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matrix4f.cpp
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//
// Copyright 2016 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.
//
////////////////////////////////////////////////////////////////////////
// This file is generated by a script. Do not edit directly. Edit the
// matrix4.template.cpp file to make changes.
#include "pxr/pxr.h"
#include "pxr/base/gf/matrix4d.h"
#include "pxr/base/gf/matrix4f.h"
#include "pxr/base/gf/math.h"
#include "pxr/base/gf/ostreamHelpers.h"
#include "pxr/base/tf/type.h"
#include "pxr/base/gf/homogeneous.h"
#include "pxr/base/gf/matrix3f.h"
#include "pxr/base/gf/quatf.h"
#include "pxr/base/gf/rotation.h"
#include <float.h>
#include <iostream>
PXR_NAMESPACE_OPEN_SCOPE
TF_REGISTRY_FUNCTION(TfType) {
TfType::Define<GfMatrix4f>();
}
std::ostream&
operator<<(std::ostream& out, const GfMatrix4f& m)
{
return out
<< "( ("
<< Gf_OstreamHelperP(m[0][0]) << ", "
<< Gf_OstreamHelperP(m[0][1]) << ", "
<< Gf_OstreamHelperP(m[0][2]) << ", "
<< Gf_OstreamHelperP(m[0][3])
<< "), ("
<< Gf_OstreamHelperP(m[1][0]) << ", "
<< Gf_OstreamHelperP(m[1][1]) << ", "
<< Gf_OstreamHelperP(m[1][2]) << ", "
<< Gf_OstreamHelperP(m[1][3])
<< "), ("
<< Gf_OstreamHelperP(m[2][0]) << ", "
<< Gf_OstreamHelperP(m[2][1]) << ", "
<< Gf_OstreamHelperP(m[2][2]) << ", "
<< Gf_OstreamHelperP(m[2][3])
<< "), ("
<< Gf_OstreamHelperP(m[3][0]) << ", "
<< Gf_OstreamHelperP(m[3][1]) << ", "
<< Gf_OstreamHelperP(m[3][2]) << ", "
<< Gf_OstreamHelperP(m[3][3])
<< ") )";
}
GfMatrix4f::GfMatrix4f(const GfMatrix4d& m)
{
Set(m[0][0], m[0][1], m[0][2], m[0][3],
m[1][0], m[1][1], m[1][2], m[1][3],
m[2][0], m[2][1], m[2][2], m[2][3],
m[3][0], m[3][1], m[3][2], m[3][3]);
}
GfMatrix4f::GfMatrix4f(const std::vector< std::vector<double> >& v)
{
float m[4][4] = {{1.0, 0.0, 0.0, 0.0},
{0.0, 1.0, 0.0, 0.0},
{0.0, 0.0, 1.0, 0.0},
{0.0, 0.0, 0.0, 1.0}};
for(size_t row = 0; row < 4 && row < v.size(); ++row) {
for (size_t col = 0; col < 4 && col < v[row].size(); ++col) {
m[row][col] = v[row][col];
}
}
Set(m);
}
GfMatrix4f::GfMatrix4f(const std::vector< std::vector<float> >& v)
{
float m[4][4] = {{1.0, 0.0, 0.0, 0.0},
{0.0, 1.0, 0.0, 0.0},
{0.0, 0.0, 1.0, 0.0},
{0.0, 0.0, 0.0, 1.0}};
for(size_t row = 0; row < 4 && row < v.size(); ++row) {
for (size_t col = 0; col < 4 && col < v[row].size(); ++col) {
m[row][col] = v[row][col];
}
}
Set(m);
}
GfMatrix4f::GfMatrix4f(const std::vector<double>& r0,
const std::vector<double>& r1,
const std::vector<double>& r2,
const std::vector<double>& r3)
{
float m[4][4] = {{1.0, 0.0, 0.0, 0.0},
{0.0, 1.0, 0.0, 0.0},
{0.0, 0.0, 1.0, 0.0},
{0.0, 0.0, 0.0, 1.0}};
for (size_t col = 0; col < 4 && col < r0.size(); ++col) {
m[0][col] = r0[col];
}
for (size_t col = 0; col < 4 && col < r1.size(); ++col) {
m[1][col] = r1[col];
}
for (size_t col = 0; col < 4 && col < r2.size(); ++col) {
m[2][col] = r2[col];
}
for (size_t col = 0; col < 4 && col < r3.size(); ++col) {
