OpenSubdiv/opensubdiv/far/interpolate.cpp
manuelk c646ac2e3c Refactor & cleanup patch interpolation
- move patch interpolation code out of Far::PatchTables into far/interpolate
- add bilinear quad interpolation function with derivatives
- switch OsdCpuEvalLimitController to far/interpolate
- add support for bilinear quad interpolation & clean varying interpolation
2015-01-27 15:38:30 -08:00

314 lines
9.6 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/interpolate.h"
#include <cassert>
#include <cstring>
namespace OpenSubdiv {
namespace OPENSUBDIV_VERSION {
namespace Far {
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::BitField bits,
float s, float t, float point[], float deriv1[], float deriv2[]);
};
template <>
inline void Spline<BASIS_BEZIER>::GetWeights(
float t, float point[4], float deriv[3]) {
// The weights for the four uniform cubic Bezier basis functions are:
// (1 - t)^3
// 3 * t * (1-t)
// 3 * t^2 * (1-t)
// t^3
float t2 = t*t,
w0 = 1.0f - t,
w2 = w0 * w0;
assert(point);
point[0] = w0*w2;
point[1] = 3.0f * t * w2;
point[2] = 3.0f * t2 * w0;
point[3] = t * t2;
// The weights for the three uniform quadratic basis functions are:
// (1-t)^2
// 2 * t * (1-t)
// t^2
if (deriv) {
deriv[0] = w2;
deriv[1] = 2.0f * t * w0;
deriv[2] = t2;
}
}
template <>
inline void Spline<BASIS_BSPLINE>::GetWeights(
float t, float point[4], float deriv[3]) {
// The weights for the four uniform cubic B-Spline basis functions are:
// (1/6)(1 - t)^3
// (1/6)(3t^3 - 6t^2 + 4)
// (1/6)(-3t^3 + 3t^2 + 3t + 1)
// (1/6)t^3
float t2 = t*t,
t3 = 3.0f*t2*t,
w0 = 1.0f-t;
assert(point);
point[0] = (w0*w0*w0) / 6.0f;
point[1] = (t3 - 6.0f*t2 + 4.0f) / 6.0f;
point[2] = (3.0f*t2 - t3 + 3.0f*t + 1.0f) / 6.0f;
point[3] = t3 / 18.0f;
// The weights for the three uniform quadratic basis functions are:
// (1/2)(1-t)^2
// (1/2)(1 + 2t - 2t^2)
// (1/2)t^2
if (deriv) {
deriv[0] = 0.5f * w0 * w0;
deriv[1] = 0.5f + t - t2;
deriv[2] = 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::BitField bits,
float s, float t, float point[4], float deriv1[4], float deriv2[4]) {
static int const rots[4][4] =
{ { 0, 1, 2, 3 },
{ 3, 0, 1, 2 },
{ 2, 3, 0, 1 },
{ 1, 2, 3, 0 } };
assert(bits.GetRotation()<4);
int const * rot = rots[bits.GetRotation()];
bits.Normalize(s,t);
float os = 1.0f - s,
ot = 1.0f - t;
if (point) {
point[rot[0]] = os*ot;
point[rot[1]] = s*ot;
point[rot[2]] = s*t;
point[rot[3]] = os*t;
}
if (deriv1 and deriv2) {
deriv1[rot[0]] = t-1.0f;
deriv1[rot[1]] = ot;
deriv1[rot[2]] = t;
deriv1[rot[3]] = -t;
deriv2[rot[0]] = s-1.0f;
deriv2[rot[1]] = -s;
deriv2[rot[2]] = s;
deriv2[rot[3]] = os;
}
}
template <SplineBasis BASIS>
void Spline<BASIS>::GetPatchWeights(PatchParam::BitField bits,
float s, float t, float point[16], float deriv1[16], float deriv2[16]) {
static int const rots[4][16] =
{ { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 },
{ 12, 8, 4, 0, 13, 9, 5, 1, 14, 10, 6, 2, 15, 11, 7, 3 },
{ 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0 },
{ 3, 7, 11, 15, 2, 6, 10, 14, 1, 5, 9, 13, 0, 4, 8, 12 } };
assert(bits.GetRotation()<4);
int const * rot = rots[bits.GetRotation()];
float sWeights[4], tWeights[4], d1Weights[3], d2Weights[3];
bits.Normalize(s,t);
Spline<BASIS>::GetWeights(s, point ? sWeights : 0, deriv1 ? d1Weights : 0);
Spline<BASIS>::GetWeights(t, point ? tWeights : 0, deriv2 ? d2Weights : 0);
if (point) {
// Compute the tensor product weight corresponding to each control
// vertex
memset(point, 0, 16*sizeof(float));
for (int i = 0; i < 4; ++i) {
for (int j = 0; j < 4; ++j) {
point[rot[4*i+j]] += sWeights[j] * tWeights[i];
}
}
}
if (deriv1 and deriv2) {
// Compute the tangent stencil. This is done by taking the tensor
// product between the quadratic weights computed for s and the cubic
// weights computed for t. The stencil is constructed using
// differences between consecutive vertices in each row (i.e.
// in the s direction).
memset(deriv1, 0, 16*sizeof(float));
for (int i = 0, k = 0; i < 4; ++i) {
float prevWeight = 0.0f;
for (int j = 0; j < 3; ++j) {
float weight = d1Weights[j]*tWeights[i];
deriv1[rot[k++]] += prevWeight - weight;
prevWeight = weight;
}
deriv1[rot[k++]]+=prevWeight;
}
memset(deriv2, 0, 16*sizeof(float));
#define FASTER_TENSOR
#ifdef FASTER_TENSOR
// XXXX manuelk this might be slightly more efficient ?
float dW[4];
dW[0] = - d2Weights[0];
dW[1] = d2Weights[0] - d2Weights[1];
dW[2] = d2Weights[1] - d2Weights[2];
dW[3] = d2Weights[2];
for (int i = 0, k = 0; i < 4; ++i) {
for (int j = 0; j < 4; ++j) {
deriv2[rot[k++]] = sWeights[j] * dW[i];
}
}
#else
for (int j = 0; j < 4; ++j) {
float prevWeight = 0.0f;
for (int i = 0; i < 3; ++i) {
float weight = sWeights[j]*d2Weights[i];
deriv2[rot[4*i+j]]+=prevWeight - weight;
prevWeight = weight;
}
deriv2[rot[12+j]] += prevWeight;
}
#endif
// Scale derivatives up based on level of subdivision
float scale = float(1 << bits.GetDepth());
for (int k=0; k<16; ++k) {
deriv1[k] *= scale;
deriv2[k] *= scale;
}
}
}
void GetBilinearWeights(PatchParam::BitField bits,
float s, float t, float point[4], float deriv1[4], float deriv2[4]) {
Spline<BASIS_BILINEAR>::GetPatchWeights(bits, s, t, point, deriv1, deriv2);
}
void GetBezierWeights(PatchParam::BitField bits,
float s, float t, float point[16], float deriv1[16], float deriv2[16]) {
Spline<BASIS_BEZIER>::GetPatchWeights(bits, s, t, point, deriv1, deriv2);
}
void GetBSplineWeights(PatchParam::BitField bits,
float s, float t, float point[16], float deriv1[16], float deriv2[16]) {
Spline<BASIS_BSPLINE>::GetPatchWeights(bits, s, t, point, deriv1, deriv2);
}
} // end namespace Far
} // end namespace OPENSUBDIV_VERSION
} // end namespace OpenSubdiv