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OpenSubdiv/opensubdiv/far/catmarkPatchBuilder.cpp

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//
// Copyright 2018 DreamWorks Animation LLC.
//
// 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/catmarkPatchBuilder.h"
#include "../vtr/stackBuffer.h"
#include <cassert>
#include <cmath>
#include <cstdio>
namespace OpenSubdiv {
namespace OPENSUBDIV_VERSION {
using Vtr::Array;
using Vtr::ConstArray;
using Vtr::internal::StackBuffer;
namespace Far {
//
// Core functions for computing Catmark limit properties that are used
// in the conversion to multiple patch types.
//
// This struct/class is just a means of grouping common functions.
//
// There is a long and unclear history to the details of the computations
// involved in the patch conversion here...
//
// The formulae for computing the Gregory patch points do not follow the
// more widely accepted work of Loop, Shaefer et al or Myles et al. The
// formulae for the limit points and tangents also ultimately need to be
// retrieved from Sdc::Scheme to ensure they conform, so future factoring
// of the formulae is still necessary.
//
// Regarding support for multiple precision, like Sdc, some intermediate
// calculations are performed in double and cast to float. Historically
// this conversion code has been purely float and later extended to
// support template <typename REAL>. For math functions such as cos(),
// sin(), etc., we rely on overloading via <cmath> through the use of
// std::cos(), std::sin(), etc.
//
template <typename REAL>
struct CatmarkLimits {
public:
typedef REAL Weight;
static void ComputeInteriorPointWeights(int valence, int faceInRing,
Weight* pWeights, Weight* epWeights, Weight* emWeights);
static void ComputeBoundaryPointWeights(int valence, int faceInRing,
Weight* pWeights, Weight* epWeights, Weight* emWeights);
private:
static double computeCoefficient(int valence);
};
//
// Lookup table and formula for the scale factor applied to limit
// tangents that arises from eigen values of the subdivision matrix.
// Historically 30 values have been stored -- up to valence 29.
//
template <typename REAL>
inline double
CatmarkLimits<REAL>::computeCoefficient(int valence) {
static double const efTable[] = {
0.0, 0.0, 0.0,
8.1281572906372312e-01, 0.5, 3.6364406329142801e-01,
2.8751379706077085e-01, 2.3868786685851678e-01, 2.0454364190756097e-01,
1.7922903958061159e-01, 1.5965737079986253e-01, 1.4404233443011302e-01,
1.3127568415883017e-01, 1.2063172212675841e-01, 1.1161437506676930e-01,
1.0387245516114274e-01, 9.7150019090724835e-02, 9.1255917505950648e-02,
8.6044378511602668e-02, 8.1402211336798411e-02, 7.7240129516184072e-02,
7.3486719751997026e-02, 7.0084157479797987e-02, 6.6985104030725440e-02,
6.4150420569810074e-02, 6.1547457638637268e-02, 5.9148757447233989e-02,
5.6931056818776957e-02, 5.4874512279256417e-02, 5.2962091433796134e-02
};
assert(valence > 0);
if (valence < 30) return efTable[valence];
double invValence = 1.0 / valence;
double cosT = std::cos(2.0 * M_PI * invValence);
double divisor = (cosT + 5.0) + std::sqrt((cosT + 9.0) * (cosT + 1.0));
return (16.0 * invValence / divisor);
}
template <typename REAL>
void
CatmarkLimits<REAL>::ComputeInteriorPointWeights(int valence, int faceInRing,
Weight* pWeights, Weight* epWeights, Weight* emWeights) {
//
// For the limit tangents of an interior vertex, the second tangent is a
// rotation of the first, i.e. the coefficients for the ring around the
// vertex can be simply shifted by two. So there is really no need to
// compute it explicitly here. The single tangent can similarly be
// oriented along the corresponding edges for Ep and Em and scaled and
// offset by P accordingly.
//
// The formula used for tangents here differs from Sdc::Scheme for
// Catmark -- the direction is the same but the length varies due to the
// different terms used to scale the results (both based on eigenvalues).
// The main difference in the computation here though is that each edge-
// point is a function of three cos() terms:
// cos(i*theta), cos((i-1)*theta), cos((i+1)theta)
// while the Sdc::Scheme weight depends only on cos(i*theta), and so they
// are accumulated here rather than assigned directly.
//
// Ultimately the Sdc::Scheme formulae are a little more efficient but we
// don't want to impact positions of Ep and Em slightly by switching to
// them until such a change can be given more justification and visibility
// (e.g. major version).
//
bool computeEdgePoints = epWeights && emWeights;
double fValence = (double) valence;
double oneOverValence = 1.0f / fValence;
double oneOverValPlus5 = 1.0f / (fValence + 5.0f);
double pCoeff = oneOverValence * oneOverValPlus5;
double tanCoeff = computeCoefficient(valence) * 0.5f * oneOverValPlus5;
double faceAngle = 2.0 * M_PI * oneOverValence;
//
// Assign position weights directly while accumulating an intermediate set
// of weights for the limit tangent. And skip over the first weight for
// the corner vertex once assigned (zero for tangents) so that we don't
// have to deal with the off-by-one offset within the loop:
//
int weightWidth = 1 + 2 * valence;
StackBuffer<Weight, 64, true> tanWeights(weightWidth);
std::memset(&tanWeights[0], 0, weightWidth * sizeof(Weight));
pWeights[0] = (Weight) (fValence * oneOverValPlus5);
Weight *pW = &pWeights[1];
Weight *tW = &tanWeights[1];
for (int i = 0; i < valence; ++i) {
pW[2*i] = (Weight) (pCoeff * 4.0f);
pW[2*i + 1] = (Weight) pCoeff;
if (computeEdgePoints) {
int iPrev = (i + valence - 1) % valence;
int iNext = (i + 1) % valence;
double cosICoeff = tanCoeff * std::cos(faceAngle * i);
tW[2*iPrev] += (Weight) (cosICoeff * 2.0f);
tW[2*iPrev + 1] += (Weight) cosICoeff;
tW[2*i] += (Weight) (cosICoeff * 4.0f);
tW[2*i + 1] += (Weight) cosICoeff;
tW[2*iNext] += (Weight) (cosICoeff * 2.0f);
}
}
//
// Rotate/permute the scaled tangent weights along edges and add to P:
//
if (computeEdgePoints) {
int epOffset = 2 * ((valence - faceInRing) % valence);
int emOffset = 2 * ((valence - faceInRing - 1 + valence) % valence);
epWeights[0] = pWeights[0];
emWeights[0] = pWeights[0];
for (int i = 1; i < weightWidth; ++i) {
int ip = i + epOffset;
if (ip >= weightWidth) ip -= weightWidth - 1;
int im = i + emOffset;
if (im >= weightWidth) im -= weightWidth - 1;
epWeights[i] = pWeights[i] + tanWeights[ip];
emWeights[i] = pWeights[i] + tanWeights[im];
}
}
}
template <typename REAL>
void
CatmarkLimits<REAL>::ComputeBoundaryPointWeights(int valence, int faceInRing,
Weight* pWeights, Weight* epWeights, Weight* emWeights) {
int numFaces = valence - 1;
double faceAngle = M_PI / numFaces;
int weightWidth = 2 * valence;
int N = weightWidth - 1;
//
// Position weights are trivial:
//
std::memset(&pWeights[0], 0, weightWidth * sizeof(Weight));
pWeights[0] = (Weight) (4.0 / 6.0);
pWeights[1] = (Weight) (1.0 / 6.0);
pWeights[N] = (Weight) (1.0 / 6.0);
if ((epWeights == 0) && (emWeights == 0)) return;
//
// Ep and Em weights are computed by combining weights for the boundary
// and interior tangents. The boundary tangent is trivially represented
// by two non-zero weights, so allocate and compute weights for the
// interior tangent:
//
double tBoundaryCoeff_1 = ( 1.0 / 6.0);
double tBoundaryCoeff_N = (-1.0 / 6.0);
StackBuffer<Weight, 64, true> tanWeights(weightWidth);
{
double k = (double) numFaces;
double theta = faceAngle;
double c = std::cos(theta);
double s = std::sin(theta);
double div3 = 1.0 / 3.0;
double div3kc = 1.0f / (3.0f * k + c);
double gamma = -4.0f * s * div3kc;
double alpha_0k = -((1.0f + 2.0f * c) * std::sqrt(1.0f + c)) * div3kc
/ std::sqrt(1.0f - c);
double beta_0 = s * div3kc;
tanWeights[0] = (Weight) (gamma * div3);
tanWeights[1] = (Weight) (alpha_0k * div3);
tanWeights[2] = (Weight) (beta_0 * div3);
tanWeights[N] = (Weight) (alpha_0k * div3);
for (int i = 1; i < valence - 1; ++i) {
double sinThetaI = std::sin(theta * i);
double sinThetaIplus1 = std::sin(theta * (i+1));
double alpha = 4.0f * sinThetaI * div3kc;
double beta = (sinThetaI + sinThetaIplus1) * div3kc;
tanWeights[1 + 2*i] = (Weight) (alpha * div3);
tanWeights[1 + 2*i + 1] = (Weight) (beta * div3);
}
}
//
// Compute Ep weights -- trivial case if on the leading face and edge:
//
if (faceInRing == 0) {
// Ep is on boundary edge and has only two weights: w[1] and w[N]
std::memset(&epWeights[0], 0, weightWidth * sizeof(Weight));
epWeights[0] = (Weight) (2.0 / 3.0);
epWeights[1] = (Weight) (1.0 / 3.0);
} else {
// Ep is on interior edge and has all weights
int iEdgeNext = faceInRing;
double faceAngleNext = faceAngle * iEdgeNext;
double cosAngleNext = std::cos(faceAngleNext);
double sinAngleNext = std::sin(faceAngleNext);
for (int i = 0; i < weightWidth; ++i) {
epWeights[i] = (Weight)(tanWeights[i] * sinAngleNext);
}
epWeights[0] += pWeights[0];
epWeights[1] += pWeights[1] + (Weight)(tBoundaryCoeff_1 * cosAngleNext);
epWeights[N] += pWeights[N] + (Weight)(tBoundaryCoeff_N * cosAngleNext);
}
//
// Compute Em weights -- trivial case if on the trailing face and edge:
//
if (faceInRing == (numFaces - 1)) {
// Em is on boundary edge and has only two weights: w[1] and w[N]
std::memset(&emWeights[0], 0, weightWidth * sizeof(Weight));
emWeights[0] = (Weight) (2.0 / 3.0);
emWeights[N] = (Weight) (1.0 / 3.0);
} else {
// Em is on interior edge and has all weights
int iEdgePrev = (faceInRing + 1) % valence;
double faceAnglePrev = faceAngle * iEdgePrev;
double cosAnglePrev = std::cos(faceAnglePrev);
double sinAnglePrev = std::sin(faceAnglePrev);
for (int i = 0; i < weightWidth; ++i) {
emWeights[i] = (Weight)(tanWeights[i] * sinAnglePrev);
}
emWeights[0] += pWeights[0];
emWeights[1] += pWeights[1] + (Weight)(tBoundaryCoeff_1 * cosAnglePrev);
emWeights[N] += pWeights[N] + (Weight)(tBoundaryCoeff_N * cosAnglePrev);
}
}
//
// SparseMatrixPoint
//
// This is a utility class representing a row of a SparseMatrix -- which
// in turn corresponds to a point of a resulting patch.