m[3][col] = r3[col];
}
Set(m);
}
GfMatrix4f::GfMatrix4f(const std::vector<float>& r0,
const std::vector<float>& r1,
const std::vector<float>& r2,
const std::vector<float>& r3)
{
float m[4][4] = {{1.0, 0.0, 0.0, 0.0},
{0.0, 1.0, 0.0, 0.0},
{0.0, 0.0, 1.0, 0.0},
{0.0, 0.0, 0.0, 1.0}};
for (size_t col = 0; col < 4 && col < r0.size(); ++col) {
m[0][col] = r0[col];
}
for (size_t col = 0; col < 4 && col < r1.size(); ++col) {
m[1][col] = r1[col];
}
for (size_t col = 0; col < 4 && col < r2.size(); ++col) {
m[2][col] = r2[col];
}
for (size_t col = 0; col < 4 && col < r3.size(); ++col) {
m[3][col] = r3[col];
}
Set(m);
}
GfMatrix4f::GfMatrix4f(const GfRotation& rotate,
const GfVec3f& translate)
{
SetTransform(rotate, translate);
}
GfMatrix4f::GfMatrix4f(const GfMatrix3f& rotmx,
const GfVec3f& translate)
{
SetTransform(rotmx, translate);
}
GfMatrix4f &
GfMatrix4f::SetDiagonal(float s)
{
_mtx[0][0] = s;
_mtx[0][1] = 0.0;
_mtx[0][2] = 0.0;
_mtx[0][3] = 0.0;
_mtx[1][0] = 0.0;
_mtx[1][1] = s;
_mtx[1][2] = 0.0;
_mtx[1][3] = 0.0;
_mtx[2][0] = 0.0;
_mtx[2][1] = 0.0;
_mtx[2][2] = s;
_mtx[2][3] = 0.0;
_mtx[3][0] = 0.0;
_mtx[3][1] = 0.0;
_mtx[3][2] = 0.0;
_mtx[3][3] = s;
return *this;
}
GfMatrix4f &
GfMatrix4f::SetDiagonal(const GfVec4f& v)
{
_mtx[0][0] = v[0]; _mtx[0][1] = 0.0; _mtx[0][2] = 0.0; _mtx[0][3] = 0.0;
_mtx[1][0] = 0.0; _mtx[1][1] = v[1]; _mtx[1][2] = 0.0; _mtx[1][3] = 0.0;
_mtx[2][0] = 0.0; _mtx[2][1] = 0.0; _mtx[2][2] = v[2]; _mtx[2][3] = 0.0;
_mtx[3][0] = 0.0; _mtx[3][1] = 0.0; _mtx[3][2] = 0.0; _mtx[3][3] = v[3];
return *this;
}
float *
GfMatrix4f::Get(float m[4][4]) const
{
m[0][0] = _mtx[0][0];
m[0][1] = _mtx[0][1];
m[0][2] = _mtx[0][2];
m[0][3] = _mtx[0][3];
m[1][0] = _mtx[1][0];
m[1][1] = _mtx[1][1];
m[1][2] = _mtx[1][2];
m[1][3] = _mtx[1][3];
m[2][0] = _mtx[2][0];
m[2][1] = _mtx[2][1];
m[2][2] = _mtx[2][2];
m[2][3] = _mtx[2][3];
m[3][0] = _mtx[3][0];
m[3][1] = _mtx[3][1];
m[3][2] = _mtx[3][2];
m[3][3] = _mtx[3][3];
return &m[0][0];
}
bool
GfMatrix4f::operator ==(const GfMatrix4d &m) const
{
return (_mtx[0][0] == m._mtx[0][0] &&
_mtx[0][1] == m._mtx[0][1] &&
_mtx[0][2] == m._mtx[0][2] &&
_mtx[0][3] == m._mtx[0][3] &&
_mtx[1][0] == m._mtx[1][0] &&
_mtx[1][1] == m._mtx[1][1] &&
_mtx[1][2] == m._mtx[1][2] &&
_mtx[1][3] == m._mtx[1][3] &&
_mtx[2][0] == m._mtx[2][0] &&
_mtx[2][1] == m._mtx[2][1] &&
_mtx[2][2] == m._mtx[2][2] &&
_mtx[2][3] == m._mtx[2][3] &&
_mtx[3][0] == m._mtx[3][0] &&
_mtx[3][1] == m._mtx[3][1] &&
_mtx[3][2] == m._mtx[3][2] &&
_mtx[3][3] == m._mtx[3][3]);
}
bool
GfMatrix4f::operator ==(const GfMatrix4f &m) const
{
return (_mtx[0][0] == m._mtx[0][0] &&
_mtx[0][1] == m._mtx[0][1] &&
_mtx[0][2] == m._mtx[0][2] &&
_mtx[0][3] == m._mtx[0][3] &&
_mtx[1][0] == m._mtx[1][0] &&
_mtx[1][1] == m._mtx[1][1] &&
_mtx[1][2] == m._mtx[1][2] &&
_mtx[1][3] == m._mtx[1][3] &&
_mtx[2][0] == m._mtx[2][0] &&
_mtx[2][1] == m._mtx[2][1] &&
_mtx[2][2] == m._mtx[2][2] &&
