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Geometry/EulerAngles: introduce canonicalEulerAngles

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Juraj Oršulić 2023-05-19 15:42:22 +00:00 committed by Rasmus Munk Larsen
parent 7d9bb90f15
commit c18f94e3b0
3 changed files with 308 additions and 107 deletions
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5
Eigen/src/Core/MatrixBase.h
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@ -399,9 +399,12 @@ template<typename Derived> class MatrixBase
EIGEN_DEVICE_FUNC EIGEN_DEVICE_FUNC
inline PlainObject unitOrthogonal(void) const; inline PlainObject unitOrthogonal(void) const;
EIGEN_DEVICE_FUNC EIGEN_DEPRECATED EIGEN_DEVICE_FUNC
inline Matrix<Scalar,3,1> eulerAngles(Index a0, Index a1, Index a2) const; inline Matrix<Scalar,3,1> eulerAngles(Index a0, Index a1, Index a2) const;
EIGEN_DEVICE_FUNC
inline Matrix<Scalar,3,1> canonicalEulerAngles(Index a0, Index a1, Index a2) const;
// put this as separate enum value to work around possible GCC 4.3 bug (?) // put this as separate enum value to work around possible GCC 4.3 bug (?)
enum { HomogeneousReturnTypeDirection = ColsAtCompileTime==1&&RowsAtCompileTime==1 ? ((internal::traits<Derived>::Flags&RowMajorBit)==RowMajorBit ? Horizontal : Vertical) enum { HomogeneousReturnTypeDirection = ColsAtCompileTime==1&&RowsAtCompileTime==1 ? ((internal::traits<Derived>::Flags&RowMajorBit)==RowMajorBit ? Horizontal : Vertical)
: ColsAtCompileTime==1 ? Vertical : Horizontal }; : ColsAtCompileTime==1 ? Vertical : Horizontal };

192
Eigen/src/Geometry/EulerAngles.h
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@ -2,6 +2,7 @@
// for linear algebra. // for linear algebra.
// //
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr> // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2023 Juraj Oršulić, University of Zagreb <juraj.orsulic@fer.hr>
// //
// This Source Code Form is subject to the terms of the Mozilla // 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 // Public License v. 2.0. If a copy of the MPL was not distributed
@ -17,7 +18,7 @@ namespace Eigen {
/** \geometry_module \ingroup Geometry_Module /** \geometry_module \ingroup Geometry_Module
* *
* *
* \returns the Euler-angles of the rotation matrix \c *this using the convention defined by the triplet (\a a0,\a a1,\a a2) * \returns the canonical Euler-angles of the rotation matrix \c *this using the convention defined by the triplet (\a a0,\a a1,\a a2)
* *
* Each of the three parameters \a a0,\a a1,\a a2 represents the respective rotation axis as an integer in {0,1,2}. * Each of the three parameters \a a0,\a a1,\a a2 represents the respective rotation axis as an integer in {0,1,2}.
* For instance, in: * For instance, in:
@ -30,46 +31,54 @@ 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[-pi:pi]x[-pi:pi]. * For Tait-Bryan angle configurations (a0 != a2), the returned angles are in the ranges [-pi:pi]x[-pi/2:pi/2]x[-pi:pi].
* For proper Euler angle configurations (a0 == a2), the returned angles are in the ranges [-pi:pi]x[0:pi]x[-pi:pi].