//
// This interface was originally transitional (supporting a migration away
// from the former GregoryBasis::Point class) and its unclear if it will
// persist. Its needs have been simplified and given the usual pre-sizing
// of a sparse row, a simple Assign() method may be all that is necessary.
//
// Use of the AddOrAppend() method is highly discouraged as it requires
// iteration and testing of potentially all entries, before appending if
// the specified entry does not exist. It is currently only used to
// simplify the awkward case of valence-2 interior vertices -- where the
// 1-ring of neighboring vertices overlaps and has duplicate entries.
// Alternative to simplify this without resorting to AddOrAppend() are
// under consideration.
//
template <typename REAL>
class SparseMatrixPoint {
public:
typedef Index index_type;
typedef REAL weight_type;
typedef SparseMatrix<weight_type> matrix_type;
public:
SparseMatrixPoint(matrix_type & matrix, int row, int size = -1);
int GetSize() const { return _size; }
int GetCapacity() const { return _indices.size(); }
void Append( index_type index, weight_type weight);
void AddOrAppend( index_type index, weight_type weight);
void Assign(int rowEntry, index_type index, weight_type weight);
void Copy(SparseMatrixPoint<weight_type> const & other);
public:
int _size;
Array<index_type> _indices;
Array<weight_type> _weights;
};
template <typename REAL>
inline
SparseMatrixPoint<REAL>::SparseMatrixPoint(matrix_type & matrix, int row, int size) {
_indices = matrix.SetRowColumns(row);
_weights = matrix.SetRowElements(row);
_size = (size < 0) ? _weights.size() : size;
}
template <typename REAL>
inline void
SparseMatrixPoint<REAL>::Assign(int rowEntry, index_type index, weight_type weight) {
_indices[rowEntry] = index;
_weights[rowEntry] = weight;
}
template <typename REAL>
inline void
SparseMatrixPoint<REAL>::Append(index_type index, weight_type weight) {
assert(GetSize() < GetCapacity());
_indices[_size] = index;
_weights[_size] = weight;
_size ++;
}
template <typename REAL>
inline void
SparseMatrixPoint<REAL>::AddOrAppend(index_type index, weight_type weight) {
for (int i = 0; i < GetSize(); ++i) {
if (_indices[i] == index) {
_weights[i] += weight;
return;
}
}
Append(index, weight);
}
template <typename REAL>
inline void
SparseMatrixPoint<REAL>::Copy(SparseMatrixPoint const & other) {
assert(GetCapacity() == other.GetCapacity());
_size = other._size;
std::memcpy(&_indices[0], &other._indices[0], _size * sizeof(index_type));
std::memcpy(&_weights[0], &other._weights[0], _size * sizeof(weight_type));
}
//
// Simple utility functions for dealing with SparseMatrix:
//
namespace {
template <typename REAL>
void
_printMatrix(SparseMatrix<REAL> const & matrix, bool printIndices = true,
bool printWeights = true) {
printf("Matrix %d x %d, %d elements:\n",
matrix.GetNumRows(), matrix.GetNumColumns(), matrix.GetNumElements());
for (int i = 0; i < matrix.GetNumRows(); ++i) {
int rowSize = matrix.GetRowSize(i);
printf(" Row %d (size = %d):\n", i, rowSize);
if (printIndices) {
ConstArray<int> indices = matrix.GetRowColumns(i);
printf(" Indices: ");
for (int j = 0; j < rowSize; ++j) {
printf("%6d ", indices[j]);
}
printf("\n");
}
if (printWeights) {
ConstArray<REAL> weights = matrix.GetRowElements(i);
printf(" Weights: ");
for (int j = 0; j < rowSize; ++j) {
printf("%6.3f ", (REAL)weights[j]);
}
printf("\n");
}
}
}
template <typename REAL>
void
_initializeFullMatrix(SparseMatrix<REAL> & M, int nRows, int nColumns) {
M.Resize(nRows, nColumns, nRows * nColumns);
// Fill row 0 with index for every column:
M.SetRowSize(0, nColumns);
Array<int> row0Columns = M.SetRowColumns(0);
for (int i = 0; i < nColumns; ++i) {
row0Columns[i] = i;
}
// Copy row 0's indices into all other rows:
for (int row = 1; row < nRows; ++row) {
M.SetRowSize(row, nColumns);
Array<int> dstRowColumns = M.SetRowColumns(row);
std::memcpy(&dstRowColumns[0], &row0Columns[0], nColumns * sizeof(int));
}
}
template <typename REAL>
void
_resizeMatrix(SparseMatrix<REAL> & matrix,
int numRows, int numColumns, int numElements,
int const rowSizes[]) {
matrix.Resize(numRows, numColumns, numElements);
for (int i = 0; i < numRows; ++i) {
matrix.SetRowSize(i, rowSizes[i]);
}
assert(matrix.GetNumElements() == numElements);
}
template <typename REAL>
void
_addSparsePointToFullRow(REAL * fullRow,
SparseMatrixPoint<REAL> const & p,
REAL s, int * indexMask) {
for (int i = 0; i < p.GetSize(); ++i) {
int index = p._indices[i];
fullRow[index] += s * p._weights[i];
indexMask[index] = 1 + index;
}
}
template <typename REAL>
void
_addSparseRowToFull(REAL * fullRow,
SparseMatrix<REAL> const & M, int sparseRow, REAL s) {
ConstArray<int> indices = M.GetRowColumns(sparseRow);
ConstArray<REAL> weights = M.GetRowElements(sparseRow);
for (int i = 0; i < indices.size(); ++i) {
fullRow[indices[i]] += s * weights[i];
}
}
template <typename REAL>
void
_combineSparseMatrixRowsInFull(SparseMatrix<REAL> & dstMatrix, int dstRowIndex,
SparseMatrix<REAL> const & srcMatrix, int numSrcRows,
int const srcRowIndices[], REAL const * srcRowWeights) {
REAL * dstRow = &dstMatrix.SetRowElements(dstRowIndex)[0];
std::memset(dstRow, 0, dstMatrix.GetNumColumns() * sizeof(REAL));
for (int i = 0; i < numSrcRows; ++i) {
_addSparseRowToFull(dstRow, srcMatrix, srcRowIndices[i], srcRowWeights[i]);
}
}
template <typename REAL>
void
_matrixPrintDensity(const char* prefix, SparseMatrix<REAL> const & M) {
int fullSize = M.GetNumRows() * M.GetNumColumns();
int sparseSize = M.GetNumElements();
int nonZeroSize = 0;
for (int i = 0; i < M.GetNumRows(); ++i) {
ConstArray<REAL> elements = M.GetRowElements(i);
for (int j = 0; j < elements.size(); ++j) {
nonZeroSize += (elements[j] != 0);
}
}
printf("%s(%dx%d = %d): elements = %d, non-zero = %d, density = %.1f\n",
prefix, M.GetNumRows(), M.GetNumColumns(), fullSize,
sparseSize, nonZeroSize, (REAL)nonZeroSize * 100.0f / (REAL)fullSize);
}
} // end namespace for SparseMatrix utilities
//
// GregoryConverter
//
// The GregoryConverter class essentially provides a change-of-basis matrix
// from source vertices in a Catmull-Clark mesh to the 20 control points of a
// Gregory patch.
//
// Historically the source topology was specified as a Vtr::Level and face index,
// from which contributions of all 1-ring vertices that support the 20 points of
// the patch are determined. The source topology is now specified via a simple
// SourcePatch, so a matrix can be determined for a particular configuration and
// re-used for any similar instance.