_mtx[2][3] == m._mtx[2][3] &&
_mtx[3][0] == m._mtx[3][0] &&
_mtx[3][1] == m._mtx[3][1] &&
_mtx[3][2] == m._mtx[3][2] &&
_mtx[3][3] == m._mtx[3][3]);
}
GfMatrix4f
GfMatrix4f::GetTranspose() const
{
GfMatrix4f transpose;
transpose._mtx[0][0] = _mtx[0][0];
transpose._mtx[1][0] = _mtx[0][1];
transpose._mtx[2][0] = _mtx[0][2];
transpose._mtx[3][0] = _mtx[0][3];
transpose._mtx[0][1] = _mtx[1][0];
transpose._mtx[1][1] = _mtx[1][1];
transpose._mtx[2][1] = _mtx[1][2];
transpose._mtx[3][1] = _mtx[1][3];
transpose._mtx[0][2] = _mtx[2][0];
transpose._mtx[1][2] = _mtx[2][1];
transpose._mtx[2][2] = _mtx[2][2];
transpose._mtx[3][2] = _mtx[2][3];
transpose._mtx[0][3] = _mtx[3][0];
transpose._mtx[1][3] = _mtx[3][1];
transpose._mtx[2][3] = _mtx[3][2];
transpose._mtx[3][3] = _mtx[3][3];
return transpose;
}
GfMatrix4f &
GfMatrix4f::SetTransform(const GfRotation& rotate,
const GfVec3f& translate)
{
SetRotate(rotate);
return SetTranslateOnly(translate);
}
GfMatrix4f &
GfMatrix4f::SetTransform(const GfMatrix3f& rotate,
const GfVec3f& translate)
{
SetRotate(rotate);
return SetTranslateOnly(translate);
}
GfMatrix4f
GfMatrix4f::GetInverse(double *detPtr, double eps) const
{
float x00, x01, x02;
float x10, x11, x12;
float x20, x21, x22;
float x30, x31, x32;
double y01, y02, y03, y12, y13, y23;
double z02, z03, z12, z13, z22, z23, z32, z33;
#define x03 x01
#define x13 x11
#define x23 x21
#define x33 x31
#define z00 x02
#define z10 x12
#define z20 x22
#define z30 x32
#define z01 x03
#define z11 x13
#define z21 x23
#define z31 x33
#define det y01
#define rcp y02
// Pickle 1st two columns of matrix into registers
x00 = _mtx[0][0];
x01 = _mtx[0][1];
x10 = _mtx[1][0];
x11 = _mtx[1][1];
x20 = _mtx[2][0];
x21 = _mtx[2][1];
x30 = _mtx[3][0];
x31 = _mtx[3][1];
// Compute all six 2x2 determinants of 1st two columns
y01 = x00*x11 - x10*x01;
y02 = x00*x21 - x20*x01;
y03 = x00*x31 - x30*x01;
y12 = x10*x21 - x20*x11;
y13 = x10*x31 - x30*x11;
y23 = x20*x31 - x30*x21;
// Pickle 2nd two columns of matrix into registers
x02 = _mtx[0][2];
x03 = _mtx[0][3];
x12 = _mtx[1][2];
x13 = _mtx[1][3];
x22 = _mtx[2][2];
x23 = _mtx[2][3];
x32 = _mtx[3][2];
x33 = _mtx[3][3];
// Compute all 3x3 cofactors for 2nd two columns */
z33 = x02*y12 - x12*y02 + x22*y01;
z23 = x12*y03 - x32*y01 - x02*y13;
z13 = x02*y23 - x22*y03 + x32*y02;
z03 = x22*y13 - x32*y12 - x12*y23;
z32 = x13*y02 - x23*y01 - x03*y12;
z22 = x03*y13 - x13*y03 + x33*y01;
z12 = x23*y03 - x33*y02 - x03*y23;
z02 = x13*y23 - x23*y13 + x33*y12;
// Compute all six 2x2 determinants of 2nd two columns
y01 = x02*x13 - x12*x03;
y02 = x02*x23 - x22*x03;
y03 = x02*x33 - x32*x03;
y12 = x12*x23 - x22*x13;
y13 = x12*x33 - x32*x13;
y23 = x22*x33 - x32*x23;
// Pickle 1st two columns of matrix into registers
x00 = _mtx[0][0];
x01 = _mtx[0][1];
x10 = _mtx[1][0];
x11 = _mtx[1][1];
x20 = _mtx[2][0];
x21 = _mtx[2][1];
x30 = _mtx[3][0];
x31 = _mtx[3][1];
// Compute all 3x3 cofactors for 1st two columns
z30 = x11*y02 - x21*y01 - x01*y12;
