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290 lines
9.9 KiB
290 lines
9.9 KiB
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
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// Copyright (C) 2009 Mathieu Gautier <mathieu.gautier@cea.fr>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#include "main.h"
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#include <Eigen/Geometry>
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#include <Eigen/LU>
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#include <Eigen/SVD>
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template<typename T> T bounded_acos(T v)
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{
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using std::acos;
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using std::min;
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using std::max;
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return acos((max)(T(-1),(min)(v,T(1))));
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}
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template<typename QuatType> void check_slerp(const QuatType& q0, const QuatType& q1)
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{
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using std::abs;
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typedef typename QuatType::Scalar Scalar;
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typedef AngleAxis<Scalar> AA;
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Scalar largeEps = test_precision<Scalar>();
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Scalar theta_tot = AA(q1*q0.inverse()).angle();
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if(theta_tot>EIGEN_PI)
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theta_tot = Scalar(2.*EIGEN_PI)-theta_tot;
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for(Scalar t=0; t<=Scalar(1.001); t+=Scalar(0.1))
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{
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QuatType q = q0.slerp(t,q1);
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Scalar theta = AA(q*q0.inverse()).angle();
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VERIFY(abs(q.norm() - 1) < largeEps);
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if(theta_tot==0) VERIFY(theta_tot==0);
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else VERIFY(abs(theta - t * theta_tot) < largeEps);
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}
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}
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template<typename Scalar, int Options> void quaternion(void)
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{
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/* this test covers the following files:
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Quaternion.h
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*/
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using std::abs;
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typedef Matrix<Scalar,3,1> Vector3;
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typedef Matrix<Scalar,3,3> Matrix3;
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typedef Matrix<Scalar,4,1> Vector4;
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typedef Quaternion<Scalar,Options> Quaternionx;
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typedef AngleAxis<Scalar> AngleAxisx;
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Scalar largeEps = test_precision<Scalar>();
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if (internal::is_same<Scalar,float>::value)
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largeEps = 1e-3f;
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Scalar eps = internal::random<Scalar>() * Scalar(1e-2);
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Vector3 v0 = Vector3::Random(),
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v1 = Vector3::Random(),
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v2 = Vector3::Random(),
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v3 = Vector3::Random();
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Scalar a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI)),
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b = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI));
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// Quaternion: Identity(), setIdentity();
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Quaternionx q1, q2;
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q2.setIdentity();
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VERIFY_IS_APPROX(Quaternionx(Quaternionx::Identity()).coeffs(), q2.coeffs());
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q1.coeffs().setRandom();
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VERIFY_IS_APPROX(q1.coeffs(), (q1*q2).coeffs());
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// concatenation
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q1 *= q2;
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q1 = AngleAxisx(a, v0.normalized());
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q2 = AngleAxisx(a, v1.normalized());
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// angular distance
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Scalar refangle = abs(AngleAxisx(q1.inverse()*q2).angle());
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if (refangle>Scalar(EIGEN_PI))
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refangle = Scalar(2)*Scalar(EIGEN_PI) - refangle;
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if((q1.coeffs()-q2.coeffs()).norm() > 10*largeEps)
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{
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VERIFY_IS_MUCH_SMALLER_THAN(abs(q1.angularDistance(q2) - refangle), Scalar(1));
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}
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// rotation matrix conversion
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VERIFY_IS_APPROX(q1 * v2, q1.toRotationMatrix() * v2);
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VERIFY_IS_APPROX(q1 * q2 * v2,
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q1.toRotationMatrix() * q2.toRotationMatrix() * v2);
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VERIFY( (q2*q1).isApprox(q1*q2, largeEps)
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|| !(q2 * q1 * v2).isApprox(q1.toRotationMatrix() * q2.toRotationMatrix() * v2));
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q2 = q1.toRotationMatrix();
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VERIFY_IS_APPROX(q1*v1,q2*v1);
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Matrix3 rot1(q1);
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VERIFY_IS_APPROX(q1*v1,rot1*v1);
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Quaternionx q3(rot1.transpose()*rot1);
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VERIFY_IS_APPROX(q3*v1,v1);
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// angle-axis conversion
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AngleAxisx aa = AngleAxisx(q1);
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VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1);
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// Do not execute the test if the rotation angle is almost zero, or
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// the rotation axis and v1 are almost parallel.