* *
* \sa class AngleAxis * \sa class AngleAxis
*/ */
template<typename Derived> template<typename Derived>
EIGEN_DEVICE_FUNC inline Matrix<typename MatrixBase<Derived>::Scalar,3,1> EIGEN_DEVICE_FUNC inline Matrix<typename MatrixBase<Derived>::Scalar,3,1>
MatrixBase<Derived>::eulerAngles(Index a0, Index a1, Index a2) const MatrixBase<Derived>::canonicalEulerAngles(Index a0, Index a1, Index a2) const
{ {
EIGEN_USING_STD(atan2)
EIGEN_USING_STD(sin)
EIGEN_USING_STD(cos)
/* Implemented from Graphics Gems IV */ /* Implemented from Graphics Gems IV */
EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived,3,3) EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived, 3, 3)
Matrix<Scalar,3,1> res; Matrix<Scalar, 3, 1> res;
typedef Matrix<typename Derived::Scalar,2,1> Vector2;
const Index odd = ((a0+1)%3 == a1) ? 0 : 1; const Index odd = ((a0 + 1) % 3 == a1) ? 0 : 1;
const Index i = a0; const Index i = a0;
const Index j = (a0 + 1 + odd)%3; const Index j = (a0 + 1 + odd) % 3;
const Index k = (a0 + 2 - odd)%3; const Index k = (a0 + 2 - odd) % 3;
if (a0==a2) if (a0 == a2)
{ {
res[0] = atan2(coeff(j,i), coeff(k,i)); // Proper Euler angles (same first and last axis).
if((odd && res[0]<Scalar(0)) || ((!odd) && res[0]>Scalar(0))) // The i, j, k indices enable addressing the input matrix as the XYX archetype matrix (see Graphics Gems IV),
// where e.g. coeff(k, i) means third column, first row in the XYX archetype matrix:
// c2 s2s1 s2c1
// s2s3 -c2s1s3 + c1c3 -c2c1s3 - s1c3
// -s2c3 c2s1c3 + c1s3 c2c1c3 - s1s3
// Note: s2 is always positive.
Scalar s2 = numext::hypot(coeff(j, i), coeff(k, i));
if (odd)
{ {
if(res[0] > Scalar(0)) { res[0] = numext::atan2(coeff(j, i), coeff(k, i));
res[0] -= Scalar(EIGEN_PI); // s2 is always positive, so res[1] will be within the canonical [0, pi] range
} res[1] = numext::atan2(s2, coeff(i, i));
else {
res[0] += Scalar(EIGEN_PI);
}
Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();
res[1] = -atan2(s2, coeff(i,i));
} }
else else
{ {
Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm(); // In the !odd case, signs of all three angles are flipped at the very end. To keep the solution within the canonical range,
res[1] = atan2(s2, coeff(i,i)); // we flip the solution and make res[1] always negative here (since s2 is always positive, -atan2(s2, c2) will always be negative).
// The final flip at the end due to !odd will thus make res[1] positive and canonical.
// NB: in the general case, there are two correct solutions, but only one is canonical. For proper Euler angles,
// flipping from one solution to the other involves flipping the sign of the second angle res[1] and adding/subtracting pi
// to the first and third angles. The addition/subtraction of pi to the first angle res[0] is handled here by flipping
// the signs of arguments to atan2, while the calculation of the third angle does not need special adjustment since
// it uses the adjusted res[0] as the input and produces a correct result.
res[0] = numext::atan2(-coeff(j, i), -coeff(k, i));
res[1] = -numext::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, // With a=(0,1,0), we have i=0; j=1; k=2, and after computing the first two angles,
@ -82,31 +91,126 @@ MatrixBase<Derived>::eulerAngles(Index a0, Index a1, Index a2) const
// //
// Thus: m11.c1 - m21.s1 = c3 & m12.c1 - m22.s1 = s3 // Thus: m11.c1 - m21.s1 = c3 & m12.c1 - m22.s1 = s3
Scalar s1 = sin(res[0]); Scalar s1 = numext::sin(res[0]);
Scalar c1 = cos(res[0]); Scalar c1 = numext::cos(res[0]);
res[2] = atan2(c1*coeff(j,k)-s1*coeff(k,k), c1*coeff(j,j) - s1 * coeff(k,j)); res[2] = numext::atan2(c1 * coeff(j, k) - s1 * coeff(k, k), c1 * coeff(j, j) - s1 * coeff(k, j));
} }
else else
{ {
res[0] = atan2(coeff(j,k), coeff(k,k)); // Tait-Bryan angles (all three axes are different; typically used for yaw-pitch-roll calculations).
