces(vIndex),
vEdges = level.getVertexEdges(vIndex);
int thisFaceInVFaces = -1;
for (int j = 0; j < vFaces.size(); ++j) {
if (fIndex == vFaces[j]) {
thisFaceInVFaces = j;
break;
}
}
assert(thisFaceInVFaces != -1);
// we have to use the number of incident edges to modulo the local index
// because there could be 2 consecutive edges in the face belonging to
// the Gregory patch.
offsets[i*2+0] = thisFaceInVFaces;
offsets[i*2+1] = (thisFaceInVFaces + 1)%vEdges.size();
}
}
#define GetNumMaxElems( maxvalence ) \
16 + maxvalence - 3
// limit valence of 30 because we use a pre-computed closed-form 'ef' table
static const int MAX_VALENCE=30,
MAX_ELEMS = GetNumMaxElems(MAX_VALENCE);
namespace Far {
//
// Basis point
//
// Implements arithmetic operators to manipulate the influence of the
// 1-ring control vertices supporting the patch basis
//
class Point {
public:
Point() : _size(0) { }
Point(Index idx, float weight = 1.0f) {
_size = 1;
_indices[0] = idx;
_weights[0] = weight;
}
Point(Point const & other) {
*this = other;
}
int GetSize() const {
return _size;
}
Index const * GetIndices() const {
return _indices;
}
float const * GetWeights() const {
return _weights;
}
Point & operator = (Point const & other) {
_size = other._size;
memcpy(_indices, other._indices, other._size*sizeof(Index));
memcpy(_weights, other._weights, other._size*sizeof(float));
return *this;
}
Point & operator += (Point const & other) {
for (int i=0; i<other._size; ++i) {
Index idx = findIndex(other._indices[i]);
_weights[idx] += other._weights[i];
}
return *this;
}
Point & operator -= (Point const & other) {
for (int i=0; i<other._size; ++i) {
Index idx = findIndex(other._indices[i]);
_weights[idx] -= other._weights[i];
}
return *this;
}
Point & operator *= (float f) {
for (int i=0; i<_size; ++i) {
_weights[i] *= f;
}
return *this;
}
Point & operator /= (float f) {
return (*this)*=(1.0f/f);
}
friend Point operator * (Point const & src, float f) {
Point p( src ); return p*=f;
}
friend Point operator / (Point const & src, float f) {
Point p( src ); return p*= (1.0f/f);
}
Point operator + (Point const & other) {
Point p(*this); return p+=other;
}
Point operator - (Point const & other) {
Point p(*this); return p-=other;
}
void OffsetIndices(Index offset) {
for (int i=0; i<_size; ++i) {
_indices[i] += offset;
}
}
void Copy(int ** size, Index ** indices, float ** weights) const;
private:
int findIndex(Index idx) {
for (int i=0; i<_size; ++i) {
if (_indices[i]==idx) {
return i;
}
}
_indices[_size]=idx;
_weights[_size]=0.0f;
++_size;
return _size-1;
}
int _size;
// XXXX this would really be better with VLA where we only allocate
// space based on the max vertex valence in the mesh, not the
// absolute maximum supported by the closed-form tangents table.
Index _indices[MAX_ELEMS];
float _weights[MAX_ELEMS];
};
void
Point::Copy(int ** size, Index ** indices, float ** weights) const {
memcpy(*indices, _indices, _size*sizeof(Index));
memcpy(*weights, _weights, _size*sizeof(float));
**size = _size;
*indices += _size;
*weights += _size;
++(*size);
}
//
// ProtoBasis
//
// Given a Vtr::Level and a face index, gathers all the influences of the 1-ring
// that supports the 20 CVs of a Gregory patch basis.