z20 = x01*y13 - x11*y03 + x31*y01;
z10 = x21*y03 - x31*y02 - x01*y23;
z00 = x11*y23 - x21*y13 + x31*y12;
z31 = x00*y12 - x10*y02 + x20*y01;
z21 = x10*y03 - x30*y01 - x00*y13;
z11 = x00*y23 - x20*y03 + x30*y02;
z01 = x20*y13 - x30*y12 - x10*y23;
// compute 4x4 determinant & its reciprocal
det = x30*z30 + x20*z20 + x10*z10 + x00*z00;
if (detPtr) {
*detPtr = det;
}
GfMatrix4f inverse;
if (GfAbs(det) > eps) {
rcp = 1.0 / det;
// Multiply all 3x3 cofactors by reciprocal & transpose
inverse._mtx[0][0] = static_cast<float>(z00*rcp);
inverse._mtx[0][1] = static_cast<float>(z10*rcp);
inverse._mtx[1][0] = static_cast<float>(z01*rcp);
inverse._mtx[0][2] = static_cast<float>(z20*rcp);
inverse._mtx[2][0] = static_cast<float>(z02*rcp);
inverse._mtx[0][3] = static_cast<float>(z30*rcp);
inverse._mtx[3][0] = static_cast<float>(z03*rcp);
inverse._mtx[1][1] = static_cast<float>(z11*rcp);
inverse._mtx[1][2] = static_cast<float>(z21*rcp);
inverse._mtx[2][1] = static_cast<float>(z12*rcp);
inverse._mtx[1][3] = static_cast<float>(z31*rcp);
inverse._mtx[3][1] = static_cast<float>(z13*rcp);
inverse._mtx[2][2] = static_cast<float>(z22*rcp);
inverse._mtx[2][3] = static_cast<float>(z32*rcp);
inverse._mtx[3][2] = static_cast<float>(z23*rcp);
inverse._mtx[3][3] = static_cast<float>(z33*rcp);
#undef x03
#undef x13
#undef x23
#undef x33
#undef z00
#undef z10
#undef z20
#undef z30
#undef z01
#undef z11
#undef z21
#undef z31
#undef det
#undef rcp
}
else {
inverse.SetScale(FLT_MAX);
}
return inverse;
}
double
GfMatrix4f::GetDeterminant() const
{
return (- _mtx[0][3] * _GetDeterminant3(1, 2, 3, 0, 1, 2)
+ _mtx[1][3] * _GetDeterminant3(0, 2, 3, 0, 1, 2)
- _mtx[2][3] * _GetDeterminant3(0, 1, 3, 0, 1, 2)
+ _mtx[3][3] * _GetDeterminant3(0, 1, 2, 0, 1, 2));
}
double
GfMatrix4f::_GetDeterminant3(size_t row1, size_t row2, size_t row3,
size_t col1, size_t col2, size_t col3) const
{
return (_mtx[row1][col1] * _mtx[row2][col2] * _mtx[row3][col3] +
_mtx[row1][col2] * _mtx[row2][col3] * _mtx[row3][col1] +
_mtx[row1][col3] * _mtx[row2][col1] * _mtx[row3][col2] -
_mtx[row1][col1] * _mtx[row2][col3] * _mtx[row3][col2] -
_mtx[row1][col2] * _mtx[row2][col1] * _mtx[row3][col3] -
_mtx[row1][col3] * _mtx[row2][col2] * _mtx[row3][col1]);
}
double
GfMatrix4f::GetHandedness() const
{
// Note: This can be computed with fewer arithmetic operations using a
// cross and dot product, but it is more important that the result
// is consistent with the way the determinant is computed.
return GfSgn(GetDeterminant3());
}
/*
* Make the matrix orthonormal in place using an iterative method.
* It is potentially slower if the matrix is far from orthonormal (i.e. if
* the row basis vectors are close to colinear) but in the common case
* of near-orthonormality it should be just as fast.
*
* The translation part is left intact. If the translation is represented as
* a homogenous coordinate (i.e. a non-unity lower right corner), it is divided
* out.
