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eigen/test/geo_quaternion.cpp

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// 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) 2009 Mathieu Gautier <mathieu.gautier@cea.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>
#include <Eigen/SVD>
template<typename Scalar, int Options> void quaternion(void)
{
/* this test covers the following files:
Quaternion.h
*/
typedef Matrix<Scalar,3,3> Matrix3;
typedef Matrix<Scalar,3,1> Vector3;
typedef Quaternion<Scalar,Options> Quaternionx;
typedef AngleAxis<Scalar> AngleAxisx;
Scalar largeEps = test_precision<Scalar>();
if (internal::is_same<Scalar,float>::value)
largeEps = 1e-3f;
Scalar eps = internal::random<Scalar>() * Scalar(1e-2);
Vector3 v0 = Vector3::Random(),
v1 = Vector3::Random(),
v2 = Vector3::Random(),
v3 = Vector3::Random();
Scalar a = internal::random<Scalar>(-Scalar(M_PI), Scalar(M_PI));
// Quaternion: Identity(), setIdentity();
Quaternionx q1, q2;
q2.setIdentity();
VERIFY_IS_APPROX(Quaternionx(Quaternionx::Identity()).coeffs(), q2.coeffs());
q1.coeffs().setRandom();
VERIFY_IS_APPROX(q1.coeffs(), (q1*q2).coeffs());
// concatenation
q1 *= q2;
q1 = AngleAxisx(a, v0.normalized());
q2 = AngleAxisx(a, v1.normalized());
// angular distance
Scalar refangle = internal::abs(AngleAxisx(q1.inverse()*q2).angle());
if (refangle>Scalar(M_PI))
refangle = Scalar(2)*Scalar(M_PI) - refangle;
if((q1.coeffs()-q2.coeffs()).norm() > 10*largeEps)
{
VERIFY_IS_MUCH_SMALLER_THAN(internal::abs(q1.angularDistance(q2) - refangle), Scalar(1));
}
// rotation matrix conversion
VERIFY_IS_APPROX(q1 * v2, q1.toRotationMatrix() * v2);
VERIFY_IS_APPROX(q1 * q2 * v2,
q1.toRotationMatrix() * q2.toRotationMatrix() * v2);
VERIFY( (q2*q1).isApprox(q1*q2, largeEps)
|| !(q2 * q1 * v2).isApprox(q1.toRotationMatrix() * q2.toRotationMatrix() * v2));
q2 = q1.toRotationMatrix();
VERIFY_IS_APPROX(q1*v1,q2*v1);
// angle-axis conversion
AngleAxisx aa = AngleAxisx(q1);
VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1);
// Do not execute the test if the rotation angle is almost zero, or
// the rotation axis and v1 are almost parallel.
if (internal::abs(aa.angle()) > 5*test_precision<Scalar>()
&& (aa.axis() - v1.normalized()).norm() < 1.99
&& (aa.axis() + v1.normalized()).norm() < 1.99)
{
VERIFY_IS_NOT_APPROX(q1 * v1, Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1);
}
// from two vector creation
VERIFY_IS_APPROX( v2.normalized(),(q2.setFromTwoVectors(v1, v2)*v1).normalized());
VERIFY_IS_APPROX( v1.normalized(),(q2.setFromTwoVectors(v1, v1)*v1).normalized());
VERIFY_IS_APPROX(-v1.normalized(),(q2.setFromTwoVectors(v1,-v1)*v1).normalized());
if (internal::is_same<Scalar,double>::value)
{
v3 = (v1.array()+eps).matrix();
VERIFY_IS_APPROX( v3.normalized(),(q2.setFromTwoVectors(v1, v3)*v1).normalized());
VERIFY_IS_APPROX(-v3.normalized(),(q2.setFromTwoVectors(v1,-v3)*v1).normalized());
}
// inverse and conjugate
VERIFY_IS_APPROX(q1 * (q1.inverse() * v1), v1);
VERIFY_IS_APPROX(q1 * (q1.conjugate() * v1), v1);
// test casting
Quaternion<float> q1f = q1.template cast<float>();
VERIFY_IS_APPROX(q1f.template cast<Scalar>(),q1);
Quaternion<double> q1d = q1.template cast<double>();
VERIFY_IS_APPROX(q1d.template cast<Scalar>(),q1);