Scalar c2 = Vector2(coeff(i,i), coeff(i,j)).norm(); // The i, j, k indices enable addressing the input matrix as the XYZ archetype matrix (see Graphics Gems IV),
if((odd && res[0]<Scalar(0)) || ((!odd) && res[0]>Scalar(0))) { // where e.g. coeff(k, i) means third column, first row in the XYZ archetype matrix:
if(res[0] > Scalar(0)) { // c2c3 s2s1c3 - c1s3 s2c1c3 + s1s3
res[0] -= Scalar(EIGEN_PI); // c2s3 s2s1s3 + c1c3 s2c1s3 - s1c3
} // -s2 c2s1 c2c1
else {
res[0] += Scalar(EIGEN_PI); res[0] = numext::atan2(coeff(j, k), coeff(k, k));
}
res[1] = atan2(-coeff(i,k), -c2); Scalar c2 = numext::hypot(coeff(i, i), coeff(i, j));
} // c2 is always positive, so the following atan2 will always return a result in the correct canonical middle angle range [-pi/2, pi/2]
else res[1] = numext::atan2(-coeff(i, k), c2);
res[1] = atan2(-coeff(i,k), c2);
Scalar s1 = sin(res[0]); Scalar s1 = numext::sin(res[0]);
Scalar c1 = cos(res[0]); Scalar c1 = numext::cos(res[0]);
res[2] = atan2(s1*coeff(k,i)-c1*coeff(j,i), c1*coeff(j,j) - s1 * coeff(k,j)); res[2] = numext::atan2(s1 * coeff(k, i) - c1 * coeff(j, i), c1 * coeff(j, j) - s1 * coeff(k, j));
} }
if (!odd) if (!odd)
{
res = -res; res = -res;
}
return res;
}
/** \geometry_module \ingroup Geometry_Module
*
*
* \returns the Euler-angles of the rotation matrix \c *this using the convention defined by the triplet (\a a0,\a a1,\a a2)
*
* NB: The returned angles are in non-canonical ranges [0:pi]x[-pi:pi]x[-pi:pi]. For canonical Tait-Bryan/proper Euler ranges, use canonicalEulerAngles.
*
* \sa MatrixBase::canonicalEulerAngles
* \sa class AngleAxis
*/
template<typename Derived>
EIGEN_DEPRECATED EIGEN_DEVICE_FUNC inline Matrix<typename MatrixBase<Derived>::Scalar,3,1>
MatrixBase<Derived>::eulerAngles(Index a0, Index a1, Index a2) const
{
/* Implemented from Graphics Gems IV */
EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived, 3, 3)
Matrix<Scalar, 3, 1> res;
const Index odd = ((a0 + 1) % 3 == a1) ? 0 : 1;
const Index i = a0;
const Index j = (a0 + 1 + odd) % 3;
const Index k = (a0 + 2 - odd) % 3;
if (a0 == a2)
{
res[0] = numext::atan2(coeff(j, i), coeff(k, i));
if ((odd && res[0] < Scalar(0)) || ((!odd) && res[0] > Scalar(0)))
{
if (res[0] > Scalar(0))
{
res[0] -= Scalar(EIGEN_PI);
}
else
{
res[0] += Scalar(EIGEN_PI);
}
Scalar s2 = numext::hypot(coeff(j, i), coeff(k, i));
res[1] = -numext::atan2(s2, coeff(i, i));
}
else
{
Scalar s2 = numext::hypot(coeff(j, i), coeff(k, i));
res[1] = numext::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 = numext::sin(res[0]);
Scalar c1 = numext::cos(res[0]);
res[2] = numext::atan2(c1 * coeff(j, k) - s1 * coeff(k, k), c1 * coeff(j, j) - s1 * coeff(k, j));
}
else
{
res[0] = numext::atan2(coeff(j, k), coeff(k, k));
Scalar c2 = numext::hypot(coeff(i, i), coeff(i, j));
if ((odd && res[0] < Scalar(0)) || ((!odd) && res[0] > Scalar(0)))
{
if (res[0] > Scalar(0))
{
res[0] -= Scalar(EIGEN_PI);
}
else
{
res[0] += Scalar(EIGEN_PI);
}
res[1] = numext::atan2(-coeff(i, k), -c2);
}
else
{
res[1] = numext::atan2(-coeff(i, k), c2);
}
Scalar s1 = numext::sin(res[0]);
Scalar c1 = numext::cos(res[0]);
res[2] = numext::atan2(s1 * coeff(k, i) - c1 * coeff(j, i), c1 * coeff(j, j) - s1 * coeff(k, j));
}
if (!odd)
{
res = -res;
}
return res; return res;
} }

182
test/geo_eulerangles.cpp
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@ -2,11 +2,15 @@
// for linear algebra. // for linear algebra.
