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OpenSubdiv/opensubdiv/far/patchBasis.cpp
David G. Yu f0128a5f5e Fixed Far::PatchParam encoding of refinement level 
This change restores the use of 4-bits in Far::PatchParam to
encode the refinement level of a patch. This restores one bit
that was stolen to allow for more general encoding of boundary
edge and transition edge masks. In order to accommodate all
of the bits that are required, the transition edge mask bits
are now stored along with the faceId bits.

Also, accessors are now exposed directly as members of Far::PatchParam
and the internal bitfield class is no longer directly exposed.
2015-06-11 15:10:30 -07:00

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//
// 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/patchBasis.h"
#include <cassert>
#include <cstring>
namespace OpenSubdiv {
namespace OPENSUBDIV_VERSION {
namespace Far {
namespace internal {
enum SplineBasis {
BASIS_BILINEAR,
BASIS_BEZIER,
BASIS_BSPLINE,
BASIS_BOX_SPLINE
};
template <SplineBasis BASIS>
class Spline {
public:
// curve weights
static void GetWeights(float t, float point[], float deriv[]);
// box-spline weights
static void GetWeights(float v, float w, float point[]);
// patch weights
static void GetPatchWeights(PatchParam const & param,
float s, float t, float point[], float deriv1[], float deriv2[]);
// adjust patch weights for boundary (and corner) edges
static void AdjustBoundaryWeights(PatchParam const & param,
float sWeights[4], float tWeights[4]);
};
template <>
inline void Spline<BASIS_BEZIER>::GetWeights(
float t, float point[4], float deriv[4]) {
// The four uniform cubic Bezier basis functions (in terms of t and its
// complement tC) evaluated at t:
float t2 = t*t;
float tC = 1.0f - t;
float tC2 = tC * tC;
assert(point);
point[0] = tC2 * tC;
point[1] = tC2 * t * 3.0f;
point[2] = t2 * tC * 3.0f;
point[3] = t2 * t;
// Derivatives of the above four basis functions at t:
if (deriv) {
deriv[0] = -3.0f * tC2;
deriv[1] = 9.0f * t2 - 12.0f * t + 3.0f;
deriv[2] = -9.0f * t2 + 6.0f * t;
deriv[3] = 3.0f * t2;
}
}
template <>
inline void Spline<BASIS_BSPLINE>::GetWeights(
float t, float point[4], float deriv[4]) {
// The four uniform cubic B-Spline basis functions evaluated at t:
float const one6th = 1.0f / 6.0f;
float t2 = t * t;
float t3 = t * t2;
assert(point);
point[0] = one6th * (1.0f - 3.0f*(t - t2) - t3);
point[1] = one6th * (4.0f - 6.0f*t2 + 3.0f*t3);
point[2] = one6th * (1.0f + 3.0f*(t + t2 - t3));
point[3] = one6th * ( t3);
// Derivatives of the above four basis functions at t:
if (deriv) {
deriv[0] = -0.5f*t2 + t - 0.5f;
deriv[1] = 1.5f*t2 - 2.0f*t;
deriv[2] = -1.5f*t2 + t + 0.5f;
deriv[3] = 0.5f*t2;
}
}
template <>
inline void Spline<BASIS_BOX_SPLINE>::GetWeights(
float v, float w, float point[12]) {
float u = 1.0f - v - w;
//
// The 12 basis functions of the quartic box spline (unscaled by their common
// factor of 1/12 until later, and formatted to make it easy to spot any
// typing errors):
//
// 15 terms for the 3 points above the triangle corners
// 9 terms for the 3 points on faces opposite the triangle edges
// 2 terms for the 6 points on faces opposite the triangle corners
//
// Powers of each variable for notational convenience:
float u2 = u*u;