//
// Control points are labeled using the convention from: "Approximating
// Subdivision Surfaces with Gregory Patches for Hardware Tessellation" Loop,
// Schaefer, Ni, Castano (ACM ToG Siggraph Asia 2009)
//
// P3 e3- e2+ P2
// x--------x--------x--------x
// | | | |
// | | | |
// | | f3- | f2+ |
// | x x |
// e3+ x------x x------x e2-
// | f3+ f2- |
// | |
// | |
// | f0- f1+ |
// e0- x------x x------x e1+
// | x x |
// | | f0+ | f1- |
// | | | |
// | | | |
// x--------x--------x--------x
// P0 e0+ e1- P1
//
template <typename REAL>
class GregoryConverter {
public:
typedef REAL Weight;
typedef SparseMatrix<Weight> Matrix;
typedef SparseMatrixPoint<Weight> Point;
public:
GregoryConverter() : _numSourcePoints(0) { }
GregoryConverter(SourcePatch const & sourcePatch);
GregoryConverter(SourcePatch const & sourcePatch, Matrix & sparseMatrix);
void Initialize(SourcePatch const & sourcePatch);
bool IsIsolatedInteriorPatch() const { return _isIsolatedInteriorPatch; }
int GetIsolatedInteriorCorner() const { return _isolatedCorner; }
int GetIsolatedInteriorValence() const { return _isolatedValence; }
void Convert(Matrix & sparseMatrix) const;
private:
//
// Local nested class for GregoryConverter to cache information for the
// corners of the source patch. It copies some information from the
// SourcePatch so that we don't have to keep it around, but it contains
// additional information relevant to the determination of the Gregory
// points -- most notably classifications of the face-points and the
// sines/cosines of angles for the face corners that are used repeatedly.
//
struct CornerTopology {
// Basic flags copied from the SourcePatch
unsigned int isBoundary : 1;
unsigned int isSharp : 1;
unsigned int isDart : 1;
unsigned int isRegular : 1;
unsigned int isVal2Int : 1;
// Flags for edge- and face-points relating to adjacent corners:
unsigned int fpIsRegular : 1;
unsigned int fmIsRegular : 1;
unsigned int fpIsCopied : 1;
unsigned int fmIsCopied : 1;
unsigned int val2InRing : 1;
unsigned int epAdjToVal2 : 1;
unsigned int emAdjToVal2 : 1;
// Other values stored for repeated use:
int valence;
int numFaces;
int faceInRing;
REAL faceAngle;
REAL cosFaceAngle;
REAL sinFaceAngle;
// Its useful to have the ring for each corner immediately available:
StackBuffer<int, 40, true> ringPoints;
};
//
// Methods to resize the matrix before populating it:
//
void resizeMatrixUnisolated(Matrix & matrix) const;
void resizeMatrixIsolatedIrregular(Matrix & matrix, int irregCornerIndex,
int irregValence) const;
//
// Methods to compute the various rows of points in the matrix:
//
void assignRegularEdgePoints(int cornerIndex, Matrix & matrix) const;
void computeIrregularEdgePoints(int cornerIndex, Matrix & matrix,
Weight *weightBuffer) const;
void assignRegularFacePoints(int cornerIndex, Matrix & matrix) const;
void computeIrregularFacePoints(int cornerIndex, Matrix & matrix,
Weight *weightBuffer, int *indexBuffer) const;
void computeIrregularInteriorEdgePoints(int cornerIndex,
Point & P, Point & Ep, Point & Em,
Weight *weightBuffer) const;
void computeIrregularBoundaryEdgePoints(int cornerIndex,
Point & P, Point & Ep, Point & Em,
Weight *weightBuffer) const;
int getIrregularFacePointSize(int cornerNear, int cornerFar) const;
void computeIrregularFacePoint(
int cornerNear, int edgeInNearRing, int cornerFar,
Point const & p, Point const & eNear, Point const & eFar,
Point & fNear, REAL signForSideOfEdge /* -1.0 or 1.0 */,
Weight *rowWeights, int *columnMask) const;
private:
int _numSourcePoints;
int _maxValence;
bool _isIsolatedInteriorPatch;
int _isolatedCorner;
int _isolatedValence;
CornerTopology _corners[4];
};
//
// GregoryConverter
//
// Construction and initialization/computation of the change-of-basis
// matrix to a Gregory patch.
//
template <typename REAL>
GregoryConverter<REAL>::GregoryConverter(
SourcePatch const & sourcePatch) {
Initialize(sourcePatch);
}
template <typename REAL>
GregoryConverter<REAL>::GregoryConverter(
SourcePatch const & sourcePatch, Matrix & sparseMatrix) {
Initialize(sourcePatch);
Convert(sparseMatrix);
}
template <typename REAL>
void
GregoryConverter<REAL>::Initialize(SourcePatch const & sourcePatch) {
//
// Allocate and gather the 1-rings for the corner vertices and other
// topological information for more immediate access:
//
int width = sourcePatch.GetNumSourcePoints();
_numSourcePoints = width;
_maxValence = sourcePatch.GetMaxValence();
int boundaryCount = 0;
int irregularCount = 0;
int irregularCorner = -1;
int irregularValence = -1;
int sharpCount = 0;
for (int cIndex = 0; cIndex < 4; ++cIndex) {
SourcePatch::Corner srcCorner = sourcePatch._corners[cIndex];
CornerTopology& corner = _corners[cIndex];
corner.isBoundary = srcCorner._boundary;
corner.isSharp = srcCorner._sharp;
corner.isDart = srcCorner._dart;
corner.numFaces = srcCorner._numFaces;
corner.faceInRing = srcCorner._patchFace;
corner.isVal2Int = srcCorner._val2Interior;
corner.val2InRing = srcCorner._val2Adjacent;
corner.valence = corner.numFaces + corner.isBoundary;
corner.isRegular = ((corner.numFaces << corner.isBoundary) == 4)
&& !corner.isSharp;
if (corner.isRegular) {
corner.faceAngle = REAL(M_PI_2);
corner.cosFaceAngle = 0.0f;
corner.sinFaceAngle = 1.0f;
} else {
corner.faceAngle =
(corner.isBoundary ? REAL(M_PI) : (2.0f * REAL(M_PI)))
/ REAL(corner.numFaces);
corner.cosFaceAngle = std::cos(corner.faceAngle);
corner.sinFaceAngle = std::sin(corner.faceAngle);
}
corner.ringPoints.SetSize(sourcePatch.GetCornerRingSize(cIndex));
sourcePatch.GetCornerRingPoints(cIndex, corner.ringPoints);
// Accumulate topology information to categorize the patch as a whole:
boundaryCount += corner.isBoundary;
if (!corner.isRegular) {
irregularCount ++;
irregularCorner = cIndex;
irregularValence = corner.valence;
}
sharpCount += corner.isSharp;
}
// Make a second pass to assign tags dependent on adjacent corners
for (int cIndex = 0; cIndex < 4; ++cIndex) {
CornerTopology& corner = _corners[cIndex];
int cNext = (cIndex + 1) & 0x3;
int cPrev = (cIndex + 3) & 0x3;
corner.epAdjToVal2 = _corners[cNext].isVal2Int;
corner.emAdjToVal2 = _corners[cPrev].isVal2Int;
//
// Identify if the face points are regular or shared/copied from
// one of the pair:
//
corner.fpIsRegular = corner.isRegular && _corners[cNext].isRegular;
corner.fmIsRegular = corner.isRegular && _corners[cPrev].isRegular;
corner.fpIsCopied = false;
corner.fmIsCopied = false;
if (corner.isBoundary) {
// Both face points are same when one of the two corners' edges
// is discontinuous -- one is then copied from the other (unless
// regular)
if (corner.numFaces > 1) {
if (_corners[cNext].isBoundary || _corners[cNext].isDart) {
corner.fpIsRegular = corner.fmIsRegular;
corner.fpIsCopied = !corner.fpIsRegular;
}
if (_corners[cPrev].isBoundary || _corners[cPrev].isDart) {
corner.fmIsRegular = corner.fpIsRegular;
corner.fmIsCopied = !corner.fmIsRegular;
}
} else {
// The case of a corner patch is always regular
corner.fpIsRegular = true;
corner.fmIsRegular = true;
}
}
}
_isIsolatedInteriorPatch = (irregularCount == 1) && (boundaryCount == 0) &&
(irregularValence > 2) && (sharpCount == 0);
if (_isIsolatedInteriorPatch) {
_isolatedCorner = irregularCorner;
_isolatedValence = irregularValence;
}
}
template <typename REAL>
void
