433 lines
15 KiB
C++
433 lines
15 KiB
C++
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// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra. Eigen itself is part of the KDE project.
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//
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// Copyright (C) 2008 Gael Guennebaud <g.gael@free.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 Scalar> void geometry(void)
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{
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/* this test covers the following files:
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Cross.h Quaternion.h, Transform.cpp
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*/
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typedef Matrix<Scalar,2,2> Matrix2;
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typedef Matrix<Scalar,3,3> Matrix3;
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typedef Matrix<Scalar,4,4> Matrix4;
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typedef Matrix<Scalar,2,1> Vector2;
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typedef Matrix<Scalar,3,1> Vector3;
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typedef Matrix<Scalar,4,1> Vector4;
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typedef Quaternion<Scalar> Quaternionx;
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typedef AngleAxis<Scalar> AngleAxisx;
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typedef Transform<Scalar,2> Transform2;
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typedef Transform<Scalar,3> Transform3;
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typedef Scaling<Scalar,2> Scaling2;
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typedef Scaling<Scalar,3> Scaling3;
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typedef Translation<Scalar,2> Translation2;
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typedef Translation<Scalar,3> Translation3;
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Scalar largeEps = test_precision<Scalar>();
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if (ei_is_same_type<Scalar,float>::ret)
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largeEps = 1e-2f;
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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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Vector2 u0 = Vector2::Random();
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Matrix3 matrot1;
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Scalar a = ei_random<Scalar>(-Scalar(M_PI), Scalar(M_PI));
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// cross product
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VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(v2).eigen2_dot(v1), Scalar(1));
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Matrix3 m;
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m << v0.normalized(),
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(v0.cross(v1)).normalized(),
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(v0.cross(v1).cross(v0)).normalized();
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VERIFY(m.isUnitary());
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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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// unitOrthogonal
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VERIFY_IS_MUCH_SMALLER_THAN(u0.unitOrthogonal().eigen2_dot(u0), Scalar(1));
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VERIFY_IS_MUCH_SMALLER_THAN(v0.unitOrthogonal().eigen2_dot(v0), Scalar(1));
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VERIFY_IS_APPROX(u0.unitOrthogonal().norm(), Scalar(1));
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VERIFY_IS_APPROX(v0.unitOrthogonal().norm(), Scalar(1));
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VERIFY_IS_APPROX(v0, AngleAxisx(a, v0.normalized()) * v0);
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VERIFY_IS_APPROX(-v0, AngleAxisx(Scalar(M_PI), v0.unitOrthogonal()) * v0);
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VERIFY_IS_APPROX(ei_cos(a)*v0.squaredNorm(), v0.eigen2_dot(AngleAxisx(a, v0.unitOrthogonal()) * v0));
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m = AngleAxisx(a, v0.normalized()).toRotationMatrix().adjoint();
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VERIFY_IS_APPROX(Matrix3::Identity(), m * AngleAxisx(a, v0.normalized()));
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VERIFY_IS_APPROX(Matrix3::Identity(), AngleAxisx(a, v0.normalized()) * m);
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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 = ei_abs(AngleAxisx(q1.inverse()*q2).angle());
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if (refangle>Scalar(M_PI))
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refangle = Scalar(2)*Scalar(M_PI) - refangle;
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if((q1.coeffs()-q2.coeffs()).norm() > 10*largeEps)
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{
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VERIFY(ei_isApprox(q1.angularDistance(q2), refangle, largeEps));
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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) || !(q2 * q1 * v2).isApprox(
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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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matrot1 = AngleAxisx(Scalar(0.1), Vector3::UnitX())
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* AngleAxisx(Scalar(0.2), Vector3::UnitY())
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* AngleAxisx(Scalar(0.3), Vector3::UnitZ());
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VERIFY_IS_APPROX(matrot1 * v1,
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AngleAxisx(Scalar(0.1), Vector3(1,0,0)).toRotationMatrix()
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* (AngleAxisx(Scalar(0.2), Vector3(0,1,0)).toRotationMatrix()
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* (AngleAxisx(Scalar(0.3), Vector3(0,0,1)).toRotationMatrix() * v1)));
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// angle-axis conversion
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AngleAxisx aa = q1;
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VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1);
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VERIFY_IS_NOT_APPROX(q1 * v1, Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1);
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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(v2.normalized(),(q2.setFromTwoVectors(v1,v2)*v1).normalized());
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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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// AngleAxis
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VERIFY_IS_APPROX(AngleAxisx(a,v1.normalized()).toRotationMatrix(),
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Quaternionx(AngleAxisx(a,v1.normalized())).toRotationMatrix());
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AngleAxisx aa1;
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m = q1.toRotationMatrix();
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aa1 = m;
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VERIFY_IS_APPROX(AngleAxisx(m).toRotationMatrix(),
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Quaternionx(m).toRotationMatrix());
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// Transform
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// TODO complete the tests !