float u3 = u*u2;
float u4 = u*u3;
float v2 = v*v;
float v3 = v*v2;
float v4 = v*v3;
float w2 = w*w;
float w3 = w*w2;
float w4 = w*w3;
// And now the basis functions:
point[ 0] = u4 + 2.0f*u3*v;
point[ 1] = u4 + 2.0f*u3*w;
point[ 8] = w4 + 2.0f*w3*u;
point[11] = w4 + 2.0f*w3*v;
point[ 9] = v4 + 2.0f*v3*w;
point[ 5] = v4 + 2.0f*v3*u;
point[ 2] = u4 + 2.0f*u3*w + 6.0f*u3*v + 6.0f*u2*v*w + 12.0f*u2*v2 +
v4 + 2.0f*v3*w + 6.0f*v3*u + 6.0f*v2*u*w;
point[ 4] = w4 + 2.0f*w3*v + 6.0f*w3*u + 6.0f*w2*u*v + 12.0f*w2*u2 +
u4 + 2.0f*u3*v + 6.0f*u3*w + 6.0f*u2*v*w;
point[10] = v4 + 2.0f*v3*u + 6.0f*v3*w + 6.0f*v2*w*u + 12.0f*v2*w2 +
w4 + 2.0f*w3*u + 6.0f*w3*v + 6.0f*w3*u*v;
point[ 3] = v4 + 6*v3*w + 8*v3*u + 36*v2*w*u + 24*v2*u2 + 24*v*u3 +
w4 + 6*w3*v + 8*w3*u + 36*w2*v*u + 24*w2*u2 + 24*w*u3 + 6*u4 + 60*u2*v*w + 12*v2*w2;
point[ 6] = w4 + 6*w3*u + 8*w3*v + 36*w2*u*v + 24*w2*v2 + 24*w*v3 +
u4 + 6*u3*w + 8*u3*v + 36*u2*v*w + 24*u2*v2 + 24*u*v3 + 6*v4 + 60*v2*w*u + 12*w2*u2;
point[ 7] = u4 + 6*u3*v + 8*u3*w + 36*u2*v*w + 24*u2*w2 + 24*u*w3 +
v4 + 6*v3*u + 8*v3*w + 36*v2*u*w + 24*v2*w2 + 24*v*w3 + 6*w4 + 60*w2*u*v + 12*u2*v2;
for (int i = 0; i < 12; ++i) {
point[i] *= 1.0f / 12.0f;
}
}
template <>
inline void Spline<BASIS_BILINEAR>::GetPatchWeights(PatchParam const & param,
float s, float t, float point[4], float derivS[4], float derivT[4]) {
param.Normalize(s,t);
float sC = 1.0f - s,
tC = 1.0f - t;
if (point) {
point[0] = sC * tC;
point[1] = s * tC;
point[2] = s * t;
point[3] = sC * t;
}
if (derivS and derivT) {
float dScale = (float)(1 << param.GetDepth());
derivS[0] = -tC * dScale;
derivS[1] = tC * dScale;
derivS[2] = t * dScale;
derivS[3] = -t * dScale;
derivT[0] = -sC * dScale;
derivT[1] = -s * dScale;
derivT[2] = s * dScale;
derivT[3] = sC * dScale;
}
}
template <SplineBasis BASIS>
void Spline<BASIS>::AdjustBoundaryWeights(PatchParam const & param,
float sWeights[4], float tWeights[4]) {
int boundary = param.GetBoundary();
if (boundary & 1) {
tWeights[2] -= tWeights[0];
tWeights[1] += 2*tWeights[0];
tWeights[0] = 0;
}
if (boundary & 2) {
sWeights[1] -= sWeights[3];
sWeights[2] += 2*sWeights[3];
sWeights[3] = 0;
}
if (boundary & 4) {
tWeights[1] -= tWeights[3];
tWeights[2] += 2*tWeights[3];
tWeights[3] = 0;
}
if (boundary & 8) {
sWeights[2] -= sWeights[0];
sWeights[1] += 2*sWeights[0];
sWeights[0] = 0;
}
}
template <SplineBasis BASIS>
void Spline<BASIS>::GetPatchWeights(PatchParam const & param,
float s, float t, float point[16], float derivS[16], float derivT[16]) {
float sWeights[4], tWeights[4], dsWeights[4], dtWeights[4];
param.Normalize(s,t);
Spline<BASIS>::GetWeights(s, point ? sWeights : 0, derivS ? dsWeights : 0);
Spline<BASIS>::GetWeights(t, point ? tWeights : 0, derivT ? dtWeights : 0);
if (point) {
// Compute the tensor product weight of the (s,t) basis function
// corresponding to each control vertex:
AdjustBoundaryWeights(param, sWeights, tWeights);
for (int i = 0; i < 4; ++i) {
for (int j = 0; j < 4; ++j) {
point[4*i+j] = sWeights[j] * tWeights[i];
}
}
}
if (derivS and derivT) {
// Compute the tensor product weight of the differentiated (s,t) basis
// function corresponding to each control vertex (scaled accordingly):
float dScale = (float)(1 << param.GetDepth());
AdjustBoundaryWeights(param, dsWeights, dtWeights);