// //
// Copyright (C) 2008-2012 Gael Guennebaud <gael.guennebaud@inria.fr> // Copyright (C) 2008-2012 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2023 Juraj Oršulić, University of Zagreb <juraj.orsulic@fer.hr>
// //
// This Source Code Form is subject to the terms of the Mozilla // 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 // Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
// Silence warnings about using the deprecated non-canonical .eulerAngles(), which are still being tested.
#define EIGEN_NO_DEPRECATED_WARNING
#include "main.h" #include "main.h"
#include <Eigen/Geometry> #include <Eigen/Geometry>
#include <Eigen/LU> #include <Eigen/LU>
@ -14,53 +18,89 @@
template<typename Scalar> template<typename Scalar>
void verify_euler(const Matrix<Scalar,3,1>& ea, int i, int j, int k) 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; const Matrix3 m(AngleAxisx(ea[0], Vector3::Unit(i)) * AngleAxisx(ea[1], Vector3::Unit(j)) * AngleAxisx(ea[2], Vector3::Unit(k)));
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 || !numext::is_exactly_zero(ea[1])) && (i == k || !internal::isApprox(abs(ea[1]), Scalar(EIGEN_PI / 2), test_precision<Scalar>())) )
VERIFY((ea-eabis).norm() <= test_precision<Scalar>());
// approx_or_less_than does not work for 0 // Test non-canonical eulerAngles
VERIFY(0 < eabis[0] || test_isMuchSmallerThan(eabis[0], Scalar(1))); {
VERIFY_IS_APPROX_OR_LESS_THAN(eabis[0], Scalar(EIGEN_PI)); Vector3 eabis = m.eulerAngles(i, j, k);
VERIFY_IS_APPROX_OR_LESS_THAN(-Scalar(EIGEN_PI), eabis[1]); Matrix3 mbis(AngleAxisx(eabis[0], Vector3::Unit(i)) * AngleAxisx(eabis[1], Vector3::Unit(j)) * AngleAxisx(eabis[2], Vector3::Unit(k)));
VERIFY_IS_APPROX_OR_LESS_THAN(eabis[1], Scalar(EIGEN_PI)); VERIFY_IS_APPROX(m, mbis);
VERIFY_IS_APPROX_OR_LESS_THAN(-Scalar(EIGEN_PI), eabis[2]);
VERIFY_IS_APPROX_OR_LESS_THAN(eabis[2], Scalar(EIGEN_PI)); // approx_or_less_than does not work for 0
VERIFY(0 < eabis[0] || test_isMuchSmallerThan(eabis[0], Scalar(1)));
VERIFY_IS_APPROX_OR_LESS_THAN(eabis[0], Scalar(EIGEN_PI));
VERIFY_IS_APPROX_OR_LESS_THAN(-Scalar(EIGEN_PI), eabis[1]);
VERIFY_IS_APPROX_OR_LESS_THAN(eabis[1], Scalar(EIGEN_PI));
VERIFY_IS_APPROX_OR_LESS_THAN(-Scalar(EIGEN_PI), eabis[2]);
VERIFY_IS_APPROX_OR_LESS_THAN(eabis[2], Scalar(EIGEN_PI));
}
// Test canonicalEulerAngles
{
Vector3 eabis = m.canonicalEulerAngles(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);
VERIFY_IS_APPROX_OR_LESS_THAN(-Scalar(EIGEN_PI), eabis[0]);
VERIFY_IS_APPROX_OR_LESS_THAN(eabis[0], Scalar(EIGEN_PI));
if (i != k)
{
// Tait-Bryan sequence
VERIFY_IS_APPROX_OR_LESS_THAN(-Scalar(EIGEN_PI / 2), eabis[1]);