//
struct ProtoBasis {
ProtoBasis(Vtr::Level const & level, Index faceIndex);
int GetNumElements() const;
void OffsetIndices(Index offset);
void Copy(int * sizes, Index * indices, float * weights) const;
// Control Vertices based on :
// "Approximating Subdivision Surfaces with Gregory Patches for Hardware Tessellation"
// Loop, Schaefer, Ni, Castafio (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
//
Point P[4], Ep[4], Em[4], Fp[4], Fm[4];
};
int
ProtoBasis::GetNumElements() const {
int nelems=0;
for (int vid=0; vid<4; ++vid) {
nelems += P[vid].GetSize();
nelems += Ep[vid].GetSize();
nelems += Em[vid].GetSize();
nelems += Fp[vid].GetSize();
nelems += Fm[vid].GetSize();
}
return nelems;
}
void
ProtoBasis::OffsetIndices(Index offset) {
for (int vid=0; vid<4; ++vid) {
P[vid].OffsetIndices(offset);
Ep[vid].OffsetIndices(offset);
Em[vid].OffsetIndices(offset);
Fp[vid].OffsetIndices(offset);
Fm[vid].OffsetIndices(offset);
}
}
void
ProtoBasis::Copy(int * sizes, Index * indices, float * weights) const {
for (int vid=0; vid<4; ++vid) {
P[vid].Copy(&sizes, &indices, &weights);
Ep[vid].Copy(&sizes, &indices, &weights);
Em[vid].Copy(&sizes, &indices, &weights);
Fp[vid].Copy(&sizes, &indices, &weights);
Fm[vid].Copy(&sizes, &indices, &weights);
}
}
inline float csf(Index n, Index j) {
if (j%2 == 0) {
return cosf((2.0f * float(M_PI) * float(float(j-0)/2.0f))/(float(n)+3.0f));
} else {
return sinf((2.0f * float(M_PI) * float(float(j-1)/2.0f))/(float(n)+3.0f));
}
}
ProtoBasis::ProtoBasis(Vtr::Level const & level, Index faceIndex) {
static float ef[MAX_VALENCE-3] = {
0.812816f, 0.500000f, 0.363644f, 0.287514f,
0.238688f, 0.204544f, 0.179229f, 0.159657f,
0.144042f, 0.131276f, 0.120632f, 0.111614f,
0.103872f, 0.09715f, 0.0912559f, 0.0860444f,
0.0814022f, 0.0772401f, 0.0734867f, 0.0700842f,
0.0669851f, 0.0641504f, 0.0615475f, 0.0591488f,
0.0569311f, 0.0548745f, 0.0529621f
};
Vtr::ConstIndexArray faceVerts = level.getFaceVertices(faceIndex);
assert(faceVerts.size()==4);
int maxvalence = level.getMaxValence(),
valences[4],
zerothNeighbors[4];
Index * manifoldRing = (int *)alloca((maxvalence+2)*2 * sizeof(int));
// Because MSVC does not support VLAs, we have to run alloca() in a macro and
// call in-place constructors - it's only been standardized for 15 years after
// all...
#define AllocaPointsArrays(variable, npoints) \
Point * variable = (Point *)alloca(npoints*sizeof(Point)); \
{ for (int i=0; i<npoints; ++i) { new (&variable[i]) Point; } }
AllocaPointsArrays(f, maxvalence);
AllocaPointsArrays(r, maxvalence*4);
Point e0[4], e1[4], org[4];
for (int vid=0; vid<4; ++vid) {
org[vid] = faceVerts[vid];
int ringSize = level.gatherManifoldVertexRingFromIncidentQuads(faceVerts[vid], 0, manifoldRing),
valence;
if (ringSize & 1) {
// boundary vertex
++ringSize;
manifoldRing[ringSize] = manifoldRing[ringSize-1];
valence = -ringSize/2;
} else {
valence = ringSize/2;
}
int ivalence = abs(valence);
valences[vid] = valence;
Index boundaryEdgeNeighbors[2],
currentNeighbor = 0,
zerothNeighbor=0,
ibefore=0;
Point pos(faceVerts[vid]);
for (int i=0; i<ivalence; ++i) {
Index im = (i+ivalence-1)%ivalence,
ip = (i+1)%ivalence;
Index idx_neighbor = (manifoldRing[2*i + 0]),
idx_diagonal = (manifoldRing[2*i + 1]),