GregoryConverter<REAL>::Convert(Matrix & matrix) const {
//
// Initialize the sparse matrix to accomodate the coefficients for each
// row/point -- identify common topological cases to treat more easily
// (and note that specializing the popoluation of the matrix may also be
// worthwhile in such cases)
//
if (_isIsolatedInteriorPatch) {
resizeMatrixIsolatedIrregular(matrix, _isolatedCorner, _isolatedValence);
} else {
resizeMatrixUnisolated(matrix);
}
//
// Compute the corner and edge points P, Ep and Em first. Since face
// points Fp and Fm involve edge points for two adjacent corners, their
// computation must follow:
//
int maxRingSize = 1 + 2 * _maxValence;
int weightBufferSize = std::max(3 * maxRingSize, 2 * _numSourcePoints);
StackBuffer<Weight, 128, true> weightBuffer(weightBufferSize);
StackBuffer<int, 128, true> indexBuffer(weightBufferSize);
for (int cIndex = 0; cIndex < 4; ++cIndex) {
if (_corners[cIndex].isRegular) {
assignRegularEdgePoints(cIndex, matrix);
} else {
computeIrregularEdgePoints(cIndex, matrix, weightBuffer);
}
}
for (int cIndex = 0; cIndex < 4; ++cIndex) {
if (_corners[cIndex].fpIsRegular || _corners[cIndex].fmIsRegular) {
assignRegularFacePoints(cIndex, matrix);
}
if (!_corners[cIndex].fpIsRegular || !_corners[cIndex].fmIsRegular) {
computeIrregularFacePoints(cIndex, matrix, weightBuffer, indexBuffer);
}
}
}
template <typename REAL>
void
GregoryConverter<REAL>::resizeMatrixIsolatedIrregular(
Matrix & matrix, int cornerIndex, int cornerValence) const {
int irregRingSize = 1 + 2 * cornerValence;
int irregCorner = cornerIndex;
int irregPlus = (cornerIndex + 1) & 0x3;
int irregOpposite = (cornerIndex + 2) & 0x3;
int irregMinus = (cornerIndex + 3) & 0x3;
int rowSizes[20];
int * rowSizePtr = 0;
rowSizePtr = rowSizes + irregCorner * 5;
*rowSizePtr++ = irregRingSize;
*rowSizePtr++ = irregRingSize;
*rowSizePtr++ = irregRingSize;
*rowSizePtr++ = irregRingSize;
*rowSizePtr++ = irregRingSize;
rowSizePtr = rowSizes + irregPlus * 5;
*rowSizePtr++ = 9;
*rowSizePtr++ = 6;
*rowSizePtr++ = 6;
*rowSizePtr++ = 4;
*rowSizePtr++ = 3 + irregRingSize;
rowSizePtr = rowSizes + irregOpposite * 5;
*rowSizePtr++ = 9;
*rowSizePtr++ = 6;
*rowSizePtr++ = 6;
*rowSizePtr++ = 4;
*rowSizePtr++ = 4;
rowSizePtr = rowSizes + irregMinus * 5;
*rowSizePtr++ = 9;
*rowSizePtr++ = 6;
*rowSizePtr++ = 6;
*rowSizePtr++ = 3 + irregRingSize;
*rowSizePtr++ = 4;
int numElements = 7*irregRingSize + 85;
_resizeMatrix(matrix, 20, _numSourcePoints, numElements, rowSizes);
}
template <typename REAL>
void
GregoryConverter<REAL>::resizeMatrixUnisolated(Matrix & matrix) const {
int rowSizes[20];
int numElements = 0;
for (int cIndex = 0; cIndex < 4; ++cIndex) {
int * rowSize = rowSizes + cIndex*5;
CornerTopology const & corner = _corners[cIndex];
// First, the corner and pair of edge points:
if (corner.isRegular) {
if (! corner.isBoundary) {
rowSize[0] = 9 - corner.val2InRing;
rowSize[1] = 6 - corner.epAdjToVal2;
rowSize[2] = 6 - corner.emAdjToVal2;
} else {
rowSize[0] = 3;
rowSize[1] = corner.faceInRing ? 6 : 2;
rowSize[2] = corner.faceInRing ? 2 : 6;
}
} else {
if (corner.isSharp) {
rowSize[0] = 1;
rowSize[1] = 2;
rowSize[2] = 2;
} else if (! corner.isBoundary) {
int ringSize = 1 + 2 * corner.valence - corner.val2InRing;
rowSize[0] = ringSize;
rowSize[1] = ringSize;
rowSize[2] = ringSize;
} else if (corner.numFaces > 1) {
int ringSize = 1 + corner.valence + corner.numFaces - corner.val2InRing;
rowSize[0] = 3;
rowSize[1] = (corner.faceInRing > 0) ? ringSize : 2;
rowSize[2] = (corner.faceInRing < (corner.numFaces - 1)) ? ringSize : 2;
} else {
rowSize[0] = 3;
rowSize[1] = 2;
rowSize[2] = 2;
}
}
numElements += rowSize[0] + rowSize[1] + rowSize[2];
// Second, the pair of face points:
rowSize[3] = 4;
rowSize[4] = 4;
if (!corner.fpIsRegular || !corner.fmIsRegular) {
int cNext = (cIndex + 1) & 0x3;
int cPrev = (cIndex + 3) & 0x3;
if (!corner.fpIsRegular) {
rowSize[3] = getIrregularFacePointSize(cIndex,
corner.fpIsCopied ? cPrev : cNext);
}
if (!corner.fmIsRegular) {
rowSize[4] = getIrregularFacePointSize(cIndex,
corner.fmIsCopied ? cNext : cPrev);
}
}
numElements += rowSize[3] + rowSize[4];
}
_resizeMatrix(matrix, 20, _numSourcePoints, numElements, rowSizes);
}
template <typename REAL>
void
GregoryConverter<REAL>::assignRegularEdgePoints(int cIndex, Matrix & matrix) const {
// Declare with 0 size for use with Append()
Point p (matrix, 5*cIndex + 0, 0);
Point ep(matrix, 5*cIndex + 1, 0);
Point em(matrix, 5*cIndex + 2, 0);
CornerTopology const & corner = _corners[cIndex];
int const * cRing = corner.ringPoints;
if (! corner.isBoundary) {
p.Append(cIndex, 4.0f / 9.0f);
p.Append(cRing[0], 1.0f / 9.0f);
p.Append(cRing[2], 1.0f / 9.0f);
p.Append(cRing[4], 1.0f / 9.0f);
p.Append(cRing[6], 1.0f / 9.0f);
p.Append(cRing[1], 1.0f / 36.0f);
if (!corner.val2InRing) {
p.Append(cRing[3], 1.0f / 36.0f);
p.Append(cRing[5], 1.0f / 36.0f);
p.Append(cRing[7], 1.0f / 36.0f);
} else {
p.AddOrAppend(cRing[3], 1.0f / 36.0f);
p.AddOrAppend(cRing[5], 1.0f / 36.0f);
p.AddOrAppend(cRing[7], 1.0f / 36.0f);
}
// Identify the edges along Ep and Em and those opposite them:
int iEdgeEp = 2 * corner.faceInRing;
int iEdgeEm = 2 * ((corner.faceInRing + 1) & 0x3);
int iEdgeOp = 2 * ((corner.faceInRing + 2) & 0x3);
int iEdgeOm = 2 * ((corner.faceInRing + 3) & 0x3);
ep.Append(cIndex, 4.0f / 9.0f);
ep.Append(cRing[iEdgeEp], 2.0f / 9.0f);
ep.Append(cRing[iEdgeEm], 1.0f / 9.0f);
ep.Append(cRing[iEdgeOm], 1.0f / 9.0f);
ep.Append(cRing[iEdgeEp + 1], 1.0f / 18.0f);
if (corner.epAdjToVal2) {
ep.AddOrAppend(cRing[iEdgeOm + 1], 1.0f / 18.0f);
} else {
ep.Append(cRing[iEdgeOm + 1], 1.0f / 18.0f);
}
em.Append(cIndex, 4.0f / 9.0f);
em.Append(cRing[iEdgeEm], 2.0f / 9.0f);
em.Append(cRing[iEdgeEp], 1.0f / 9.0f);
em.Append(cRing[iEdgeOp], 1.0f / 9.0f);
em.Append(cRing[iEdgeEp + 1], 1.0f / 18.0f);
if (corner.emAdjToVal2) {
em.AddOrAppend(cRing[iEdgeEm + 1], 1.0f / 18.0f);
} else {
em.Append(cRing[iEdgeEm + 1], 1.0f / 18.0f);
}
} else {
// Decide which point corresponds to interior vs exterior tangent:
Point & eInterior = corner.faceInRing ? ep : em;
Point & eBoundary = corner.faceInRing ? em : ep;
int iBoundary = corner.faceInRing ? 4 : 0;
p.Append(cIndex, 2.0f / 3.0f);
p.Append(cRing[0], 1.0f / 6.0f);
p.Append(cRing[4], 1.0f / 6.0f);
eBoundary.Append(cIndex, 2.0f / 3.0f);
eBoundary.Append(cRing[iBoundary], 1.0f / 3.0f);
eInterior.Append(cIndex, 4.0f / 9.0f);
eInterior.Append(cRing[2], 2.0f / 9.0f);
eInterior.Append(cRing[0], 1.0f / 9.0f);
eInterior.Append(cRing[4], 1.0f / 9.0f);
eInterior.Append(cRing[1], 1.0f / 18.0f);
eInterior.Append(cRing[3], 1.0f / 18.0f);
}
assert(matrix.GetRowSize(5*cIndex + 0) == p.GetSize());
assert(matrix.GetRowSize(5*cIndex + 1) == ep.GetSize());
assert(matrix.GetRowSize(5*cIndex + 2) == em.GetSize());
}
template <typename REAL>
void
GregoryConverter<REAL>::computeIrregularEdgePoints(int cIndex,
Matrix & matrix, Weight *weightBuffer) const {
// Declare with 0 size for use with Append()
Point p (matrix, 5*cIndex + 0, 0);
Point ep(matrix, 5*cIndex + 1, 0);
Point em(matrix, 5*cIndex + 2, 0);
//
// The corner and edge points P, Ep and Em are completely determined
// by the 1-ring of vertices around (and including) the corner vertex.
// We combine full sets of coefficients for the vertex and its 1-ring.