*/
bool
GfMatrix4f::Orthonormalize(bool issueWarning)
{
// orthogonalize and normalize row vectors
GfVec3d r0(_mtx[0][0],_mtx[0][1],_mtx[0][2]);
GfVec3d r1(_mtx[1][0],_mtx[1][1],_mtx[1][2]);
GfVec3d r2(_mtx[2][0],_mtx[2][1],_mtx[2][2]);
bool result = GfVec3d::OrthogonalizeBasis(&r0, &r1, &r2, true);
_mtx[0][0] = r0[0];
_mtx[0][1] = r0[1];
_mtx[0][2] = r0[2];
_mtx[1][0] = r1[0];
_mtx[1][1] = r1[1];
_mtx[1][2] = r1[2];
_mtx[2][0] = r2[0];
_mtx[2][1] = r2[1];
_mtx[2][2] = r2[2];
// divide out any homogeneous coordinate - unless it's zero
if (_mtx[3][3] != 1.0 && !GfIsClose(_mtx[3][3], 0.0, GF_MIN_VECTOR_LENGTH))
{
_mtx[3][0] /= _mtx[3][3];
_mtx[3][1] /= _mtx[3][3];
_mtx[3][2] /= _mtx[3][3];
_mtx[3][3] = 1.0;
}
if (!result && issueWarning)
TF_WARN("OrthogonalizeBasis did not converge, matrix may not be "
"orthonormal.");
return result;
}
GfMatrix4f
GfMatrix4f::GetOrthonormalized(bool issueWarning) const
{
GfMatrix4f result = *this;
result.Orthonormalize(issueWarning);
return result;
}
/*
** Scaling
*/
GfMatrix4f&
GfMatrix4f::operator*=(double d)
{
_mtx[0][0] *= d; _mtx[0][1] *= d; _mtx[0][2] *= d; _mtx[0][3] *= d;
_mtx[1][0] *= d; _mtx[1][1] *= d; _mtx[1][2] *= d; _mtx[1][3] *= d;
_mtx[2][0] *= d; _mtx[2][1] *= d; _mtx[2][2] *= d; _mtx[2][3] *= d;
_mtx[3][0] *= d; _mtx[3][1] *= d; _mtx[3][2] *= d; _mtx[3][3] *= d;
return *this;
}
/*
** Addition
*/
GfMatrix4f &
GfMatrix4f::operator+=(const GfMatrix4f &m)
{
_mtx[0][0] += m._mtx[0][0];
_mtx[0][1] += m._mtx[0][1];
_mtx[0][2] += m._mtx[0][2];
_mtx[0][3] += m._mtx[0][3];
_mtx[1][0] += m._mtx[1][0];
_mtx[1][1] += m._mtx[1][1];
_mtx[1][2] += m._mtx[1][2];
_mtx[1][3] += m._mtx[1][3];
_mtx[2][0] += m._mtx[2][0];
_mtx[2][1] += m._mtx[2][1];
_mtx[2][2] += m._mtx[2][2];
_mtx[2][3] += m._mtx[2][3];
_mtx[3][0] += m._mtx[3][0];
_mtx[3][1] += m._mtx[3][1];
_mtx[3][2] += m._mtx[3][2];
_mtx[3][3] += m._mtx[3][3];
return *this;
}
/*
** Subtraction
*/
GfMatrix4f &
GfMatrix4f::operator-=(const GfMatrix4f &m)
{
_mtx[0][0] -= m._mtx[0][0];
_mtx[0][1] -= m._mtx[0][1];
_mtx[0][2] -= m._mtx[0][2];
_mtx[0][3] -= m._mtx[0][3];
_mtx[1][0] -= m._mtx[1][0];
_mtx[1][1] -= m._mtx[1][1];
_mtx[1][2] -= m._mtx[1][2];
_mtx[1][3] -= m._mtx[1][3];
_mtx[2][0] -= m._mtx[2][0];
_mtx[2][1] -= m._mtx[2][1];
_mtx[2][2] -= m._mtx[2][2];
_mtx[2][3] -= m._mtx[2][3];
_mtx[3][0] -= m._mtx[3][0];
_mtx[3][1] -= m._mtx[3][1];
_mtx[3][2] -= m._mtx[3][2];
_mtx[3][3] -= m._mtx[3][3];
return *this;
}
/*
** Negation
*/
GfMatrix4f
operator -(const GfMatrix4f& m)
{
return
GfMatrix4f(-m._mtx[0][0], -m._mtx[0][1], -m._mtx[0][2], -m._mtx[0][3],
-m._mtx[1][0], -m._mtx[1][1], -m._mtx[1][2], -m._mtx[1][3],
-m._mtx[2][0], -m._mtx[2][1], -m._mtx[2][2], -m._mtx[2][3],
-m._mtx[3][0], -m._mtx[3][1], -m._mtx[3][2], -m._mtx[3][3]);
}
GfMatrix4f &
GfMatrix4f::operator*=(const GfMatrix4f &m)
{
// Save current values before they are overwritten
GfMatrix4f tmp = *this;
_mtx[0][0] = tmp._mtx[0][0] * m._mtx[0][0] +
tmp._mtx[0][1] * m._mtx[1][0] +