VERIFY_IS_APPROX_OR_LESS_THAN(eabis[1], Scalar(EIGEN_PI / 2));
}
else
{
// Proper Euler sequence
// approx_or_less_than does not work for 0
VERIFY(0 < eabis[1] || test_isMuchSmallerThan(eabis[1], Scalar(1)));
VERIFY_IS_APPROX_OR_LESS_THAN(eabis[1], Scalar(EIGEN_PI));
}
VERIFY_IS_APPROX_OR_LESS_THAN(-Scalar(EIGEN_PI), eabis[2]);
VERIFY_IS_APPROX_OR_LESS_THAN(eabis[2], Scalar(EIGEN_PI));
}
} }
template<typename Scalar> void check_all_var(const Matrix<Scalar,3,1>& ea) template<typename Scalar> void check_all_var(const Matrix<Scalar, 3, 1>& ea)
{ {
verify_euler(ea, 0,1,2); auto verify_permutation = [](const Matrix<Scalar, 3, 1>& eap)
verify_euler(ea, 0,1,0); {
verify_euler(ea, 0,2,1); verify_euler(eap, 0, 1, 2);
verify_euler(ea, 0,2,0); verify_euler(eap, 0, 1, 0);
verify_euler(eap, 0, 2, 1);
verify_euler(eap, 0, 2, 0);
verify_euler(ea, 1,2,0); verify_euler(eap, 1, 2, 0);
verify_euler(ea, 1,2,1); verify_euler(eap, 1, 2, 1);
verify_euler(ea, 1,0,2); verify_euler(eap, 1, 0, 2);
verify_euler(ea, 1,0,1); verify_euler(eap, 1, 0, 1);
verify_euler(ea, 2,0,1); verify_euler(eap, 2, 0, 1);
verify_euler(ea, 2,0,2); verify_euler(eap, 2, 0, 2);
verify_euler(ea, 2,1,0); verify_euler(eap, 2, 1, 0);
verify_euler(ea, 2,1,2); verify_euler(eap, 2, 1, 2);
};
int i, j, k;
for (i = 0; i < 3; i++)
for (j = 0; j < 3; j++)
for (k = 0; k < 3; k++)
{
Matrix<Scalar,3,1> eap(ea(i), ea(j), ea(k));
verify_permutation(eap);
}
} }
template<typename Scalar> void eulerangles() template<typename Scalar> void eulerangles()
{ {
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 Array<Scalar,3,1> Array3; typedef Array<Scalar, 3, 1> Array3;
typedef Quaternion<Scalar> Quaternionx; typedef Quaternion<Scalar> Quaternionx;
typedef AngleAxis<Scalar> AngleAxisx; typedef AngleAxis<Scalar> AngleAxisx;
@ -70,27 +110,80 @@ template<typename Scalar> void eulerangles()
Matrix3 m; Matrix3 m;
m = q1; m = q1;
Vector3 ea = m.eulerAngles(0,1,2); Vector3 ea = m.eulerAngles(0, 1, 2);
check_all_var(ea); check_all_var(ea);
ea = m.eulerAngles(0,1,0); ea = m.eulerAngles(0, 1, 0);
check_all_var(ea); check_all_var(ea);
// Check with purely random Quaternion: // Check with purely random Quaternion:
q1.coeffs() = Quaternionx::Coefficients::Random().normalized(); q1.coeffs() = Quaternionx::Coefficients::Random().normalized();
m = q1; m = q1;
ea = m.eulerAngles(0,1,2); ea = m.eulerAngles(0, 1, 2);
check_all_var(ea); check_all_var(ea);
ea = m.eulerAngles(0,1,0); ea = m.eulerAngles(0, 1, 0);
check_all_var(ea); check_all_var(ea);
// Check with random angles in range [0:pi]x[-pi:pi]x[-pi:pi]. // Check with random angles in range [-pi:pi]x[-pi:pi]x[-pi:pi].