//
CornerTopology const & corner = _corners[cIndex];
if (corner.isSharp) {
//
// The sharp case -- both interior and boundary...
//
p.Append(cIndex, 1.0f);
// Approximating these for now, pending future investigation...
ep.Append(cIndex, (REAL)(2.0 / 3.0));
ep.Append((cIndex+1) & 0x3, (REAL)(1.0 / 3.0));
em.Append(cIndex, (REAL)(2.0 / 3.0));
em.Append((cIndex+3) & 0x3, (REAL)(1.0 / 3.0));
} else if (! corner.isBoundary) {
//
// The irregular interior case:
//
computeIrregularInteriorEdgePoints(cIndex, p, ep, em, weightBuffer);
} else if (corner.numFaces > 1) {
//
// The irregular boundary case:
//
computeIrregularBoundaryEdgePoints(cIndex, p, ep, em, weightBuffer);
} else {
//
// The irregular/smooth corner case:
//
p.Append(cIndex, (REAL)(4.0 / 6.0));
p.Append((cIndex+1) & 0x3, (REAL)(1.0 / 6.0));
p.Append((cIndex+3) & 0x3, (REAL)(1.0 / 6.0));
ep.Append(cIndex, (REAL)(2.0 / 3.0));
ep.Append((cIndex+1) & 0x3, (REAL)(1.0 / 3.0));
em.Append(cIndex, (REAL)(2.0 / 3.0));
em.Append((cIndex+3) & 0x3, (REAL)(1.0 / 3.0));
}
assert(matrix.GetRowSize(5*cIndex + 0) == p.GetSize());
assert(matrix.GetRowSize(5*cIndex + 1) == ep.GetSize());
assert(matrix.GetRowSize(5*cIndex + 2) == em.GetSize());
}
template <typename REAL>
void
GregoryConverter<REAL>::computeIrregularInteriorEdgePoints(
int cIndex,
Point& p, Point& ep, Point& em,
Weight *ringWeights) const {
CornerTopology const & corner = _corners[cIndex];
int valence = corner.valence;
int weightWidth = 1 + 2 * valence;
Weight* pWeights = &ringWeights[0];
Weight* epWeights = pWeights + weightWidth;
Weight* emWeights = pWeights + weightWidth * 2;
//
// The interior (smooth) case -- invoke the public static method that
// computes pre-allocated ring weights for P, Ep and Em:
//
CatmarkLimits<REAL>::ComputeInteriorPointWeights(valence, corner.faceInRing,
pWeights, epWeights, emWeights);
//
// Transer the weights for the ring into the stencil form of the required
// Point type. The limit mask for position involves all ring weights, and
// since Ep and Em depend on it, there should be no need to filter weights
// with value 0:
//
// The presence of overlapping contributions in the ring when a neighboring
// vertex is valence-2 interior is a nuisance and highly unlikely but still
// possible if we have a triangle near a valence-2 interior vertex -- they
// will still not be isolated at level 1.
//
// For now just use the much-less-efficient AddOrAppend() in this case
// until we can identify the overlap more specifically and have a more
// general mechanism availble to deal with it.
//
p.Append( cIndex, pWeights[0]);
ep.Append(cIndex, epWeights[0]);
em.Append(cIndex, emWeights[0]);
if (!corner.val2InRing) {
for (int i = 1; i < weightWidth; ++i) {
int pRingPoint = corner.ringPoints[i-1];
p.Append( pRingPoint, pWeights[i]);
ep.Append(pRingPoint, epWeights[i]);
em.Append(pRingPoint, emWeights[i]);
}
} else {
for (int i = 1; i < weightWidth; ++i) {
int pRingPoint = corner.ringPoints[i-1];
p.AddOrAppend( pRingPoint, pWeights[i]);
ep.AddOrAppend(pRingPoint, epWeights[i]);
em.AddOrAppend(pRingPoint, emWeights[i]);
}
}
}
template <typename REAL>
void
GregoryConverter<REAL>::computeIrregularBoundaryEdgePoints(
int cIndex,
Point& p, Point& ep, Point& em,
Weight *ringWeights) const {
CornerTopology const & corner = _corners[cIndex];
int valence = corner.valence;
int weightWidth = 1 + corner.valence + corner.numFaces;
Weight* pWeights = &ringWeights[0];
Weight* epWeights = pWeights + weightWidth;
Weight* emWeights = pWeights + weightWidth * 2;
//
// The boundary (smooth) case -- invoke the public static method that
// computes pre-allocated ring weights for P, Ep and Em:
//
CatmarkLimits<REAL>::ComputeBoundaryPointWeights(valence, corner.faceInRing,
pWeights, epWeights, emWeights);
//
// Transfer ring weights into points -- exploiting cases where they
// are known to be non-zero only along the two boundary edges:
//
int N = weightWidth - 1;
int p0 = cIndex;
int p1 = corner.ringPoints[0];
int pN = corner.ringPoints[2*(valence-1)];
p.Append(p0, pWeights[0]);
p.Append(p1, pWeights[1]);
p.Append(pN, pWeights[N]);
// If Ep is on the boundary edge, it has only two non-zero weights along
// that edge:
ep.Append(p0, epWeights[0]);
ep.Append(p1, epWeights[1]);
if (corner.faceInRing > 0) {
for (int i = 2; i < weightWidth; ++i) {
ep.Append(corner.ringPoints[i-1], epWeights[i]);
}
}
// If Em is on the boundary edge, it has only two non-zero weights along
// that edge:
em.Append(p0, emWeights[0]);
if (corner.faceInRing < (corner.numFaces - 1)) {
for (int i = 1; i < N; ++i) {
em.Append(corner.ringPoints[i-1], emWeights[i]);
}
}
em.Append(pN, emWeights[N]);
}
template <typename REAL>
int
GregoryConverter<REAL>::getIrregularFacePointSize(
int cIndexNear, int cIndexFar) const {
CornerTopology const & corner = _corners[cIndexNear];
CornerTopology const & adjCorner = _corners[cIndexFar];
int thisSize = corner.isSharp
? (6 - (corner.valence == 2))
: (1 + corner.ringPoints.GetSize() - corner.val2InRing);
int adjSize = (adjCorner.isRegular || adjCorner.isSharp || (adjCorner.valence == 2))
? 0
: (1 + adjCorner.ringPoints.GetSize() - 6);
return thisSize + adjSize;
}
template <typename REAL>
void
GregoryConverter<REAL>::computeIrregularFacePoint(
int cIndexNear, int edgeInNearCornerRing, int cIndexFar,
Point const & p, Point const & eNear, Point const & eFar, Point & fNear,
REAL signForSideOfEdge, Weight *rowWeights, int *columnMask) const {
CornerTopology const & cornerNear = _corners[cIndexNear];
CornerTopology const & cornerFar = _corners[cIndexFar];
int valence = cornerNear.valence;
Weight cosNear = cornerNear.cosFaceAngle;
Weight cosFar = cornerFar.cosFaceAngle;
Weight pCoeff = cosFar / 3.0f;
Weight eNearCoeff = (3.0f - 2.0f * cosNear - cosFar) / 3.0f;
Weight eFarCoeff = 2.0f * cosNear / 3.0f;
int fullRowSize = _numSourcePoints;
std::memset(&columnMask[0], 0, fullRowSize * sizeof(int));
std::memset(&rowWeights[0], 0, fullRowSize * sizeof(Weight));
_addSparsePointToFullRow(rowWeights, p, pCoeff, columnMask);
_addSparsePointToFullRow(rowWeights, eNear, eNearCoeff, columnMask);
_addSparsePointToFullRow(rowWeights, eFar, eFarCoeff, columnMask);
// Remember that R is to be computed about an interior edge and is
// comprised of the two pairs of points opposite the interior edge
//
// Remember also that val-2-overlap may cause two of these to be the
// same -- doesn't matter if we accumulate here will if we assign:
//
int iEdgeInterior = edgeInNearCornerRing;
int iEdgePrev = (iEdgeInterior + valence - 1) % valence;
int iEdgeNext = (iEdgeInterior + 1) % valence;
rowWeights[cornerNear.ringPoints[2*iEdgePrev]] += -signForSideOfEdge / 9.0f;
rowWeights[cornerNear.ringPoints[2*iEdgePrev + 1]] += -signForSideOfEdge / 18.0f;
rowWeights[cornerNear.ringPoints[2*iEdgeInterior + 1]] += signForSideOfEdge / 18.0f;
rowWeights[cornerNear.ringPoints[2*iEdgeNext]] += signForSideOfEdge / 9.0f;
for (int i = 0; i < fullRowSize; ++i) {
if (columnMask[i]) {
fNear.Append(columnMask[i] - 1, rowWeights[i]);
}
}
}
template <typename REAL>
void
GregoryConverter<REAL>::assignRegularFacePoints(int cIndex, Matrix & matrix) const {
// Declare with 0 size for use with Append()
Point fp(matrix, 5*cIndex + 3, 0);
Point fm(matrix, 5*cIndex + 4, 0);
CornerTopology const & corner = _corners[cIndex];
int cNext = (cIndex+1) & 0x3;
int cOpp = (cIndex+2) & 0x3;
int cPrev = (cIndex+3) & 0x3;
// Assign regular Fp and/or Fm:
if (corner.fpIsRegular) {
fp.Append(cIndex, (REAL)(4.0 / 9.0));
fp.Append(cPrev, (REAL)(2.0 / 9.0));
fp.Append(cNext, (REAL)(2.0 / 9.0));
fp.Append(cOpp, (REAL)(1.0 / 9.0));
assert(matrix.GetRowSize(5*cIndex + 3) == fp.GetSize());
}
if (corner.fmIsRegular) {
fm.Append(cIndex, (REAL)(4.0 / 9.0));
fm.Append(cPrev, (REAL)(2.0 / 9.0));
fm.Append(cNext, (REAL)(2.0 / 9.0));
fm.Append(cOpp, (REAL)(1.0 / 9.0));
assert(matrix.GetRowSize(5*cIndex + 4) == fm.GetSize());
}
}
template <typename REAL>
void
GregoryConverter<REAL>::computeIrregularFacePoints(int cIndex,
Matrix & matrix, Weight *rowWeights, int *columnMask) const {
// Identify neighboring corners:
CornerTopology const & corner = _corners[cIndex];
int cNext = (cIndex+1) & 0x3;
int cPrev = (cIndex+3) & 0x3;
Point epPrev(matrix, 5*cPrev + 1);
Point em (matrix, 5*cIndex + 2);
Point p (matrix, 5*cIndex + 0);
Point ep (matrix, 5*cIndex + 1);
Point emNext(matrix, 5*cNext + 2);
// Declare with 0 size for use with Append()
Point fp(matrix, 5*cIndex + 3, 0);
Point fm(matrix, 5*cIndex + 4, 0);
//
// Compute the face points Fp and Fm in terms of the corner (P) and edge
// points (Ep and Em) previously computed. The caller provides a buffer
// of the appropriate size (twice the width of the matrix) to use for
// combining weights, along with an integer buffer used to identify
// non-zero weights and preserve the sparsity of the combinations (note
// they use index + 1 to detect index 0 when cleared with 0 entries).