tmp._mtx[0][2] * m._mtx[2][0] +
tmp._mtx[0][3] * m._mtx[3][0];
_mtx[0][1] = tmp._mtx[0][0] * m._mtx[0][1] +
tmp._mtx[0][1] * m._mtx[1][1] +
tmp._mtx[0][2] * m._mtx[2][1] +
tmp._mtx[0][3] * m._mtx[3][1];
_mtx[0][2] = tmp._mtx[0][0] * m._mtx[0][2] +
tmp._mtx[0][1] * m._mtx[1][2] +
tmp._mtx[0][2] * m._mtx[2][2] +
tmp._mtx[0][3] * m._mtx[3][2];
_mtx[0][3] = tmp._mtx[0][0] * m._mtx[0][3] +
tmp._mtx[0][1] * m._mtx[1][3] +
tmp._mtx[0][2] * m._mtx[2][3] +
tmp._mtx[0][3] * m._mtx[3][3];
_mtx[1][0] = tmp._mtx[1][0] * m._mtx[0][0] +
tmp._mtx[1][1] * m._mtx[1][0] +
tmp._mtx[1][2] * m._mtx[2][0] +
tmp._mtx[1][3] * m._mtx[3][0];
_mtx[1][1] = tmp._mtx[1][0] * m._mtx[0][1] +
tmp._mtx[1][1] * m._mtx[1][1] +
tmp._mtx[1][2] * m._mtx[2][1] +
tmp._mtx[1][3] * m._mtx[3][1];
_mtx[1][2] = tmp._mtx[1][0] * m._mtx[0][2] +
tmp._mtx[1][1] * m._mtx[1][2] +
tmp._mtx[1][2] * m._mtx[2][2] +
tmp._mtx[1][3] * m._mtx[3][2];
_mtx[1][3] = tmp._mtx[1][0] * m._mtx[0][3] +
tmp._mtx[1][1] * m._mtx[1][3] +
tmp._mtx[1][2] * m._mtx[2][3] +
tmp._mtx[1][3] * m._mtx[3][3];
_mtx[2][0] = tmp._mtx[2][0] * m._mtx[0][0] +
tmp._mtx[2][1] * m._mtx[1][0] +
tmp._mtx[2][2] * m._mtx[2][0] +
tmp._mtx[2][3] * m._mtx[3][0];
_mtx[2][1] = tmp._mtx[2][0] * m._mtx[0][1] +
tmp._mtx[2][1] * m._mtx[1][1] +
tmp._mtx[2][2] * m._mtx[2][1] +
tmp._mtx[2][3] * m._mtx[3][1];
_mtx[2][2] = tmp._mtx[2][0] * m._mtx[0][2] +
tmp._mtx[2][1] * m._mtx[1][2] +
tmp._mtx[2][2] * m._mtx[2][2] +
tmp._mtx[2][3] * m._mtx[3][2];
_mtx[2][3] = tmp._mtx[2][0] * m._mtx[0][3] +
tmp._mtx[2][1] * m._mtx[1][3] +
tmp._mtx[2][2] * m._mtx[2][3] +
tmp._mtx[2][3] * m._mtx[3][3];
_mtx[3][0] = tmp._mtx[3][0] * m._mtx[0][0] +
tmp._mtx[3][1] * m._mtx[1][0] +
tmp._mtx[3][2] * m._mtx[2][0] +
tmp._mtx[3][3] * m._mtx[3][0];
_mtx[3][1] = tmp._mtx[3][0] * m._mtx[0][1] +
tmp._mtx[3][1] * m._mtx[1][1] +
tmp._mtx[3][2] * m._mtx[2][1] +
tmp._mtx[3][3] * m._mtx[3][1];
_mtx[3][2] = tmp._mtx[3][0] * m._mtx[0][2] +
tmp._mtx[3][1] * m._mtx[1][2] +
tmp._mtx[3][2] * m._mtx[2][2] +
tmp._mtx[3][3] * m._mtx[3][2];
_mtx[3][3] = tmp._mtx[3][0] * m._mtx[0][3] +
tmp._mtx[3][1] * m._mtx[1][3] +
tmp._mtx[3][2] * m._mtx[2][3] +
tmp._mtx[3][3] * m._mtx[3][3];
return *this;
}
// Leaves the [3][3] element as 1
GfMatrix4f &
GfMatrix4f::SetScale(float s)
{
_mtx[0][0] = s; _mtx[0][1] = 0.0; _mtx[0][2] = 0.0; _mtx[0][3] = 0.0;
_mtx[1][0] = 0.0; _mtx[1][1] = s; _mtx[1][2] = 0.0; _mtx[1][3] = 0.0;
_mtx[2][0] = 0.0; _mtx[2][1] = 0.0; _mtx[2][2] = s; _mtx[2][3] = 0.0;
_mtx[3][0] = 0.0; _mtx[3][1] = 0.0; _mtx[3][2] = 0.0; _mtx[3][3] = 1.0;
return *this;
}
void
GfMatrix4f::_SetRotateFromQuat(float r, const GfVec3f& i)
{
_mtx[0][0] = 1.0 - 2.0 * (i[1] * i[1] + i[2] * i[2]);
_mtx[0][1] = 2.0 * (i[0] * i[1] + i[2] * r);
_mtx[0][2] = 2.0 * (i[2] * i[0] - i[1] * r);
_mtx[1][0] = 2.0 * (i[0] * i[1] - i[2] * r);
_mtx[1][1] = 1.0 - 2.0 * (i[2] * i[2] + i[0] * i[0]);
_mtx[1][2] = 2.0 * (i[1] * i[2] + i[0] * r);
_mtx[2][0] = 2.0 * (i[2] * i[0] + i[1] * r);
