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Fix bug #609: avoid if statement and improve consistency of eulerAngles method

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This commit is contained in:
Gael Guennebaud 2013-06-09 23:14:45 +02:00
parent e04b59929e
commit c98fd7a6ca
2 changed files with 85 additions and 31 deletions
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58
Eigen/src/Geometry/EulerAngles.h
View File

@ -27,12 +27,18 @@ namespace Eigen {
* * AngleAxisf(ea[1], Vector3f::UnitX())
* * AngleAxisf(ea[2], Vector3f::UnitZ()); \endcode
* This corresponds to the right-multiply conventions (with right hand side frames).
*
* The returned angles are in the ranges [0:pi]x[0:pi]x[-pi:pi].
*
* \sa class AngleAxis
*/
template<typename Derived>
inline Matrix<typename MatrixBase<Derived>::Scalar,3,1>
MatrixBase<Derived>::eulerAngles(Index a0, Index a1, Index a2) const
{
using std::atan2;
using std::sin;
using std::cos;
/* Implemented from Graphics Gems IV */
EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived,3,3)
@ -44,39 +50,53 @@ MatrixBase<Derived>::eulerAngles(Index a0, Index a1, Index a2) const
const Index i = a0;
const Index j = (a0 + 1 + odd)%3;
const Index k = (a0 + 2 - odd)%3;
if (a0==a2)
{
Scalar s = Vector2(coeff(j,i) , coeff(k,i)).norm();
res[1] = atan2(s, coeff(i,i));
if (s > epsilon)
res[0] = atan2(coeff(j,i), coeff(k,i));
if((odd && res[0]<0) || ((!odd) && res[0]>0))
{
res[0] = atan2(coeff(j,i), coeff(k,i));
res[2] = atan2(coeff(i,j),-coeff(i,k));
res[0] = (res[0] > 0) ? res[0] - M_PI : res[0] + M_PI;
Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();
res[1] = -atan2(s2, coeff(i,i));
}
else
{
res[0] = Scalar(0);
res[2] = (coeff(i,i)>0?1:-1)*atan2(-coeff(k,j), coeff(j,j));
Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();
res[1] = atan2(s2, coeff(i,i));
}
}
// With a=(0,1,0), we have i=0; j=1; k=2, and after computing the first two angles,
// we can compute their respective rotation, and apply its inverse to M. Since the result must
// be a rotation around x, we have:
//
// c2 s1.s2 c1.s2 1 0 0
// 0 c1 -s1 * M = 0 c3 s3
// -s2 s1.c2 c1.c2 0 -s3 c3
//
// Thus: m11.c1 - m21.s1 = c3 & m12.c1 - m22.s1 = s3
Scalar s1 = sin(res[0]);
Scalar c1 = cos(res[0]);
res[2] = atan2(c1*coeff(j,k)-s1*coeff(k,k), c1*coeff(j,j) - s1 * coeff(k,j));
}
else
{
Scalar c = Vector2(coeff(i,i) , coeff(i,j)).norm();
res[1] = atan2(-coeff(i,k), c);
if (c > epsilon)
{
res[0] = atan2(coeff(j,k), coeff(k,k));
res[2] = atan2(coeff(i,j), coeff(i,i));
res[0] = atan2(coeff(j,k), coeff(k,k));
Scalar c2 = Vector2(coeff(i,i), coeff(i,j)).norm();
if((odd && res[0]<0) || ((!odd) && res[0]>0)) {
res[0] = (res[0] > 0) ? res[0] - M_PI : res[0] + M_PI;
res[1] = atan2(-coeff(i,k), -c2);
}
else
{
res[0] = Scalar(0);
res[2] = (coeff(i,k)>0?1:-1)*atan2(-coeff(k,j), coeff(j,j));
}
res[1] = atan2(-coeff(i,k), c2);
Scalar s1 = sin(res[0]);
Scalar c1 = cos(res[0]);
res[2] = atan2(s1*coeff(k,i)-c1*coeff(j,i), c1*coeff(j,j) - s1 * coeff(k,j));
}
if (!odd)
res = -res;
return res;
}

58
test/geo_eulerangles.cpp
View File

@ -1,7 +1,7 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2008-2012 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
@ -12,22 +12,18 @@
#include <Eigen/LU>
#include <Eigen/SVD>
template<typename Scalar> void eulerangles(void)
template<typename Scalar> void check_all_var(const Matrix<Scalar,3,1>& ea)
{
typedef Matrix<Scalar,3,3> Matrix3;
typedef Matrix<Scalar,3,1> Vector3;
typedef Quaternion<Scalar> Quaternionx;
typedef AngleAxis<Scalar> AngleAxisx;
Scalar a = internal::random<Scalar>(-Scalar(M_PI), Scalar(M_PI));
Quaternionx q1;
q1 = AngleAxisx(a, Vector3::Random().normalized());
Matrix3 m;
m = q1;
#define VERIFY_EULER(I,J,K, X,Y,Z) { \
Vector3 ea = m.eulerAngles(I,J,K); \
VERIFY_IS_APPROX(m, Matrix3(AngleAxisx(ea[0], Vector3::Unit##X()) * AngleAxisx(ea[1], Vector3::Unit##Y()) * AngleAxisx(ea[2], Vector3::Unit##Z()))); \
Matrix3 m(AngleAxisx(ea[0], Vector3::Unit##X()) * AngleAxisx(ea[1], Vector3::Unit##Y()) * AngleAxisx(ea[2], Vector3::Unit##Z())); \
Vector3 eabis = m.eulerAngles(I,J,K); \
Matrix3 mbis(AngleAxisx(eabis[0], Vector3::Unit##X()) * AngleAxisx(eabis[1], Vector3::Unit##Y()) * AngleAxisx(eabis[2], Vector3::Unit##Z())); \
VERIFY_IS_APPROX(m, mbis); \
if(I!=K || ea[1]!=0) VERIFY_IS_APPROX(ea, eabis); \
}
VERIFY_EULER(0,1,2, X,Y,Z);
VERIFY_EULER(0,1,0, X,Y,X);
@ -45,6 +41,44 @@ template<typename Scalar> void eulerangles(void)
VERIFY_EULER(2,1,2, Z,Y,Z);
}
template<typename Scalar> void eulerangles(void)
{
typedef Matrix<Scalar,3,3> Matrix3;
typedef Matrix<Scalar,3,1> Vector3;
typedef Array<Scalar,3,1> Array3;
typedef Quaternion<Scalar> Quaternionx;
typedef AngleAxis<Scalar> AngleAxisx;
Scalar a = internal::random<Scalar>(-Scalar(M_PI), Scalar(M_PI));
Quaternionx q1;
q1 = AngleAxisx(a, Vector3::Random().normalized());
Matrix3 m;
m = q1;
Vector3 ea = m.eulerAngles(0,1,2);
check_all_var(ea);
ea = m.eulerAngles(0,1,0);
check_all_var(ea);
ea = (Array3::Random() + Array3(1,1,0))*M_PI*Array3(0.5,0.5,1);
check_all_var(ea);
ea[2] = ea[0] = internal::random<Scalar>(0,M_PI);
check_all_var(ea);
ea[0] = ea[1] = internal::random<Scalar>(0,M_PI);
check_all_var(ea);
ea[1] = 0;
check_all_var(ea);
ea.head(2).setZero();
check_all_var(ea);
ea.setZero();
check_all_var(ea);
}
void test_geo_eulerangles()
{
for(int i = 0; i < g_repeat; i++) {