//
if (!corner.fpIsRegular && !corner.fpIsCopied) {
int iEdgeP = corner.faceInRing;
computeIrregularFacePoint(cIndex, iEdgeP, cNext,
p, ep, emNext, fp, 1.0, rowWeights, columnMask);
}
if (!corner.fmIsRegular && !corner.fmIsCopied) {
int iEdgeM = (corner.faceInRing + 1) % corner.valence;
computeIrregularFacePoint(cIndex, iEdgeM, cPrev,
p, em, epPrev, fm, -1.0, rowWeights, columnMask);
}
// Copy Fp or Fm now that any shared values were computed above:
if (corner.fpIsCopied) {
fp.Copy(fm);
}
if (corner.fmIsCopied) {
fm.Copy(fp);
}
if (!corner.fpIsRegular) assert(matrix.GetRowSize(5*cIndex + 3) == fp.GetSize());
if (!corner.fmIsRegular) assert(matrix.GetRowSize(5*cIndex + 4) == fm.GetSize());
}
//
// BSplineConverter
//
// The BSplineConverter is far less complicated than GregoryConverter -- and
// actually makes use of GregroyConverter in some cases. It provides a direct
// mapping from the original Catmull-Clark points to a set of BSpline points
// fit to the limit position and tangent plane of a single/isolated irregular
// interior corner. In the case of all other irregularities, the set of Gregory
// points are first determined (using the GregoryConverter) and then converted
// to BSpline.
//
// In this latter case, none of the BSpline points derived correspond to the
// original source points.
//
template <typename REAL>
class BSplineConverter {
public:
typedef REAL Weight;
typedef SparseMatrix<Weight> Matrix;
public:
BSplineConverter() : _sourcePatch(0) { }
BSplineConverter(SourcePatch const & sourcePatch);
BSplineConverter(SourcePatch const & sourcePatch, Matrix & sparseMatrix);
void Initialize(SourcePatch const & sourcePatch);
void Convert(Matrix & matrix) const;
private:
void convertIrregularCorner(int irregularCornerIndex, Matrix & matrix) const;
void buildIrregularCornerMatrix(int irregularCornerValence,
int numSourcePoints,
int const rowsForXPoints[7],
Matrix & matrix) const;
void convertFromGregory(Matrix const & gregoryMatrix, Matrix & matrix) const;
private:
SourcePatch const * _sourcePatch;
GregoryConverter<REAL> _gregoryConverter;
};
template <typename REAL>
BSplineConverter<REAL>::BSplineConverter(SourcePatch const & sourcePatch) {
Initialize(sourcePatch);
}
template <typename REAL>
BSplineConverter<REAL>::BSplineConverter(SourcePatch const & sourcePatch,
Matrix & matrix) {
Initialize(sourcePatch);
Convert(matrix);
}
template <typename REAL>
void
BSplineConverter<REAL>::Initialize(SourcePatch const & sourcePatch) {
_sourcePatch = &sourcePatch;
_gregoryConverter.Initialize(sourcePatch);
}
template <typename REAL>
void
BSplineConverter<REAL>::Convert(Matrix & matrix) const {
if (_gregoryConverter.IsIsolatedInteriorPatch()) {
convertIrregularCorner(_gregoryConverter.GetIsolatedInteriorCorner(),
matrix);
} else {
Matrix gregoryMatrix;
_gregoryConverter.Convert(gregoryMatrix);
convertFromGregory(gregoryMatrix, matrix);
}
}
template <typename REAL>
void
BSplineConverter<REAL>::convertFromGregory(Matrix const & G, Matrix & B) const {
//
// The change of basis matrix from Gregory/Bezier to BSpline contains three
// unique sets of weights corresponding to corner, boundary and interior
// points:
//
static REAL const wCorner[9] = { 49.f,-42.f,-42.f, 36.f,-14.f,-14.f, 12.f, 12.f, 4.f };
static REAL const wBoundary[6] = {-14.f, 12.f, 7.f, -6.f, 4.f, -2.f };
static REAL const wInterior[4] = { 4.f, -2.f, -2.f, 1.f };
//
// The points of the BSpline and Gregory matrices are oriented and correlated
// as follows:
//
// B = { 12, 13, 14, 15 } G = { 15, 17, 11, 10 }
// { 8, 9, 10, 11 } { 16, 18, 13, 12 }
// { 4, 5, 6, 7 } { 2, 3, 8, 6 }
// { 0, 1, 2, 3 } { 0, 1, 7, 5 }
//
// With four symmetric quadrants the dependencies of the BSpline points on the
// Gregory/Bezier points are as follows -- using the "p", "ep", "em" and "f"
// naming from the Gregory points:
//
static int const pIndices[4][9] = { { 3, 1, 2, 0, 8, 18, 7, 16, 13 },
{ 8, 6, 7, 5, 3, 13, 12, 1, 18 },
{ 13, 11, 12, 10, 18, 8, 17, 6, 3 },
{ 18, 16, 17, 15, 13, 3, 2, 11, 8 } };
static int const epIndices[4][6] = { { 3, 1, 8, 7, 18, 13 },
{ 8, 6, 13, 12, 3, 18 },
{ 13, 11, 18, 17, 8, 3 },
{ 18, 16, 3, 2, 13, 8 } };
static int const emIndices[4][6] = { { 3, 2, 18, 16, 8, 13 },
{ 8, 7, 3, 1, 13, 18 },
{ 13, 12, 8, 6, 18, 3 },
{ 18, 17, 13, 11, 3, 8 } };
static int const fIndices[4][4] = { { 3, 8, 18, 13 },
{ 8, 13, 3, 18 },
{ 13, 18, 8, 3 },
{ 18, 3, 13, 8 } };
//
// The matrix is not very sparse -- build it full for now for simplicity and
// consider pruning later.
//
// Remember that to use variable/sparse row sizes requires processing rows in
// order unless we can pre-assign the row sizes (difficult here).
//
_initializeFullMatrix(B, 16, G.GetNumColumns());
_combineSparseMatrixRowsInFull(B, 0, G, 9, pIndices[0], wCorner);
_combineSparseMatrixRowsInFull(B, 1, G, 6, epIndices[0], wBoundary);
_combineSparseMatrixRowsInFull(B, 2, G, 6, emIndices[1], wBoundary);
_combineSparseMatrixRowsInFull(B, 3, G, 9, pIndices[1], wCorner);
_combineSparseMatrixRowsInFull(B, 4, G, 6, emIndices[0], wBoundary);
_combineSparseMatrixRowsInFull(B, 5, G, 4, fIndices[0], wInterior);
_combineSparseMatrixRowsInFull(B, 6, G, 4, fIndices[1], wInterior);
_combineSparseMatrixRowsInFull(B, 7, G, 6, epIndices[1], wBoundary);
_combineSparseMatrixRowsInFull(B, 8, G, 6, epIndices[3], wBoundary);
_combineSparseMatrixRowsInFull(B, 9, G, 4, fIndices[3], wInterior);
_combineSparseMatrixRowsInFull(B, 10, G, 4, fIndices[2], wInterior);
_combineSparseMatrixRowsInFull(B, 11, G, 6, emIndices[2], wBoundary);
_combineSparseMatrixRowsInFull(B, 12, G, 9, pIndices[3], wCorner);
_combineSparseMatrixRowsInFull(B, 13, G, 6, emIndices[3], wBoundary);
_combineSparseMatrixRowsInFull(B, 14, G, 6, epIndices[2], wBoundary);
_combineSparseMatrixRowsInFull(B, 15, G, 9, pIndices[2], wCorner);
}
template <typename REAL>
void
BSplineConverter<REAL>::buildIrregularCornerMatrix(
int irregularCornerValence,
int numSourcePoints, int const rowsForXPoints[7],
Matrix & matrix) const {
int ringSizePlusCorner = 1 + 2 * irregularCornerValence;
int numElements = 7 * ringSizePlusCorner + 11;
int rowSizes[16];
for (int i = 0; i < 16; ++i) {
rowSizes[i] = 1;
}
rowSizes[rowsForXPoints[0]] = ringSizePlusCorner;
rowSizes[rowsForXPoints[1]] = ringSizePlusCorner;
rowSizes[rowsForXPoints[2]] = ringSizePlusCorner;
rowSizes[rowsForXPoints[3]] = ringSizePlusCorner;
rowSizes[rowsForXPoints[4]] = ringSizePlusCorner;
rowSizes[rowsForXPoints[5]] = ringSizePlusCorner + 1;
rowSizes[rowsForXPoints[6]] = ringSizePlusCorner + 1;
matrix.Resize(16, numSourcePoints, numElements);
for (int i = 0; i < 16; ++i) {
matrix.SetRowSize(i, rowSizes[i]);
REAL * firstElement = &matrix.SetRowElements(i)[0];
if (rowSizes[i] == 1) {
*firstElement = REAL(1.0);
} else {
std::memset(firstElement, 0, rowSizes[i] * sizeof(REAL));
}
}
}
template <typename REAL>
void
BSplineConverter<REAL>::convertIrregularCorner(int irregularCorner,
Matrix & matrix) const {
//
// Labeling/ordering of source points P[] and derived points X[] for the
// final patch, where P0* denotes the extra-ordinary vertex and P5 "does
// not exist", i.e. it serves as a place-holder for the remainder of the
// exterior ring of arbitrary size around P0:
//
// ...