_mtx[2][1] = 2.0 * (i[1] * i[2] - i[0] * r);
_mtx[2][2] = 1.0 - 2.0 * (i[1] * i[1] + i[0] * i[0]);
}
GfMatrix4f &
GfMatrix4f::SetRotate(const GfQuatf &rot)
{
SetRotateOnly(rot);
_mtx[0][3] = 0.0;
_mtx[1][3] = 0.0;
_mtx[2][3] = 0.0;
_mtx[3][0] = 0.0;
_mtx[3][1] = 0.0;
_mtx[3][2] = 0.0;
_mtx[3][3] = 1.0;
return *this;
}
GfMatrix4f &
GfMatrix4f::SetRotateOnly(const GfQuatf &rot)
{
_SetRotateFromQuat(rot.GetReal(), rot.GetImaginary());
return *this;
}
GfMatrix4f &
GfMatrix4f::SetRotate(const GfRotation &rot)
{
SetRotateOnly(rot);
_mtx[0][3] = 0.0;
_mtx[1][3] = 0.0;
_mtx[2][3] = 0.0;
_mtx[3][0] = 0.0;
_mtx[3][1] = 0.0;
_mtx[3][2] = 0.0;
_mtx[3][3] = 1.0;
return *this;
}
GfMatrix4f &
GfMatrix4f::SetRotateOnly(const GfRotation &rot)
{
GfQuaternion quat = rot.GetQuaternion();
_SetRotateFromQuat(quat.GetReal(), GfVec3f(quat.GetImaginary()));
return *this;
}
GfMatrix4f &
GfMatrix4f::SetRotate(const GfMatrix3f &mx3)
{
_mtx[0][0] = mx3[0][0];
_mtx[0][1] = mx3[0][1];
_mtx[0][2] = mx3[0][2];
_mtx[0][3] = 0.0;
_mtx[1][0] = mx3[1][0];
_mtx[1][1] = mx3[1][1];
_mtx[1][2] = mx3[1][2];
_mtx[1][3] = 0.0;
_mtx[2][0] = mx3[2][0];
_mtx[2][1] = mx3[2][1];
_mtx[2][2] = mx3[2][2];
_mtx[2][3] = 0.0;
_mtx[3][0] = 0.0;
_mtx[3][1] = 0.0;
_mtx[3][2] = 0.0;
_mtx[3][3] = 1.0;
return *this;
}
GfMatrix4f &
GfMatrix4f::SetRotateOnly(const GfMatrix3f &mx3)
{
_mtx[0][0] = mx3[0][0];
_mtx[0][1] = mx3[0][1];
_mtx[0][2] = mx3[0][2];
_mtx[1][0] = mx3[1][0];
_mtx[1][1] = mx3[1][1];
_mtx[1][2] = mx3[1][2];
_mtx[2][0] = mx3[2][0];
_mtx[2][1] = mx3[2][1];
_mtx[2][2] = mx3[2][2];
return *this;
}
GfMatrix4f &
GfMatrix4f::SetScale(const GfVec3f &s)
{
_mtx[0][0] = s[0]; _mtx[0][1] = 0.0; _mtx[0][2] = 0.0; _mtx[0][3] = 0.0;
_mtx[1][0] = 0.0; _mtx[1][1] = s[1]; _mtx[1][2] = 0.0; _mtx[1][3] = 0.0;
_mtx[2][0] = 0.0; _mtx[2][1] = 0.0; _mtx[2][2] = s[2]; _mtx[2][3] = 0.0;
_mtx[3][0] = 0.0; _mtx[3][1] = 0.0; _mtx[3][2] = 0.0; _mtx[3][3] = 1.0;
return *this;
}
GfMatrix4f &
GfMatrix4f::SetTranslate(const GfVec3f &t)
{
_mtx[0][0] = 1.0; _mtx[0][1] = 0.0; _mtx[0][2] = 0.0; _mtx[0][3] = 0.0;
_mtx[1][0] = 0.0; _mtx[1][1] = 1.0; _mtx[1][2] = 0.0; _mtx[1][3] = 0.0;
_mtx[2][0] = 0.0; _mtx[2][1] = 0.0; _mtx[2][2] = 1.0; _mtx[2][3] = 0.0;
_mtx[3][0] = t[0]; _mtx[3][1] = t[1]; _mtx[3][2] = t[2]; _mtx[3][3] = 1.0;
return *this;
}
GfMatrix4f &
GfMatrix4f::SetTranslateOnly(const GfVec3f &t)
{
_mtx[3][0] = t[0]; _mtx[3][1] = t[1]; _mtx[3][2] = t[2]; _mtx[3][3] = 1.0;
return *this;
}
GfMatrix4f &
GfMatrix4f::SetLookAt(const GfVec3f &eyePoint,
const GfVec3f ¢erPoint,
const GfVec3f &upDirection)
{
// Get the normalized view vector
GfVec3f view = (centerPoint - eyePoint).GetNormalized();
// Compute vector orthogonal to view and up
GfVec3f right = GfCross(view, upDirection).GetNormalized();
// Compute the "real" up vector orthogonal to both view and right
GfVec3f realUp = GfCross(right, view);
// Set matrix to rotate from world-space coordinate system,
// translating eye position to origin.