}
template<typename Scalar> void mapQuaternion(void){
typedef Map<Quaternion<Scalar>, Aligned> MQuaternionA;
typedef Map<Quaternion<Scalar> > MQuaternionUA;
typedef Map<const Quaternion<Scalar> > MCQuaternionUA;
typedef Quaternion<Scalar> Quaternionx;
EIGEN_ALIGN16 Scalar array1[4];
EIGEN_ALIGN16 Scalar array2[4];
EIGEN_ALIGN16 Scalar array3[4+1];
Scalar* array3unaligned = array3+1;
// std::cerr << array1 << " " << array2 << " " << array3 << "\n";
MQuaternionA(array1).coeffs().setRandom();
(MQuaternionA(array2)) = MQuaternionA(array1);
(MQuaternionUA(array3unaligned)) = MQuaternionA(array1);
Quaternionx q1 = MQuaternionA(array1);
Quaternionx q2 = MQuaternionA(array2);
Quaternionx q3 = MQuaternionUA(array3unaligned);
Quaternionx q4 = MCQuaternionUA(array3unaligned);
VERIFY_IS_APPROX(q1.coeffs(), q2.coeffs());
VERIFY_IS_APPROX(q1.coeffs(), q3.coeffs());
VERIFY_IS_APPROX(q4.coeffs(), q3.coeffs());
#ifdef EIGEN_VECTORIZE
if(internal::packet_traits<Scalar>::Vectorizable)
VERIFY_RAISES_ASSERT((MQuaternionA(array3unaligned)));
#endif
}
template<typename Scalar> void quaternionAlignment(void){
typedef Quaternion<Scalar,AutoAlign> QuaternionA;
typedef Quaternion<Scalar,DontAlign> QuaternionUA;
EIGEN_ALIGN16 Scalar array1[4];
EIGEN_ALIGN16 Scalar array2[4];
EIGEN_ALIGN16 Scalar array3[4+1];
Scalar* arrayunaligned = array3+1;
QuaternionA *q1 = ::new(reinterpret_cast<void*>(array1)) QuaternionA;
QuaternionUA *q2 = ::new(reinterpret_cast<void*>(array2)) QuaternionUA;
QuaternionUA *q3 = ::new(reinterpret_cast<void*>(arrayunaligned)) QuaternionUA;
q1->coeffs().setRandom();
*q2 = *q1;
*q3 = *q1;
VERIFY_IS_APPROX(q1->coeffs(), q2->coeffs());
VERIFY_IS_APPROX(q1->coeffs(), q3->coeffs());
#if defined(EIGEN_VECTORIZE) && EIGEN_ALIGN_STATICALLY
if(internal::packet_traits<Scalar>::Vectorizable)
VERIFY_RAISES_ASSERT((::new(reinterpret_cast<void*>(arrayunaligned)) QuaternionA));
#endif
}
template<typename PlainObjectType> void check_const_correctness(const PlainObjectType&)
{
// there's a lot that we can't test here while still having this test compile!
// the only possible approach would be to run a script trying to compile stuff and checking that it fails.
// CMake can help with that.
// verify that map-to-const don't have LvalueBit
typedef typename internal::add_const<PlainObjectType>::type ConstPlainObjectType;
VERIFY( !(internal::traits<Map<ConstPlainObjectType> >::Flags & LvalueBit) );
VERIFY( !(internal::traits<Map<ConstPlainObjectType, Aligned> >::Flags & LvalueBit) );
VERIFY( !(Map<ConstPlainObjectType>::Flags & LvalueBit) );
VERIFY( !(Map<ConstPlainObjectType, Aligned>::Flags & LvalueBit) );
}
void test_geo_quaternion()
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1(( quaternion<float,AutoAlign>() ));
CALL_SUBTEST_1( check_const_correctness(Quaternionf()) );
CALL_SUBTEST_2(( quaternion<double,AutoAlign>() ));
CALL_SUBTEST_2( check_const_correctness(Quaterniond()) );
CALL_SUBTEST_3(( quaternion<float,DontAlign>() ));
CALL_SUBTEST_4(( quaternion<double,DontAlign>() ));
CALL_SUBTEST_5(( quaternionAlignment<float>() ));
CALL_SUBTEST_6(( quaternionAlignment<double>() ));
CALL_SUBTEST_1( mapQuaternion<float>() );
CALL_SUBTEST_2( mapQuaternion<double>() );
}
}
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