// (P5) P4----P15---P14 X0----X2----X4----X6
// . | | | | | | |
// . | | | | | | |
// P6----P0*---P3----P13 X1----P0*---P3----P13
// | |P' Em| | ---> | | | |
// | |Ep | | | | | |
// P7----P1----P2----P12 X3----P1----P2----P12
// | | | | | | | |
// | | | | | | | |
// P8----P9----P10---P11 X5----P9----P10---P11
//
// The formulae deriving X[] on the right are in terms of the P[] on the
// left along with the limit position and edge points (P', Ep and Em) and
// other X[]. Given dependencies between the Xi formulae, the order of
// evaluation is important.
//
// Listed in terms of symmetric pairs, we compute X0 last:
//
// X1 = 1/3 * ( 36Ep - 16P0 - 8P1 - 2P2 - 4P3 - P6 - 2P7)
// X2 = 1/3 * ( 36Em - 16P0 - 4P1 - 2P2 - 8P3 - P4 - 2P15)
//
// X3 = 1/3 * (-18Ep + 8P0 + 4P1 + P2 + 2P3 + 4P7 + 2P6)
// X4 = 1/3 * (-18Em + 8P0 + 2P1 + P2 + 4P3 + 4P15 + 2P4)
//
// X5 = X1 + (P8 - P6)
// X6 = X2 + (P14 - P4)
//
// X0 = 36P' - 16P0 - 4(P1 + P3 + X2 + X1) - (P2 + X3 + X4)
//
// Since the limit points (P', Ep and Em) are all defined in terms of the
// 1-ring around P0, and with terms generally involving source points P[]
// also part of that ring, almost all Xi are fully determined by points in
// the ring. Only X5 and X6 involve additional points, and then only one
// additional point each, so its simple to amend these cases separately.
//
// So we compute the Xi by combining sets of coefficients for the 1-ring
// around P0 (with that ring including PO as the first entry).
//
//
// Compute limit points P, Ep and Em in terms of weights of the 1-ring for the
// corner and identify the indices of relevant points within the ring:
//
int valence = _sourcePatch->_corners[irregularCorner]._numFaces;
int faceInRing = _sourcePatch->_corners[irregularCorner]._patchFace;
int ringSizePlusCorner = 1 + 2 * valence;
StackBuffer<REAL, 120, true> limitPointWeights(3 * ringSizePlusCorner);
Weight * wP = &limitPointWeights[0];
Weight * wEp = wP + ringSizePlusCorner;
Weight * wEm = wEp + ringSizePlusCorner;
assert(valence > 2);
CatmarkLimits<REAL>::ComputeInteriorPointWeights(valence, faceInRing, wP, wEp, wEm);
//
// Resize the sparse matrix (and all of its rows) to hold coefficients for
// X and identify arrays for each X where we will compute the weights:
//
static int const xRowsAll[4][7] = { { 0, 1, 4, 2, 8, 3, 12 },
{ 3, 7, 2, 11, 1, 15, 0 },
{ 15, 14, 11, 13, 7, 12, 3 },
{ 12, 8, 13, 4, 14, 0, 15 } };
int const * xRows = xRowsAll[irregularCorner];
int numSourcePoints = _sourcePatch->GetNumSourcePoints();
buildIrregularCornerMatrix(valence, numSourcePoints, xRows, matrix);
Weight * wX0 = &matrix.SetRowElements(xRows[0])[0];
Weight * wX1 = &matrix.SetRowElements(xRows[1])[0];
Weight * wX2 = &matrix.SetRowElements(xRows[2])[0];
Weight * wX3 = &matrix.SetRowElements(xRows[3])[0];
Weight * wX4 = &matrix.SetRowElements(xRows[4])[0];
Weight * wX5 = &matrix.SetRowElements(xRows[5])[0];
Weight * wX6 = &matrix.SetRowElements(xRows[6])[0];
//
// We use the ordering of points in the retrieved 1-ring for which weights
// of the Catmark limit points are computed. So rather than re-order the
// ring to accomodate contributing source points, identify the locations
// of the source points in the 1-ring so we can set coefficients
// appropriately:
//
int faceInRingPlus1 = (faceInRing + 1) % valence;
int faceInRingPlus2 = (faceInRing + 2) % valence;
int faceInRingMinus1 = (faceInRing + valence - 1) % valence;
int p0inRing = 0;
int p1inRing = 1 + 2*faceInRing;
int p2inRing = 1 + 2*faceInRing + 1;
int p3inRing = 1 + 2*faceInRingPlus1;
int p15inRing = 1 + 2*faceInRingPlus1 + 1;
int p4inRing = 1 + 2*faceInRingPlus2;
int p6inRing = 1 + 2*faceInRingMinus1;
int p7inRing = 1 + 2*faceInRingMinus1 + 1;
int p8inRing = ringSizePlusCorner;
int p14inRing = ringSizePlusCorner;
//
// Assign the weights for the X[] in symmetric pairs -- first initializing
// entries for contributions of source points P[], then combining the
// contributions of P[] with those for the limit points and dependent X[]:
//
// X1 = 1/3 * (36Ep - (16P0 + 8P1 + 2P2 + 4P3 + P6 + 2P7))
// X2 = 1/3 * (36pm - (16P0 + 8P3 + 2P2 + 4P1 + P4 + 2P15))
wX1[p0inRing] = wX2[p0inRing] = 16.0f;
wX1[p1inRing] = wX2[p3inRing] = 8.0f;
wX1[p2inRing] = wX2[p2inRing] = 2.0f;
wX1[p3inRing] = wX2[p1inRing] = 4.0f;
wX1[p6inRing] = wX2[p4inRing] = 1.0f;
wX1[p7inRing] = wX2[p15inRing] = 2.0f;
// X3 = 1/3 * (-18Ep + (8P0 + 4P1 + P2 + 2P3 + 2P6 + 4P7))
// X4 = 1/3 * (-18Em + (8P0 + 4P3 + P2 + 2P1 + 2P4 + 4P15))
wX3[p0inRing] = wX4[p0inRing] = 8.0f;
wX3[p1inRing] = wX4[p3inRing] = 4.0f;
wX3[p2inRing] = wX4[p2inRing] = 1.0f;
wX3[p3inRing] = wX4[p1inRing] = 2.0f;
wX3[p6inRing] = wX4[p4inRing] = 2.0f;
wX3[p7inRing] = wX4[p15inRing] = 4.0f;
// X5 = X1 + (P8 - P6)
// X6 = X2 + (P14 - P4)
wX5[p6inRing] = wX6[p4inRing] = -1.0f;
wX5[p8inRing] = wX6[p14inRing] = 1.0f;
// X0 = 36P' - 16P0 - 4(P1 + P3 + X2 + X1) - (P2 + X3 + X4)
// = 36P' - (16P0 + 4P1 + P2 + 4P3) - 4(X2 + X1) - (X3 + X4)
wX0[p0inRing] = 16.0f;
wX0[p1inRing] = 4.0f;
wX0[p2inRing] = 1.0f;
wX0[p3inRing] = 4.0f;
// Combine weights for all X[] in one iteration through the ring:
const REAL oneThird = (REAL) (1.0 / 3.0);
for (int i = 0; i < ringSizePlusCorner; ++i) {
wX1[i] = (36.0f * wEp[i] - wX1[i]) * oneThird;
wX2[i] = (36.0f * wEm[i] - wX2[i]) * oneThird;
wX3[i] = - wEp[i] * 6.0f + wX3[i] * oneThird;
wX4[i] = - wEm[i] * 6.0f + wX4[i] * oneThird;
wX5[i] += wX1[i];
wX6[i] += wX2[i];
wX0[i] = wP[i] * 36.0f - wX0[i] - (wX2[i] + wX1[i]) * 4.0f - (wX3[i] + wX4[i]);
}
//
// The weights for the rows for X[] are now computed, and with identity
// rows of the remaining source points already assigned a weight of 1.0,
// all weights in the conversion matrix are now assigned.
