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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#include "main.h"
#include <Eigen/Geometry>
#include <Eigen/LU>
template<typename Scalar> void geometry(void)
{
/* this test covers the following files:
Cross.h Quaternion.h, Transform.cpp
*/
typedef Matrix<Scalar,2,2> Matrix2;
typedef Matrix<Scalar,3,3> Matrix3;
typedef Matrix<Scalar,4,4> Matrix4;
typedef Matrix<Scalar,2,1> Vector2;
typedef Matrix<Scalar,3,1> Vector3;
typedef Matrix<Scalar,4,1> Vector4;
typedef Quaternion<Scalar> Quaternion;
typedef AngleAxis<Scalar> AngleAxis;
typedef EulerAngles<Scalar> EulerAngles;
Quaternion q1, q2;
Vector3 v0 = Vector3::random(),
v1 = Vector3::random(),
v2 = Vector3::random();
Scalar a = ei_random<Scalar>(-M_PI, M_PI);
q1 = AngleAxis(ei_random<Scalar>(-M_PI, M_PI), v0.normalized());
q2 = AngleAxis(ei_random<Scalar>(-M_PI, M_PI), v1.normalized());
// rotation matrix conversion
VERIFY_IS_APPROX(q1 * v2, q1.toRotationMatrix() * v2);
VERIFY_IS_APPROX(q1 * q2 * v2,
q1.toRotationMatrix() * q2.toRotationMatrix() * v2);
VERIFY_IS_NOT_APPROX(q2 * q1 * v2,
q1.toRotationMatrix() * q2.toRotationMatrix() * v2);
q2 = q1.toRotationMatrix();
VERIFY_IS_APPROX(q1*v1,q2*v1);
// Euler angle conversion
VERIFY_IS_APPROX(Quaternion(EulerAngles(q1)) * v1, q1 * v1);
EulerAngles ea = q2;
VERIFY_IS_APPROX(EulerAngles(Quaternion(ea)).coeffs(), ea.coeffs());
VERIFY_IS_NOT_APPROX(EulerAngles(Quaternion(EulerAngles(v2.cwiseProduct(Vector3(0.2,-0.2,1))))).coeffs(), v2);
// angle-axis conversion
AngleAxis aa = q1;
VERIFY_IS_APPROX(q1 * v1, Quaternion(aa) * v1);
VERIFY_IS_NOT_APPROX(q1 * v1, Quaternion(AngleAxis(aa.angle()*2,aa.axis())) * v1);
// from two vector creation
VERIFY_IS_APPROX(v2.normalized(),(q2.setFromTwoVectors(v1,v2)*v1).normalized());
VERIFY_IS_APPROX(v2.normalized(),(q2.setFromTwoVectors(v1,v2)*v1).normalized());
// inverse and conjugate
VERIFY_IS_APPROX(q1 * (q1.inverse() * v1), v1);
VERIFY_IS_APPROX(q1 * (q1.conjugate() * v1), v1);
// cross product
VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(v2).dot(v1), Scalar(1));
Matrix3 m;
m << v0.normalized(),
(v0.cross(v1)).normalized(),
(v0.cross(v1).cross(v0)).normalized();
VERIFY(m.isUnitary());
// AngleAxis
VERIFY_IS_APPROX(AngleAxis(a,v1.normalized()).toRotationMatrix(),
Quaternion(AngleAxis(a,v1.normalized())).toRotationMatrix());
AngleAxis aa1;
m = q1.toRotationMatrix();
aa1 = m;
VERIFY_IS_APPROX(AngleAxis(m).toRotationMatrix(),
Quaternion(m).toRotationMatrix());
// Transform
// TODO complete the tests !
typedef Transform<Scalar,2> Transform2;
typedef Transform<Scalar,3> Transform3;
a = 0;
while (ei_abs(a)<0.1)
a = ei_random<Scalar>(-0.4*M_PI, 0.4*M_PI);
q1 = AngleAxis(a, v0.normalized());
Transform3 t0, t1, t2;
t0.setIdentity();
t0.affine() = q1.toRotationMatrix();
t1.setIdentity();
t1.affine() = q1.toRotationMatrix();
v0 << 50, 2, 1;//= Vector3::random().cwiseProduct(Vector3(10,2,0.5));
t0.scale(v0);
t1.prescale(v0);
VERIFY_IS_APPROX( (t0 * Vector3(1,0,0)).norm(), v0.x());
VERIFY_IS_NOT_APPROX((t1 * Vector3(1,0,0)).norm(), v0.x());
t0.setIdentity();
t1.setIdentity();
v1 << 1, 2, 3;
t0.affine() = q1.toRotationMatrix();
t0.pretranslate(v0);
t0.scale(v1);
t1.affine() = q1.conjugate().toRotationMatrix();
t1.prescale(v1.cwiseInverse());
t1.translate(-v0);
VERIFY((t0.matrix() * t1.matrix()).isIdentity());
t1.fromPositionOrientationScale(v0, q1, v1);
VERIFY_IS_APPROX(t1.matrix(), t0.matrix());
// 2D transformation
Transform2 t20, t21;
Vector2 v20 = Vector2::random();
Vector2 v21 = Vector2::random();
t21.setIdentity();
t21.affine() = Rotation2D<Scalar>(a).toRotationMatrix();
VERIFY_IS_APPROX(t20.fromPositionOrientationScale(v20,a,v21).matrix(),
t21.pretranslate(v20).scale(v21).matrix());
t21.setIdentity();
t21.affine() = Rotation2D<Scalar>(-a).toRotationMatrix();
VERIFY( (t20.fromPositionOrientationScale(v20,a,v21) * (t21.prescale(v21.cwiseInverse()).translate(-v20))).isIdentity() );
}
void test_geometry()
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST( geometry<float>() );
// CALL_SUBTEST( geometry<double>() );
}
}
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