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Fix bug #609: Euler angles are in Range [0:pi]x[-pi:pi]x[-pi:pi].

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Now the unit test verifies this (also that it is bijective in this range).
This commit is contained in:
Christoph Hertzberg 2013-11-29 19:42:11 +01:00
parent 12504a79d1
commit baf2b13589
2 changed files with 45 additions and 24 deletions
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2
Eigen/src/Geometry/EulerAngles.h
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@ -28,7 +28,7 @@ namespace Eigen {
* * AngleAxisf(ea[2], Vector3f::UnitZ()); \endcode * * AngleAxisf(ea[2], Vector3f::UnitZ()); \endcode
* This corresponds to the right-multiply conventions (with right hand side frames). * 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]. * The returned angles are in the ranges [0:pi]x[-pi:pi]x[-pi:pi].
* *
* \sa class AngleAxis * \sa class AngleAxis
*/ */

67
test/geo_eulerangles.cpp
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@ -12,36 +12,48 @@
#include <Eigen/LU> #include <Eigen/LU>
#include <Eigen/SVD> #include <Eigen/SVD>
template<typename Scalar> void check_all_var(const Matrix<Scalar,3,1>& ea)
template<typename Scalar>
void verify_euler(const Matrix<Scalar,3,1>& ea, int i, int j, int k)
{ {
typedef Matrix<Scalar,3,3> Matrix3; typedef Matrix<Scalar,3,3> Matrix3;
typedef Matrix<Scalar,3,1> Vector3; typedef Matrix<Scalar,3,1> Vector3;
typedef AngleAxis<Scalar> AngleAxisx; typedef AngleAxis<Scalar> AngleAxisx;
using std::abs; using std::abs;
Matrix3 m(AngleAxisx(ea[0], Vector3::Unit(i)) * AngleAxisx(ea[1], Vector3::Unit(j)) * AngleAxisx(ea[2], Vector3::Unit(k)));
Vector3 eabis = m.eulerAngles(i, j, k);
Matrix3 mbis(AngleAxisx(eabis[0], Vector3::Unit(i)) * AngleAxisx(eabis[1], Vector3::Unit(j)) * AngleAxisx(eabis[2], Vector3::Unit(k)));
VERIFY_IS_APPROX(m, mbis);
/* If I==K, and ea[1]==0, then there no unique solution. */
/* The remark apply in the case where I!=K, and |ea[1]| is close to pi/2. */
if( (i!=k || ea[1]!=0) && (i==k || !internal::isApprox(abs(ea[1]),Scalar(M_PI/2),test_precision<Scalar>())) )
VERIFY((ea-eabis).norm() <= test_precision<Scalar>());
#define VERIFY_EULER(I,J,K, X,Y,Z) { \ // approx_or_less_than does not work for 0
Matrix3 m(AngleAxisx(ea[0], Vector3::Unit##X()) * AngleAxisx(ea[1], Vector3::Unit##Y()) * AngleAxisx(ea[2], Vector3::Unit##Z())); \ VERIFY(0 < eabis[0] || test_isMuchSmallerThan(eabis[0], Scalar(1)));
Vector3 eabis = m.eulerAngles(I,J,K); \ VERIFY_IS_APPROX_OR_LESS_THAN(eabis[0], Scalar(M_PI));
Matrix3 mbis(AngleAxisx(eabis[0], Vector3::Unit##X()) * AngleAxisx(eabis[1], Vector3::Unit##Y()) * AngleAxisx(eabis[2], Vector3::Unit##Z())); \ VERIFY_IS_APPROX_OR_LESS_THAN(-Scalar(M_PI), eabis[1]);
VERIFY_IS_APPROX(m, mbis); \ VERIFY_IS_APPROX_OR_LESS_THAN(eabis[1], Scalar(M_PI));
/* If I==K, and ea[1]==0, then there no unique solution. */ \ VERIFY_IS_APPROX_OR_LESS_THAN(-Scalar(M_PI), eabis[2]);
/* The remark apply in the case where I!=K, and |ea[1]| is close to pi/2. */ \ VERIFY_IS_APPROX_OR_LESS_THAN(eabis[2], Scalar(M_PI));
if( (I!=K || ea[1]!=0) && (I==K || !internal::isApprox(abs(ea[1]),Scalar(M_PI/2),test_precision<Scalar>())) ) VERIFY((ea-eabis).norm() <= test_precision<Scalar>()); \ }
}
VERIFY_EULER(0,1,2, X,Y,Z);
VERIFY_EULER(0,1,0, X,Y,X);
VERIFY_EULER(0,2,1, X,Z,Y);
VERIFY_EULER(0,2,0, X,Z,X);
VERIFY_EULER(1,2,0, Y,Z,X); template<typename Scalar> void check_all_var(const Matrix<Scalar,3,1>& ea)
VERIFY_EULER(1,2,1, Y,Z,Y); {
VERIFY_EULER(1,0,2, Y,X,Z); verify_euler(ea, 0,1,2);
VERIFY_EULER(1,0,1, Y,X,Y); verify_euler(ea, 0,1,0);
verify_euler(ea, 0,2,1);
verify_euler(ea, 0,2,0);
VERIFY_EULER(2,0,1, Z,X,Y); verify_euler(ea, 1,2,0);
VERIFY_EULER(2,0,2, Z,X,Z); verify_euler(ea, 1,2,1);
VERIFY_EULER(2,1,0, Z,Y,X); verify_euler(ea, 1,0,2);
VERIFY_EULER(2,1,2, Z,Y,Z); verify_euler(ea, 1,0,1);
verify_euler(ea, 2,0,1);
verify_euler(ea, 2,0,2);
verify_euler(ea, 2,1,0);
verify_euler(ea, 2,1,2);
} }
template<typename Scalar> void eulerangles() template<typename Scalar> void eulerangles()
@ -63,7 +75,16 @@ template<typename Scalar> void eulerangles()
ea = m.eulerAngles(0,1,0); ea = m.eulerAngles(0,1,0);
check_all_var(ea); check_all_var(ea);
ea = (Array3::Random() + Array3(1,1,0))*Scalar(M_PI)*Array3(0.5,0.5,1); // Check with purely random Quaternion:
q1.coeffs() = Quaternionx::Coefficients::Random().normalized();
m = q1;
ea = m.eulerAngles(0,1,2);
check_all_var(ea);
ea = m.eulerAngles(0,1,0);
check_all_var(ea);
// Check with random angles in range [0:pi]x[-pi:pi]x[-pi:pi].
ea = (Array3::Random() + Array3(1,0,0))*Scalar(M_PI)*Array3(0.5,1,1);
check_all_var(ea); check_all_var(ea);
ea[2] = ea[0] = internal::random<Scalar>(0,Scalar(M_PI)); ea[2] = ea[0] = internal::random<Scalar>(0,Scalar(M_PI));