//
// We now need to assign the indices. Indices for the 1-ring around the
// corner are trivially retrieved and complete rows for all X[] except
// the last entries for X5 and X6. So identify the source points needed
// for these two trailing entries and those for other source points that
// are referenced by the matrix.
//
// We've already identified those involved in the equations above -- the
// rest can be determined from the orientation of points in SourcePatch:
// all exterior points follow in a counter-clockwise order after the four
// interior points, and we only care about the exterior points P8 through
// P14.
//
StackBuffer<int, 40, true> ringPoints(ringSizePlusCorner);
ringPoints[0] = irregularCorner;
_sourcePatch->GetCornerRingPoints(irregularCorner, &ringPoints[1]);
// Identify P8 through P14 (no need to identify all 16):
int pPoints[16];
int pNext = ringPoints[p7inRing] + 1;
for (int i = 8; i < 16; ++i, ++pNext) {
pPoints[i] = (pNext < numSourcePoints) ? pNext
: (pNext - numSourcePoints + 4);
}
// Assign the ring of indices for the rows of X[] -- amending X5 and X6:
int * xIndices[7];
for (int i = 0; i < 7; ++i) {
xIndices[i] = &matrix.SetRowColumns(xRows[i])[0];
std::memcpy(xIndices[i], ringPoints, ringSizePlusCorner * sizeof(int));
}
xIndices[5][ringSizePlusCorner] = pPoints[8];
xIndices[6][ringSizePlusCorner] = pPoints[14];
// Assign the index for the rows of the four interior points -- these are
// fixed given the interior points precede the exterior:
matrix.SetRowColumns( 5)[0] = 0;
matrix.SetRowColumns( 6)[0] = 1;
matrix.SetRowColumns( 9)[0] = 3;
matrix.SetRowColumns(10)[0] = 2;
// Assign the index for the rows of remaining exterior source points
// (P9 through P13) -- identify the rows from a lookup table based on
// the irregular corner:
static int const extPointRowsAll[4][5] = { { 7, 11, 15, 14, 13 },
{ 14, 13, 12, 8, 4 },
{ 8, 4, 0, 1, 2 },
{ 1, 2, 3, 7, 11 } };
int const * extPointRows = extPointRowsAll[irregularCorner];
matrix.SetRowColumns(extPointRows[0])[0] = pPoints[ 9];
matrix.SetRowColumns(extPointRows[1])[0] = pPoints[10];
matrix.SetRowColumns(extPointRows[2])[0] = pPoints[11];
matrix.SetRowColumns(extPointRows[3])[0] = pPoints[12];
matrix.SetRowColumns(extPointRows[4])[0] = pPoints[13];
}
//
// LinearConverter
//
// The LinearConverter is far less complicated than any of the others. There's
// not much more to it than a single conversion method -- it follows the pattern
// for consistency.
//
template <typename REAL>
class LinearConverter {
public:
typedef REAL Weight;
typedef SparseMatrix<Weight> Matrix;
typedef SparseMatrixPoint<Weight> MatrixPoint;
public:
LinearConverter() : _sourcePatch(0) { }
LinearConverter(SourcePatch const & sourcePatch);
LinearConverter(SourcePatch const & sourcePatch, Matrix & sparseMatrix);
void Initialize(SourcePatch const & sourcePatch);
void Convert(Matrix & matrix) const;
private:
SourcePatch const * _sourcePatch;
};
template <typename REAL>
LinearConverter<REAL>::LinearConverter(SourcePatch const & sourcePatch) {
Initialize(sourcePatch);
}
template <typename REAL>
LinearConverter<REAL>::LinearConverter(SourcePatch const & sourcePatch, Matrix & matrix) {
Initialize(sourcePatch);
Convert(matrix);
}
template <typename REAL>
void
LinearConverter<REAL>::Initialize(SourcePatch const & sourcePatch) {
_sourcePatch = &sourcePatch;
}
template <typename REAL>
void
LinearConverter<REAL>::Convert(Matrix & matrix) const {
StackBuffer<Index,64,true> indexBuffer(1 + _sourcePatch->GetMaxRingSize());
StackBuffer<Weight,64,true> weightBuffer(1 + _sourcePatch->GetMaxRingSize());
int numElements = 4 * (1 + _sourcePatch->GetMaxRingSize());
matrix.Resize(4, _sourcePatch->GetNumSourcePoints(), numElements);
for (int cIndex = 0; cIndex < 4; ++cIndex) {
// Deal with the trivial sharp case first:
if (_sourcePatch->_corners[cIndex]._sharp) {
matrix.SetRowSize(cIndex, 1);
matrix.SetRowColumns(cIndex)[0] = cIndex;
matrix.SetRowElements(cIndex)[0] = 1.0f;
continue;
}
SourcePatch::Corner const & sourceCorner = _sourcePatch->_corners[cIndex];
int ringSize = _sourcePatch->GetCornerRingSize(cIndex);
if (sourceCorner._boundary) {
matrix.SetRowSize(cIndex, 3);
} else {
matrix.SetRowSize(cIndex, 1 + ringSize - sourceCorner._val2Adjacent);
}
Array<Index> rowIndices = matrix.SetRowColumns(cIndex);
Array<Weight> rowWeights = matrix.SetRowElements(cIndex);
indexBuffer[0] = cIndex;
_sourcePatch->GetCornerRingPoints(cIndex, &indexBuffer[1]);
if (sourceCorner._boundary) {
CatmarkLimits<REAL>::ComputeBoundaryPointWeights(
1 + sourceCorner._numFaces, sourceCorner._patchFace,
&weightBuffer[0], 0, 0);
rowIndices[0] = indexBuffer[0];
rowIndices[1] = indexBuffer[1];
rowIndices[2] = indexBuffer[ringSize];
rowWeights[0] = weightBuffer[0];
rowWeights[1] = weightBuffer[1];
rowWeights[2] = weightBuffer[ringSize];
} else {
CatmarkLimits<REAL>::ComputeInteriorPointWeights(
sourceCorner._numFaces, sourceCorner._patchFace,
&weightBuffer[0], 0, 0);
if (sourceCorner._val2Adjacent) {
MatrixPoint row(matrix, cIndex, 0);
for (int i = 0; i <= ringSize; ++i) {
row.AddOrAppend(indexBuffer[i], weightBuffer[i]);
}
} else {
std::memcpy(
&rowIndices[0], indexBuffer, (1 + ringSize) * sizeof(Index));
std::memcpy(
&rowWeights[0], weightBuffer, (1 + ringSize) * sizeof(Weight));
}
}
}
}
//
// Internal utilities more relevant to the CatmarkPatchBuilder:
//
namespace {
//
// The patch type associated with each basis for Catmark -- quickly
// indexed from an array. The patch type here is essentially the
// quad form of each basis.
//
PatchDescriptor::Type const patchTypeFromBasisArray[] = {
PatchDescriptor::NON_PATCH, // undefined
PatchDescriptor::REGULAR, // regular
PatchDescriptor::GREGORY_BASIS, // Gregory
PatchDescriptor::QUADS, // linear
PatchDescriptor::NON_PATCH // Bezier -- for future use
};
}
template <typename REAL>
int
CatmarkPatchBuilder::convertSourcePatch(SourcePatch const & sourcePatch,
PatchDescriptor::Type patchType,
SparseMatrix<REAL> & matrix) const {
assert(_schemeType == Sdc::SCHEME_CATMARK);
//
// XXXX (barfowl) - consider a CatmarkPatch class to wrap SourcePatch
// with the additional corner information that it initializes. That
// can then be used for conversion to all destination patch types...
//
if (patchType == PatchDescriptor::GREGORY_BASIS) {
GregoryConverter<REAL>(sourcePatch, matrix);
} else if (patchType == PatchDescriptor::REGULAR) {
BSplineConverter<REAL>(sourcePatch, matrix);
} else if (patchType == PatchDescriptor::QUADS) {
LinearConverter<REAL>(sourcePatch, matrix);
} else {
assert("Unknown or unsupported patch type" == 0);
}
return matrix.GetNumRows();
}
int
CatmarkPatchBuilder::convertToPatchType(SourcePatch const & sourcePatch,
PatchDescriptor::Type patchType,
SparseMatrix<float> & matrix) const {
return convertSourcePatch(sourcePatch, patchType, matrix);
}
int
CatmarkPatchBuilder::convertToPatchType(SourcePatch const & sourcePatch,
PatchDescriptor::Type patchType,
SparseMatrix<double> & matrix) const {
return convertSourcePatch(sourcePatch, patchType, matrix);
}
CatmarkPatchBuilder::CatmarkPatchBuilder(
TopologyRefiner const& refiner, Options const& options) :
PatchBuilder(refiner, options) {
_regPatchType = patchTypeFromBasisArray[_options.regBasisType];
_irregPatchType = (_options.irregBasisType == BASIS_UNSPECIFIED)
? _regPatchType
: patchTypeFromBasisArray[_options.irregBasisType];
_nativePatchType = patchTypeFromBasisArray[BASIS_REGULAR];
_linearPatchType = patchTypeFromBasisArray[BASIS_LINEAR];
}
CatmarkPatchBuilder::~CatmarkPatchBuilder() {
}
PatchDescriptor::Type
CatmarkPatchBuilder::patchTypeFromBasis(BasisType basis) const {
return patchTypeFromBasisArray[(int)basis];
}
} // end namespace Far
} // end namespace OPENSUBDIV_VERSION
} // end namespace OpenSubdiv
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