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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>
//
// 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
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#include "main.h"
#include <Eigen/Geometry>
#include <Eigen/LU>
#include <Eigen/SVD>
template<typename T> T bounded_acos(T v)
{
using std::acos;
using std::min;
using std::max;
return acos((max)(T(-1),(min)(v,T(1))));
}
template<typename QuatType> void check_slerp(const QuatType& q0, const QuatType& q1)
{
using std::abs;
typedef typename QuatType::Scalar Scalar;
typedef AngleAxis<Scalar> AA;
Scalar largeEps = test_precision<Scalar>();
Scalar theta_tot = AA(q1*q0.inverse()).angle();
if(theta_tot>EIGEN_PI)
theta_tot = Scalar(2.*EIGEN_PI)-theta_tot;
for(Scalar t=0; t<=Scalar(1.001); t+=Scalar(0.1))
{
QuatType q = q0.slerp(t,q1);
Scalar theta = AA(q*q0.inverse()).angle();
VERIFY(abs(q.norm() - 1) < largeEps);
if(theta_tot==0) VERIFY(theta_tot==0);
else VERIFY(abs(theta - t * theta_tot) < largeEps);
}
}
template<typename Scalar, int Options> void quaternion(void)
{
/* this test covers the following files:
Quaternion.h
*/
using std::abs;
typedef Matrix<Scalar,3,1> Vector3;
typedef Matrix<Scalar,3,3> Matrix3;
typedef Matrix<Scalar,4,1> Vector4;
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(EIGEN_PI), Scalar(EIGEN_PI)),
b = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_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 = abs(AngleAxisx(q1.inverse()*q2).angle());
if (refangle>Scalar(EIGEN_PI))
refangle = Scalar(2)*Scalar(EIGEN_PI) - refangle;
if((q1.coeffs()-q2.coeffs()).norm() > 10*largeEps)
{
VERIFY_IS_MUCH_SMALLER_THAN(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);
Matrix3 rot1(q1);
VERIFY_IS_APPROX(q1*v1,rot1*v1);
Quaternionx q3(rot1.transpose()*rot1);
VERIFY_IS_APPROX(q3*v1,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 (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());
}
// from two vector creation static function
VERIFY_IS_APPROX( v2.normalized(),(Quaternionx::FromTwoVectors(v1, v2)*v1).normalized());
VERIFY_IS_APPROX( v1.normalized(),(Quaternionx::FromTwoVectors(v1, v1)*v1).normalized());
VERIFY_IS_APPROX(-v1.normalized(),(Quaternionx::FromTwoVectors(v1,-v1)*v1).normalized());
if (internal::is_same<Scalar,double>::value)
{
v3 = (v1.array()+eps).matrix();
VERIFY_IS_APPROX( v3.normalized(),(Quaternionx::FromTwoVectors(v1, v3)*v1).normalized());
VERIFY_IS_APPROX(-v3.normalized(),(Quaternionx::FromTwoVectors(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);
// test bug 369 - improper alignment.
Quaternionx *q = new Quaternionx;
delete q;
q1 = AngleAxisx(a, v0.normalized());
q2 = AngleAxisx(b, v1.normalized());
check_slerp(q1,q2);
q1 = AngleAxisx(b, v1.normalized());
q2 = AngleAxisx(b+Scalar(EIGEN_PI), v1.normalized());
check_slerp(q1,q2);
q1 = AngleAxisx(b, v1.normalized());
q2 = AngleAxisx(-b, -v1.normalized());
check_slerp(q1,q2);
q1.coeffs() = Vector4::Random().normalized();
q2.coeffs() = -q1.coeffs();
check_slerp(q1,q2);
}
template<typename Scalar> void mapQuaternion(void){
typedef Map<Quaternion<Scalar>, Aligned> MQuaternionA;
typedef Map<const Quaternion<Scalar>, Aligned> MCQuaternionA;
typedef Map<Quaternion<Scalar> > MQuaternionUA;
typedef Map<const Quaternion<Scalar> > MCQuaternionUA;
typedef Quaternion<Scalar> Quaternionx;
typedef Matrix<Scalar,3,1> Vector3;
typedef AngleAxis<Scalar> AngleAxisx;
Vector3 v0 = Vector3::Random(),
v1 = Vector3::Random();
Scalar a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI));
EIGEN_ALIGN_MAX Scalar array1[4];
EIGEN_ALIGN_MAX Scalar array2[4];
EIGEN_ALIGN_MAX Scalar array3[4+1];
Scalar* array3unaligned = array3+1;
MQuaternionA mq1(array1);
MCQuaternionA mcq1(array1);
MQuaternionA mq2(array2);
MQuaternionUA mq3(array3unaligned);
MCQuaternionUA mcq3(array3unaligned);
// std::cerr << array1 << " " << array2 << " " << array3 << "\n";
mq1 = AngleAxisx(a, v0.normalized());
mq2 = mq1;
mq3 = mq1;
Quaternionx q1 = mq1;
Quaternionx q2 = mq2;
Quaternionx q3 = mq3;
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
VERIFY_IS_APPROX(mq1 * (mq1.inverse() * v1), v1);
VERIFY_IS_APPROX(mq1 * (mq1.conjugate() * v1), v1);
VERIFY_IS_APPROX(mcq1 * (mcq1.inverse() * v1), v1);
VERIFY_IS_APPROX(mcq1 * (mcq1.conjugate() * v1), v1);
VERIFY_IS_APPROX(mq3 * (mq3.inverse() * v1), v1);
VERIFY_IS_APPROX(mq3 * (mq3.conjugate() * v1), v1);
VERIFY_IS_APPROX(mcq3 * (mcq3.inverse() * v1), v1);
VERIFY_IS_APPROX(mcq3 * (mcq3.conjugate() * v1), v1);
VERIFY_IS_APPROX(mq1*mq2, q1*q2);
VERIFY_IS_APPROX(mq3*mq2, q3*q2);
VERIFY_IS_APPROX(mcq1*mq2, q1*q2);
VERIFY_IS_APPROX(mcq3*mq2, q3*q2);
}
template<typename Scalar> void quaternionAlignment(void){
typedef Quaternion<Scalar,AutoAlign> QuaternionA;
typedef Quaternion<Scalar,DontAlign> QuaternionUA;
EIGEN_ALIGN_MAX Scalar array1[4];
EIGEN_ALIGN_MAX Scalar array2[4];
EIGEN_ALIGN_MAX 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_MAX_STATIC_ALIGN_BYTES>0
if(internal::packet_traits<Scalar>::Vectorizable && internal::packet_traits<Scalar>::size<=4)
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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