for (int i = 0; i < 4; ++i) {
for (int j = 0; j < 4; ++j) {
derivS[4*i+j] = dsWeights[j] * tWeights[i] * dScale;
derivT[4*i+j] = sWeights[j] * dtWeights[i] * dScale;
}
}
}
}
void GetBilinearWeights(PatchParam const & param,
float s, float t, float point[4], float deriv1[4], float deriv2[4]) {
Spline<BASIS_BILINEAR>::GetPatchWeights(param, s, t, point, deriv1, deriv2);
}
void GetBezierWeights(PatchParam const param,
float s, float t, float point[16], float deriv1[16], float deriv2[16]) {
Spline<BASIS_BEZIER>::GetPatchWeights(param, s, t, point, deriv1, deriv2);
}
void GetBSplineWeights(PatchParam const & param,
float s, float t, float point[16], float deriv1[16], float deriv2[16]) {
Spline<BASIS_BSPLINE>::GetPatchWeights(param, s, t, point, deriv1, deriv2);
}
void GetGregoryWeights(PatchParam const & param,
float s, float t, float point[20], float deriv1[20], float deriv2[20]) {
//
// 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 9 |
// | | f0+ | f1- |
// | | | |
// | | | |
// O--------1--------7--------5
// P0 e0+ e1- P1
//
// Indices of boundary and interior points and their corresponding Bezier points
// (this can be reduced with more direct indexing and unrolling of loops):
//
static int const boundaryGregory[12] = { 0, 1, 7, 5, 2, 6, 16, 12, 15, 17, 11, 10 };
static int const boundaryBezSCol[12] = { 0, 1, 2, 3, 0, 3, 0, 3, 0, 1, 2, 3 };
static int const boundaryBezTRow[12] = { 0, 0, 0, 0, 1, 1, 2, 2, 3, 3, 3, 3 };
static int const interiorGregory[8] = { 3, 4, 8, 9, 13, 14, 18, 19 };
static int const interiorBezSCol[8] = { 1, 1, 2, 2, 2, 2, 1, 1 };
static int const interiorBezTRow[8] = { 1, 1, 1, 1, 2, 2, 2, 2 };
//
// Bezier basis functions are denoted with B while the rational multipliers for the
// interior points will be denoted G -- so we have B(s), B(t) and G(s,t):
//
// Directional Bezier basis functions B at s and t:
float Bs[4], Bds[4];
float Bt[4], Bdt[4];
param.Normalize(s,t);
Spline<BASIS_BEZIER>::GetWeights(s, Bs, deriv1 ? Bds : 0);
Spline<BASIS_BEZIER>::GetWeights(t, Bt, deriv2 ? Bdt : 0);
// Rational multipliers G at s and t:
float sC = 1.0f - s;
float tC = 1.0f - t;
// Use <= here to avoid compiler warnings -- the sums should always be non-negative:
float df0 = s + t; df0 = (df0 <= 0.0f) ? 1.0f : (1.0f / df0);
float df1 = sC + t; df1 = (df1 <= 0.0f) ? 1.0f : (1.0f / df1);
float df2 = sC + tC; df2 = (df2 <= 0.0f) ? 1.0f : (1.0f / df2);
float df3 = s + tC; df3 = (df3 <= 0.0f) ? 1.0f : (1.0f / df3);
float G[8] = { s*df0, t*df0, t*df1, sC*df1, sC*df2, tC*df2, tC*df3, s*df3 };
// Combined weights for boundary and interior points:
for (int i = 0; i < 12; ++i) {
point[boundaryGregory[i]] = Bs[boundaryBezSCol[i]] * Bt[boundaryBezTRow[i]];
}
for (int i = 0; i < 8; ++i) {
point[interiorGregory[i]] = Bs[interiorBezSCol[i]] * Bt[interiorBezTRow[i]] * G[i];
}
//
// For derivatives, the basis functions for the interior points are rational and ideally
// require appropriate differentiation, i.e. product rule for the combination of B and G
// and the quotient rule for the rational G itself. As initially proposed by Loop et al
// though, the approximation using the 16 Bezier points arising from the G(s,t) has
// proved adequate (and is what the GPU shaders use) so we continue to use that here.