ea = (Array3::Random() + Array3(1,0,0))*Scalar(EIGEN_PI)*Array3(0.5,1,1); ea = Array3::Random() * Scalar(EIGEN_PI);
check_all_var(ea); check_all_var(ea);
ea[2] = ea[0] = internal::random<Scalar>(0,Scalar(EIGEN_PI)); auto test_with_some_zeros = [](const Vector3& eaz)
{
check_all_var(eaz);
Vector3 ea_glz = eaz;
ea_glz[0] = Scalar(0);
check_all_var(ea_glz);
ea_glz[0] = internal::random<Scalar>(-0.001, 0.001);
check_all_var(ea_glz);
ea_glz[2] = Scalar(0);
check_all_var(ea_glz);
ea_glz[2] = internal::random<Scalar>(-0.001, 0.001);
check_all_var(ea_glz);
};
// Check gimbal lock configurations and a bit noisy gimbal locks
Vector3 ea_gl = ea;
ea_gl[1] = EIGEN_PI/2;
test_with_some_zeros(ea_gl);
ea_gl[1] += internal::random<Scalar>(-0.001, 0.001);
test_with_some_zeros(ea_gl);
ea_gl[1] = -EIGEN_PI/2;
test_with_some_zeros(ea_gl);
ea_gl[1] += internal::random<Scalar>(-0.001, 0.001);
test_with_some_zeros(ea_gl);
ea_gl[1] = EIGEN_PI/2;
ea_gl[2] = ea_gl[0];
test_with_some_zeros(ea_gl);
ea_gl[1] += internal::random<Scalar>(-0.001, 0.001);
test_with_some_zeros(ea_gl);
ea_gl[1] = -EIGEN_PI/2;
test_with_some_zeros(ea_gl);
ea_gl[1] += internal::random<Scalar>(-0.001, 0.001);
test_with_some_zeros(ea_gl);
// Similar to above, but with pi instead of pi/2
Vector3 ea_pi = ea;
ea_pi[1] = EIGEN_PI;
test_with_some_zeros(ea_gl);
ea_pi[1] += internal::random<Scalar>(-0.001, 0.001);
test_with_some_zeros(ea_gl);
ea_pi[1] = -EIGEN_PI;
test_with_some_zeros(ea_gl);
ea_pi[1] += internal::random<Scalar>(-0.001, 0.001);
test_with_some_zeros(ea_gl);
ea_pi[1] = EIGEN_PI;
ea_pi[2] = ea_pi[0];
test_with_some_zeros(ea_gl);
ea_pi[1] += internal::random<Scalar>(-0.001, 0.001);
test_with_some_zeros(ea_gl);
ea_pi[1] = -EIGEN_PI;
test_with_some_zeros(ea_gl);
ea_pi[1] += internal::random<Scalar>(-0.001, 0.001);
test_with_some_zeros(ea_gl);
ea[2] = ea[0] = internal::random<Scalar>(0, Scalar(EIGEN_PI));
check_all_var(ea); check_all_var(ea);
ea[0] = ea[1] = internal::random<Scalar>(0,Scalar(EIGEN_PI)); ea[0] = ea[1] = internal::random<Scalar>(0, Scalar(EIGEN_PI));
check_all_var(ea); check_all_var(ea);
ea[1] = 0; ea[1] = 0;
@ -105,7 +198,8 @@ template<typename Scalar> void eulerangles()
EIGEN_DECLARE_TEST(geo_eulerangles) EIGEN_DECLARE_TEST(geo_eulerangles)
{ {
for(int i = 0; i < g_repeat; i++) { for(int i = 0; i < g_repeat; i++)
{
CALL_SUBTEST_1( eulerangles<float>() ); CALL_SUBTEST_1( eulerangles<float>() );
CALL_SUBTEST_2( eulerangles<double>() ); CALL_SUBTEST_2( eulerangles<double>() );
} }