idx_neighbor_p = (manifoldRing[2*ip + 0]),
idx_neighbor_m = (manifoldRing[2*im + 0]),
idx_diagonal_m = (manifoldRing[2*im + 1]);
bool boundaryNeighbor = (level.getVertexEdges(idx_neighbor).size() >
level.getVertexFaces(idx_neighbor).size());
if (boundaryNeighbor) {
if (currentNeighbor<2) {
boundaryEdgeNeighbors[currentNeighbor] = idx_neighbor;
}
++currentNeighbor;
if (currentNeighbor==1) {
ibefore = zerothNeighbor = i;
} else {
if (i-ibefore==1) {
std::swap(boundaryEdgeNeighbors[0], boundaryEdgeNeighbors[1]);
zerothNeighbor = i;
}
}
}
Point neighbor(idx_neighbor),
diagonal(idx_diagonal),
neighbor_p(idx_neighbor_p),
neighbor_m(idx_neighbor_m),
diagonal_m(idx_diagonal_m);
f[i] = (pos*float(ivalence) + (neighbor_p+neighbor)*2.0f + diagonal) / (float(ivalence)+5.0f);
P[vid] += f[i];
r[vid*maxvalence+i] = (neighbor_p-neighbor_m)/3.0f + (diagonal-diagonal_m)/6.0f;
}
P[vid] /= float(ivalence);
zerothNeighbors[vid] = zerothNeighbor;
if (currentNeighbor == 1) {
boundaryEdgeNeighbors[1] = boundaryEdgeNeighbors[0];
}
for (int i=0; i<ivalence; ++i) {
int im = (i+ivalence-1)%ivalence;
Point e = (f[i]+f[im])*0.5f;
e0[vid] += e * csf(ivalence-3, 2*i);
e1[vid] += e * csf(ivalence-3, 2*i+1);
}
e0[vid] *= ef[ivalence-3];
e1[vid] *= ef[ivalence-3];
if (valence<0) {
Point b0(boundaryEdgeNeighbors[0]),
b1(boundaryEdgeNeighbors[1]);
if (ivalence>2) {
P[vid] = (b0 + b1 + pos*4.0f)/6.0f;
} else {
P[vid] = pos;
}
float k = float(float(ivalence) - 1.0f); //k is the number of faces
float c = cosf(float(M_PI)/k);
float s = sinf(float(M_PI)/k);
float gamma = -(4.0f*s)/(3.0f*k+c);
float alpha_0k = -((1.0f+2.0f*c)*sqrtf(1.0f+c))/((3.0f*k+c)*sqrtf(1.0f-c));
float beta_0 = s/(3.0f*k + c);
Point diagonal(manifoldRing[2*zerothNeighbor + 1]);
e0[vid] = (b0 - b1)/6.0f;
e1[vid] = pos*gamma + diagonal*beta_0 + (b0 + b1)*alpha_0k;
for (int x=1; x<ivalence-1; ++x) {
Index curri = ((x + zerothNeighbor)%ivalence);
float alpha = (4.0f*sinf((float(M_PI) * float(x))/k))/(3.0f*k+c),
beta = (sinf((float(M_PI) * float(x))/k) + sinf((float(M_PI) * float(x+1))/k))/(3.0f*k+c);
Index idx_neighbor = manifoldRing[2*curri + 0],
idx_diagonal = manifoldRing[2*curri + 1];
Point p_neighbor(idx_neighbor),
p_diagonal(idx_diagonal);
e1[vid] += p_neighbor*alpha + p_diagonal*beta;
}
e1[vid] /= 3.0f;
}
}
Index quadOffsets[8];
getQuadOffsets(level, faceIndex, quadOffsets);
for (int vid=0; vid<4; ++vid) {
int n = abs(valences[vid]),
ivalence = n;
int ip = (vid+1)%4,
im = (vid+3)%4,
np = abs(valences[ip]),
nm = abs(valences[im]);
LocalIndex start = quadOffsets[vid*2+0],
prev = quadOffsets[vid*2+1],
start_m = quadOffsets[im*2],
prev_p = quadOffsets[ip*2+1];
Point Em_ip, Ep_im;
if (valences[ip]<-2) {
Index j = (np + prev_p - zerothNeighbors[ip]) % np;
Em_ip = P[ip] + e0[ip]*cosf((float(M_PI)*j)/float(np-1)) + e1[ip]*sinf((float(M_PI)*j)/float(np-1));
} else {
Em_ip = P[ip] + e0[ip]*csf(np-3,2*prev_p) + e1[ip]*csf(np-3,2*prev_p+1);
}
if (valences[im]<-2) {
Index j = (nm + start_m - zerothNeighbors[im]) % nm;
Ep_im = P[im] + e0[im]*cosf((float(M_PI)*j)/float(nm-1)) + e1[im]*sinf((float(M_PI)*j)/float(nm-1));
} else {
Ep_im = P[im] + e0[im]*csf(nm-3,2*start_m) + e1[im]*csf(nm-3,2*start_m+1);
}
if (valences[vid] < 0) {
n = (n-1)*2;