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if (abs(aa.angle()) > 5*test_precision<Scalar>()
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&& (aa.axis() - v1.normalized()).norm() < 1.99
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&& (aa.axis() + v1.normalized()).norm() < 1.99)
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{
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VERIFY_IS_NOT_APPROX(q1 * v1, Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1);
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}
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// from two vector creation
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VERIFY_IS_APPROX( v2.normalized(),(q2.setFromTwoVectors(v1, v2)*v1).normalized());
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VERIFY_IS_APPROX( v1.normalized(),(q2.setFromTwoVectors(v1, v1)*v1).normalized());
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VERIFY_IS_APPROX(-v1.normalized(),(q2.setFromTwoVectors(v1,-v1)*v1).normalized());
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if (internal::is_same<Scalar,double>::value)
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{
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v3 = (v1.array()+eps).matrix();
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VERIFY_IS_APPROX( v3.normalized(),(q2.setFromTwoVectors(v1, v3)*v1).normalized());
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VERIFY_IS_APPROX(-v3.normalized(),(q2.setFromTwoVectors(v1,-v3)*v1).normalized());
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}
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// from two vector creation static function
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VERIFY_IS_APPROX( v2.normalized(),(Quaternionx::FromTwoVectors(v1, v2)*v1).normalized());
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VERIFY_IS_APPROX( v1.normalized(),(Quaternionx::FromTwoVectors(v1, v1)*v1).normalized());
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VERIFY_IS_APPROX(-v1.normalized(),(Quaternionx::FromTwoVectors(v1,-v1)*v1).normalized());
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if (internal::is_same<Scalar,double>::value)
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{
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v3 = (v1.array()+eps).matrix();
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VERIFY_IS_APPROX( v3.normalized(),(Quaternionx::FromTwoVectors(v1, v3)*v1).normalized());
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VERIFY_IS_APPROX(-v3.normalized(),(Quaternionx::FromTwoVectors(v1,-v3)*v1).normalized());
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}
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// inverse and conjugate
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VERIFY_IS_APPROX(q1 * (q1.inverse() * v1), v1);
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VERIFY_IS_APPROX(q1 * (q1.conjugate() * v1), v1);
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// test casting
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Quaternion<float> q1f = q1.template cast<float>();
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VERIFY_IS_APPROX(q1f.template cast<Scalar>(),q1);
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Quaternion<double> q1d = q1.template cast<double>();
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VERIFY_IS_APPROX(q1d.template cast<Scalar>(),q1);
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// test bug 369 - improper alignment.
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Quaternionx *q = new Quaternionx;
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delete q;
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q1 = AngleAxisx(a, v0.normalized());
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q2 = AngleAxisx(b, v1.normalized());
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check_slerp(q1,q2);
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q1 = AngleAxisx(b, v1.normalized());
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q2 = AngleAxisx(b+Scalar(EIGEN_PI), v1.normalized());
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check_slerp(q1,q2);
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q1 = AngleAxisx(b, v1.normalized());
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q2 = AngleAxisx(-b, -v1.normalized());
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check_slerp(q1,q2);
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q1.coeffs() = Vector4::Random().normalized();
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q2.coeffs() = -q1.coeffs();
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check_slerp(q1,q2);
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}
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template<typename Scalar> void mapQuaternion(void){
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typedef Map<Quaternion<Scalar>, Aligned> MQuaternionA;
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typedef Map<const Quaternion<Scalar>, Aligned> MCQuaternionA;
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typedef Map<Quaternion<Scalar> > MQuaternionUA;
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typedef Map<const Quaternion<Scalar> > MCQuaternionUA;
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typedef Quaternion<Scalar> Quaternionx;
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typedef Matrix<Scalar,3,1> Vector3;
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typedef AngleAxis<Scalar> AngleAxisx;
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Vector3 v0 = Vector3::Random(),
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v1 = Vector3::Random();
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Scalar a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI));
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EIGEN_ALIGN_MAX Scalar array1[4];
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EIGEN_ALIGN_MAX Scalar array2[4];
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EIGEN_ALIGN_MAX Scalar array3[4+1];
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Scalar* array3unaligned = array3+1;
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MQuaternionA mq1(array1);
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MCQuaternionA mcq1(array1);
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MQuaternionA mq2(array2);
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MQuaternionUA mq3(array3unaligned);
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MCQuaternionUA mcq3(array3unaligned);
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// std::cerr << array1 << " " << array2 << " " << array3 << "\n";
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mq1 = AngleAxisx(a, v0.normalized());
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mq2 = mq1;
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mq3 = mq1;