_mtx[0][0] = right[0];
_mtx[1][0] = right[1];
_mtx[2][0] = right[2];
_mtx[3][0] = -(right[0] * eyePoint[0] +
right[1] * eyePoint[1] +
right[2] * eyePoint[2]);
_mtx[0][1] = realUp[0];
_mtx[1][1] = realUp[1];
_mtx[2][1] = realUp[2];
_mtx[3][1] = -(realUp[0] * eyePoint[0] +
realUp[1] * eyePoint[1] +
realUp[2] * eyePoint[2]);
_mtx[0][2] = -view[0];
_mtx[1][2] = -view[1];
_mtx[2][2] = -view[2];
_mtx[3][2] = (view[0] * eyePoint[0] +
view[1] * eyePoint[1] +
view[2] * eyePoint[2]);
_mtx[0][3] = 0.0;
_mtx[1][3] = 0.0;
_mtx[2][3] = 0.0;
_mtx[3][3] = 1.0;
return *this;
}
GfMatrix4f &
GfMatrix4f::SetLookAt(const GfVec3f &eyePoint, const GfRotation &orientation)
{
// To go from world space to eye space, first translate the
// world-space eye point to the origin, then rotate by the inverse
// of the orientation rotation to bring the world-space view
// direction to (0,0,-1);
GfMatrix4f m1, m2;
return *this = (m1.SetTranslate(-eyePoint) *
m2.SetRotate(orientation.GetInverse()));
}
bool
GfMatrix4f::Factor(GfMatrix4f* r, GfVec3f* s, GfMatrix4f* u,
GfVec3f* t, GfMatrix4f* p, float eps) const
{
// This was adapted from the (open source) Open Inventor
// SbMatrix::Factor().
p->SetDiagonal(1);
// Set A to the upper 3x3 and set t to the translation part of
// this matrix
GfMatrix4d a;
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++)
a._mtx[i][j] = _mtx[i][j];
a._mtx[3][i] = a._mtx[i][3] = 0.0;
(*t)[i] = _mtx[3][i];
}
a._mtx[3][3] = 1.0;
// Compute the determinant of A. If its absolute value is real
// small, the matrix is singular.
double det = a.GetDeterminant3();
double detSign = (det < 0.0 ? -1.0 : 1.0);
bool isSingular = det * detSign < eps;
// Compute B = A * A-transpose and find its eigenvalues and
// eigenvectors. Use the eigenvectors as the rotation matrix R.
GfMatrix4d b = a * a.GetTranspose();
GfVec3d eigenvalues;
GfVec3d eigenvectors[3];
b._Jacobi3(&eigenvalues, eigenvectors);
GfMatrix4d rTmp(
eigenvectors[0][0], eigenvectors[0][1], eigenvectors[0][2], 0.0,
eigenvectors[1][0], eigenvectors[1][1], eigenvectors[1][2], 0.0,
eigenvectors[2][0], eigenvectors[2][1], eigenvectors[2][2], 0.0,
0.0, 0.0, 0.0, 1.0);
// Compute s = sqrt(eigenvalues), with sign. Set sInv to the
// inverse of s, or if eigenvalue < eps, let s = eps. This allows
// us to compute factors for singular matrices.
GfMatrix4d sInv;
sInv.SetIdentity();
for (int i = 0; i < 3; i++) {
if (eigenvalues[i] < eps) {
(*s)[i] = detSign * eps;
} else {
(*s)[i] = detSign * sqrt(eigenvalues[i]);
}
sInv._mtx[i][i] = 1.0 / (*s)[i];
}
// Compute U = R S-inverse R-transpose A
*u = GfMatrix4f(rTmp * sInv * rTmp.GetTranspose() * a);
*r = GfMatrix4f(rTmp);
return !isSingular;
}
void
GfMatrix4f::_Jacobi3(GfVec3d *eigenvalues, GfVec3d eigenvectors[3]) const
{
// This was adapted from the (open source) Open Inventor
// SbMatrix::Jacobi3().
// Initialize eigenvalues to the diagonal of the 3x3 matrix and
// eigenvectors to the principal axes.
eigenvalues->Set(_mtx[0][0], _mtx[1][1], _mtx[2][2]);
eigenvectors[0] = GfVec3d::XAxis();
eigenvectors[1] = GfVec3d::YAxis();
eigenvectors[2] = GfVec3d::ZAxis();
GfMatrix4f a = (*this);
GfVec3d b = *eigenvalues;
GfVec3d z = GfVec3d(0);
for (int i = 0; i < 50; i++) {
double sm = 0.0;
for (int p = 0; p < 2; p++)
for (int q = p+1; q < 3; q++)
sm += GfAbs(a._mtx[p][q]);
if (sm == 0.0)
return;