//
// An implementation of the true derivatives is provided for future reference -- it is
// unclear if the approximations will hold up under surface analysis involving higher
// order differentiation.
//
if (deriv1 and deriv2) {
// Remember to include derivative scaling in all assignments below:
float dScale = (float)(1 << param.GetDepth());
// Combined weights for boundary points -- simple (scaled) tensor products:
for (int i = 0; i < 12; ++i) {
int iDst = boundaryGregory[i];
int tRow = boundaryBezTRow[i];
int sCol = boundaryBezSCol[i];
deriv1[iDst] = Bds[sCol] * Bt[tRow] * dScale;
deriv2[iDst] = Bdt[tRow] * Bs[sCol] * dScale;
}
#define _USE_BEZIER_PSEUDO_DERIVATIVES
#ifdef _USE_BEZIER_PSEUDO_DERIVATIVES
// Approximation to the true Gregory derivatives by differentiating the Bezier patch
// unique to the given (s,t), i.e. having F = (g^+ * f^+) + (g^- * f^-) as its four
// interior points:
//
// Combined weights for interior points -- (scaled) tensor products with G+ or G-:
for (int i = 0; i < 8; ++i) {
int iDst = interiorGregory[i];
int tRow = interiorBezTRow[i];
int sCol = interiorBezSCol[i];
deriv1[iDst] = Bds[sCol] * Bt[tRow] * G[i] * dScale;
deriv2[iDst] = Bdt[tRow] * Bs[sCol] * G[i] * dScale;
}
#else
// True Gregory derivatives using appropriate differentiation of composite functions:
//
// Note that for G(s,t) = N(s,t) / D(s,t), all N' and D' are trivial constants (which
// simplifies things for higher order derivatives). And while each pair of functions
// G (i.e. the G+ and G- corresponding to points f+ and f-) must sum to 1 to ensure
// Bezier equivalence (when f+ = f-), the pairs of G' must similarly sum to 0. So we
// can potentially compute only one of the pair and negate the result for the other
// (and with 4 or 8 computations involving these constants, this is all very SIMD
// friendly...) but for now we treat all 8 independently for simplicity.
//
//float N[8] = { s, t, t, sC, sC, tC, tC, s };
float D[8] = { df0, df0, df1, df1, df2, df2, df3, df3 };
static float const Nds[8] = { 1.0f, 0.0f, 0.0f, -1.0f, -1.0f, 0.0f, 0.0f, 1.0f };
static float const Ndt[8] = { 0.0f, 1.0f, 1.0f, 0.0f, 0.0f, -1.0f, -1.0f, 0.0f };
static float const Dds[8] = { 1.0f, 1.0f, -1.0f, -1.0f, -1.0f, -1.0f, 1.0f, 1.0f };
static float const Ddt[8] = { 1.0f, 1.0f, 1.0f, 1.0f, -1.0f, -1.0f, -1.0f, -1.0f };
// Combined weights for interior points -- (scaled) combinations of B, B', G and G':
for (int i = 0; i < 8; ++i) {
int iDst = interiorGregory[i];
int tRow = interiorBezTRow[i];
int sCol = interiorBezSCol[i];
// Quotient rule for G' (re-expressed in terms of G to simplify (and D = 1/D)):
float Gds = (Nds[i] - Dds[i] * G[i]) * D[i];
float Gdt = (Ndt[i] - Ddt[i] * G[i]) * D[i];
// Product rule combining B and B' with G and G' (and scaled):
deriv1[iDst] = (Bds[sCol] * G[i] + Bs[sCol] * Gds) * Bt[tRow] * dScale;
deriv2[iDst] = (Bdt[tRow] * G[i] + Bt[tRow] * Gdt) * Bs[sCol] * dScale;
}
#endif
}
}
} // end namespace internal
} // end namespace Far
} // end namespace OPENSUBDIV_VERSION
} // end namespace OpenSubdiv
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