}
if (valences[im] < 0) {
nm = (nm-1)*2;
}
if (valences[ip] < 0) {
np = (np-1)*2;
}
Point const * rp = &r[vid*maxvalence];
if (valences[vid] > 2) {
float s1 = 3.0f - 2.0f*csf(n-3,2)-csf(np-3,2),
s2 = 2.0f*csf(n-3,2),
s3 = 3.0f -2.0f*cosf(2.0f*float(M_PI)/float(n)) - cosf(2.0f*float(M_PI)/float(nm));
Ep[vid] = P[vid] + e0[vid]*csf(n-3, 2*start) + e1[vid]*csf(n-3, 2*start +1);
Em[vid] = P[vid] + e0[vid]*csf(n-3, 2*prev ) + e1[vid]*csf(n-3, 2*prev + 1);
Fp[vid] = (P[vid]*csf(np-3,2) + Ep[vid]*s1 + Em_ip*s2 + rp[start])/3.0f;
Fm[vid] = (P[vid]*csf(nm-3,2) + Em[vid]*s3 + Ep_im*s2 - rp[prev])/3.0f;
} else if (valences[vid] < -2) {
Index jp = (ivalence + start - zerothNeighbors[vid]) % ivalence,
jm = (ivalence + prev - zerothNeighbors[vid]) % ivalence;
float s1 = 3-2*csf(n-3,2)-csf(np-3,2),
s2 = 2*csf(n-3,2),
s3 = 3.0f-2.0f*cosf(2.0f*float(M_PI)/n)-cosf(2.0f*float(M_PI)/nm);
Ep[vid] = P[vid] + e0[vid]*cosf((float(M_PI)*jp)/float(ivalence-1)) + e1[vid]*sinf((float(M_PI)*jp)/float(ivalence-1));
Em[vid] = P[vid] + e0[vid]*cosf((float(M_PI)*jm)/float(ivalence-1)) + e1[vid]*sinf((float(M_PI)*jm)/float(ivalence-1));
Fp[vid] = (P[vid]*csf(np-3,2) + Ep[vid]*s1 + Em_ip*s2 + rp[start])/3.0f;
Fm[vid] = (P[vid]*csf(nm-3,2) + Em[vid]*s3 + Ep_im*s2 - rp[prev])/3.0f;
if (valences[im]<0) {
s1=3-2*csf(n-3,2)-csf(np-3,2);
Fp[vid] = Fm[vid] = (P[vid]*csf(np-3,2) + Ep[vid]*s1 + Em_ip*s2 + rp[start])/3.0f;
} else if (valences[ip]<0) {
s1 = 3.0f-2.0f*cosf(2.0f*float(M_PI)/n)-cosf(2.0f*float(M_PI)/nm);
Fm[vid] = Fp[vid] = (P[vid]*csf(nm-3,2) + Em[vid]*s1 + Ep_im*s2 - rp[prev])/3.0f;
}
} else if (valences[vid]==-2) {
Ep[vid] = (org[vid]*2.0f + org[ip])/3.0f;
Em[vid] = (org[vid]*2.0f + org[im])/3.0f;
Fp[vid] = Fm[vid] = (org[vid]*4.0f + org[((vid+2)%n)] + org[ip]*2.0f + org[im]*2.0f)/9.0f;
}
}
}
int GregoryBasisFactory::GetMaxValence() {
return MAX_VALENCE;
}
//
// Stateless GregoryBasisFactory
//
GregoryBasis const *
GregoryBasisFactory::Create(TopologyRefiner const & refiner, Index faceIndex) {
// Gregory patches are end-caps: they only exist on max-level
Vtr::Level const & level = refiner.getLevel(refiner.GetMaxLevel());
if (level.getMaxValence()>GetMaxValence()) {
// The proto-basis closed-form table limits valence to 'MAX_VALENCE'
return 0;
}
ProtoBasis basis(level, faceIndex);
int nelems= basis.GetNumElements();
GregoryBasis * result = new GregoryBasis;
result->_indices.resize(nelems);
result->_weights.resize(nelems);
basis.Copy(result->_sizes, &result->_indices[0], &result->_weights[0]);
for (int i=0, offset=0; i<20; ++i) {
result->_offsets[i] = offset;
offset += result->_sizes[i];
}
return result;
}
//
// GregoryBasisFactory for StencilTables
//
GregoryBasisFactory::GregoryBasisFactory(TopologyRefiner const & refiner,
StencilTables const & stencils, int numpatches, int maxvalence) :
_currentStencil(0), _refiner(refiner),
_stencils(stencils), _alloc(GetNumMaxElems(maxvalence)) {
// Sanity check: the mesh must be adaptively refined
assert(not _refiner.IsUniform());
_alloc.Resize(numpatches * 20);
// Gregory limit stencils have indices that are relative to the level
// (maxlevel) of subdivision. These indices need to be offset to match
// the indices from the multi-level adaptive stencil tables.