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Quaternionx q1 = mq1;
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Quaternionx q2 = mq2;
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Quaternionx q3 = mq3;
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Quaternionx q4 = MCQuaternionUA(array3unaligned);
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VERIFY_IS_APPROX(q1.coeffs(), q2.coeffs());
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VERIFY_IS_APPROX(q1.coeffs(), q3.coeffs());
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VERIFY_IS_APPROX(q4.coeffs(), q3.coeffs());
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#ifdef EIGEN_VECTORIZE
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if(internal::packet_traits<Scalar>::Vectorizable)
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VERIFY_RAISES_ASSERT((MQuaternionA(array3unaligned)));
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#endif
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VERIFY_IS_APPROX(mq1 * (mq1.inverse() * v1), v1);
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VERIFY_IS_APPROX(mq1 * (mq1.conjugate() * v1), v1);
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VERIFY_IS_APPROX(mcq1 * (mcq1.inverse() * v1), v1);
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VERIFY_IS_APPROX(mcq1 * (mcq1.conjugate() * v1), v1);
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VERIFY_IS_APPROX(mq3 * (mq3.inverse() * v1), v1);
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VERIFY_IS_APPROX(mq3 * (mq3.conjugate() * v1), v1);
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VERIFY_IS_APPROX(mcq3 * (mcq3.inverse() * v1), v1);
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VERIFY_IS_APPROX(mcq3 * (mcq3.conjugate() * v1), v1);
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VERIFY_IS_APPROX(mq1*mq2, q1*q2);
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VERIFY_IS_APPROX(mq3*mq2, q3*q2);
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VERIFY_IS_APPROX(mcq1*mq2, q1*q2);
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VERIFY_IS_APPROX(mcq3*mq2, q3*q2);
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}
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template<typename Scalar> void quaternionAlignment(void){
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typedef Quaternion<Scalar,AutoAlign> QuaternionA;
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typedef Quaternion<Scalar,DontAlign> QuaternionUA;
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EIGEN_ALIGN_MAX Scalar array1[4];
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EIGEN_ALIGN_MAX Scalar array2[4];
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EIGEN_ALIGN_MAX Scalar array3[4+1];
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Scalar* arrayunaligned = array3+1;
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QuaternionA *q1 = ::new(reinterpret_cast<void*>(array1)) QuaternionA;
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QuaternionUA *q2 = ::new(reinterpret_cast<void*>(array2)) QuaternionUA;
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QuaternionUA *q3 = ::new(reinterpret_cast<void*>(arrayunaligned)) QuaternionUA;
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q1->coeffs().setRandom();
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*q2 = *q1;
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*q3 = *q1;
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VERIFY_IS_APPROX(q1->coeffs(), q2->coeffs());
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VERIFY_IS_APPROX(q1->coeffs(), q3->coeffs());
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#if defined(EIGEN_VECTORIZE) && EIGEN_MAX_STATIC_ALIGN_BYTES>0
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if(internal::packet_traits<Scalar>::Vectorizable && internal::packet_traits<Scalar>::size<=4)
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VERIFY_RAISES_ASSERT((::new(reinterpret_cast<void*>(arrayunaligned)) QuaternionA));
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#endif
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}
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template<typename PlainObjectType> void check_const_correctness(const PlainObjectType&)
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{
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// there's a lot that we can't test here while still having this test compile!
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// the only possible approach would be to run a script trying to compile stuff and checking that it fails.
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// CMake can help with that.
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// verify that map-to-const don't have LvalueBit
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typedef typename internal::add_const<PlainObjectType>::type ConstPlainObjectType;
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VERIFY( !(internal::traits<Map<ConstPlainObjectType> >::Flags & LvalueBit) );
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VERIFY( !(internal::traits<Map<ConstPlainObjectType, Aligned> >::Flags & LvalueBit) );
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VERIFY( !(Map<ConstPlainObjectType>::Flags & LvalueBit) );
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VERIFY( !(Map<ConstPlainObjectType, Aligned>::Flags & LvalueBit) );
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}
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void test_geo_quaternion()
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{
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for(int i = 0; i < g_repeat; i++) {
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CALL_SUBTEST_1(( quaternion<float,AutoAlign>() ));
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CALL_SUBTEST_1( check_const_correctness(Quaternionf()) );
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CALL_SUBTEST_2(( quaternion<double,AutoAlign>() ));
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CALL_SUBTEST_2( check_const_correctness(Quaterniond()) );
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CALL_SUBTEST_3(( quaternion<float,DontAlign>() ));
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CALL_SUBTEST_4(( quaternion<double,DontAlign>() ));
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CALL_SUBTEST_5(( quaternionAlignment<float>() ));
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CALL_SUBTEST_6(( quaternionAlignment<double>() ));
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CALL_SUBTEST_1( mapQuaternion<float>() );
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CALL_SUBTEST_2( mapQuaternion<double>() );
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}
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}
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