// In addition: stencil tables can be built with singular stencils
// (single weight of 1.0f) as place-holders for coarse mesh vertices,
// which also needs to be accounted for.
_stencilsOffset=-1;
{ int maxlevel = _refiner.GetMaxLevel(),
nverts = _refiner.GetNumVerticesTotal(),
nstencils = _stencils.GetNumStencils();
if (nstencils==nverts) {
// the table contain stencils for the control vertices
_stencilsOffset = nverts - _refiner.GetNumVertices(maxlevel);
} else if (nstencils==(nverts-_refiner.GetNumVertices(0))) {
// the table does not contain stencils for the control vertices
_stencilsOffset = nverts - _refiner.GetNumVertices(maxlevel)
- _refiner.GetNumVertices(0);
} else {
// these are not the stencils you are looking for...
assert(0);
}
}
}
static inline void
factorizeBasisVertex(StencilTables const & stencils, Point const & p, ProtoStencil dst) {
// Use the Allocator to factorize the Gregory patch influence CVs with the
// supporting CVs from the stencil tables.
dst.Clear();
for (int j=0; j<p.GetSize(); ++j) {
dst.AddWithWeight(stencils,
p.GetIndices()[j], p.GetWeights()[j]);
}
}
bool
GregoryBasisFactory::AddPatchBasis(Index faceIndex) {
// Gregory patches only exist on the hight
Vtr::Level const & level = _refiner.getLevel(_refiner.GetMaxLevel());
if (level.getMaxValence()>GetMaxValence()) {
// The proto-basis closed-form table limits valence to 'MAX_VALENCE'
return false;
}
// Gather the CVs that influence the Gregory patch and their relative
// weights in a basis
ProtoBasis basis(level, faceIndex);
// The basis vertex indices are currently local to maxlevel: need to offset
// to match layout of adaptive StencilTables (see factory constructor above)
assert(_stencilsOffset>=0);
basis.OffsetIndices(_stencilsOffset);
// Factorize the basis CVs with the stencil tables: the basis is now
// expressed as a linear combination of vertices from the coarse control
// mesh with no data dependencies
for (int i=0; i<4; ++i) {
int offset = _currentStencil + i * 5;
factorizeBasisVertex(_stencils, basis.P[i], _alloc[offset]);
factorizeBasisVertex(_stencils, basis.Ep[i], _alloc[offset+1]);
factorizeBasisVertex(_stencils, basis.Em[i], _alloc[offset+2]);
factorizeBasisVertex(_stencils, basis.Fp[i], _alloc[offset+3]);
factorizeBasisVertex(_stencils, basis.Fm[i], _alloc[offset+4]);
}
_currentStencil += 20;
return true;
}
StencilTables const *
GregoryBasisFactory::CreateStencilTables(int const permute[20]) {
int nstencils = (int)_alloc.GetNumStencils(),
nelems = _alloc.GetNumVerticesTotal();
if (nstencils==0 or nelems==0) {
return 0;
}
// Finalize the stencil tables from the temporary pool allocator
StencilTables * result = new StencilTables;
result->_numControlVertices = _refiner.GetNumVertices(0);
result->resize(nstencils, nelems);
Stencil dst(&result->_sizes.at(0),
&result->_indices.at(0), &result->_weights.at(0));
for (int i=0; i<nstencils; ++i) {
Index index = i;
if (permute) {
int localIndex = i % 20,
baseIndex = i - localIndex;
index = baseIndex + permute[localIndex];
}
*dst._size = _alloc.CopyStencil(index, dst._indices, dst._weights);
dst.Next();
}
result->generateOffsets();
return result;
}
} // end namespace Far
} // end namespace OPENSUBDIV_VERSION
} // end namespace OpenSubdiv