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a = 0;
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while (ei_abs(a)<Scalar(0.1))
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a = ei_random<Scalar>(-Scalar(0.4)*Scalar(M_PI), Scalar(0.4)*Scalar(M_PI));
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q1 = AngleAxisx(a, v0.normalized());
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Transform3 t0, t1, t2;
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// first test setIdentity() and Identity()
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t0.setIdentity();
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VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());
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t0.matrix().setZero();
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t0 = Transform3::Identity();
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VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());
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t0.linear() = q1.toRotationMatrix();
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t1.setIdentity();
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t1.linear() = q1.toRotationMatrix();
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v0 << 50, 2, 1;//= ei_random_matrix<Vector3>().cwiseProduct(Vector3(10,2,0.5));
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t0.scale(v0);
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t1.prescale(v0);
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VERIFY_IS_APPROX( (t0 * Vector3(1,0,0)).norm(), v0.x());
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//VERIFY(!ei_isApprox((t1 * Vector3(1,0,0)).norm(), v0.x()));
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t0.setIdentity();
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t1.setIdentity();
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v1 << 1, 2, 3;
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t0.linear() = q1.toRotationMatrix();
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t0.pretranslate(v0);
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t0.scale(v1);
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t1.linear() = q1.conjugate().toRotationMatrix();
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t1.prescale(v1.cwise().inverse());
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t1.translate(-v0);
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VERIFY((t0.matrix() * t1.matrix()).isIdentity(test_precision<Scalar>()));
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t1.fromPositionOrientationScale(v0, q1, v1);
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VERIFY_IS_APPROX(t1.matrix(), t0.matrix());
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VERIFY_IS_APPROX(t1*v1, t0*v1);
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t0.setIdentity(); t0.scale(v0).rotate(q1.toRotationMatrix());
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t1.setIdentity(); t1.scale(v0).rotate(q1);
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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t0.setIdentity(); t0.scale(v0).rotate(AngleAxisx(q1));
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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VERIFY_IS_APPROX(t0.scale(a).matrix(), t1.scale(Vector3::Constant(a)).matrix());
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VERIFY_IS_APPROX(t0.prescale(a).matrix(), t1.prescale(Vector3::Constant(a)).matrix());
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// More transform constructors, operator=, operator*=
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Matrix3 mat3 = Matrix3::Random();
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Matrix4 mat4;
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mat4 << mat3 , Vector3::Zero() , Vector4::Zero().transpose();
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Transform3 tmat3(mat3), tmat4(mat4);
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tmat4.matrix()(3,3) = Scalar(1);
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VERIFY_IS_APPROX(tmat3.matrix(), tmat4.matrix());
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Scalar a3 = ei_random<Scalar>(-Scalar(M_PI), Scalar(M_PI));
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Vector3 v3 = Vector3::Random().normalized();
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AngleAxisx aa3(a3, v3);
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Transform3 t3(aa3);
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Transform3 t4;
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t4 = aa3;
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VERIFY_IS_APPROX(t3.matrix(), t4.matrix());
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t4.rotate(AngleAxisx(-a3,v3));
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VERIFY_IS_APPROX(t4.matrix(), Matrix4::Identity());
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t4 *= aa3;
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VERIFY_IS_APPROX(t3.matrix(), t4.matrix());
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v3 = Vector3::Random();
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Translation3 tv3(v3);
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Transform3 t5(tv3);
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t4 = tv3;
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VERIFY_IS_APPROX(t5.matrix(), t4.matrix());
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t4.translate(-v3);
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VERIFY_IS_APPROX(t4.matrix(), Matrix4::Identity());
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t4 *= tv3;
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VERIFY_IS_APPROX(t5.matrix(), t4.matrix());
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Scaling3 sv3(v3);
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Transform3 t6(sv3);
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t4 = sv3;
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VERIFY_IS_APPROX(t6.matrix(), t4.matrix());
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t4.scale(v3.cwise().inverse());
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VERIFY_IS_APPROX(t4.matrix(), Matrix4::Identity());
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t4 *= sv3;
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VERIFY_IS_APPROX(t6.matrix(), t4.matrix());
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// matrix * transform
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VERIFY_IS_APPROX(Transform3(t3.matrix()*t4).matrix(), Transform3(t3*t4).matrix());
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// chained Transform product
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VERIFY_IS_APPROX(((t3*t4)*t5).matrix(), (t3*(t4*t5)).matrix());
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// check that Transform product doesn't have aliasing problems
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t5 = t4;
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t5 = t5*t5;
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VERIFY_IS_APPROX(t5, t4*t4);
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// 2D transformation
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Transform2 t20, t21;
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Vector2 v20 = Vector2::Random();
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Vector2 v21 = Vector2::Random();
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for (int k=0; k<2; ++k)
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if (ei_abs(v21[k])<Scalar(1e-3)) v21[k] = Scalar(1e-3);
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t21.setIdentity();
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t21.linear() = Rotation2D<Scalar>(a).toRotationMatrix();
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VERIFY_IS_APPROX(t20.fromPositionOrientationScale(v20,a,v21).matrix(),
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t21.pretranslate(v20).scale(v21).matrix());
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t21.setIdentity();
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t21.linear() = Rotation2D<Scalar>(-a).toRotationMatrix();
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VERIFY( (t20.fromPositionOrientationScale(v20,a,v21)
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* (t21.prescale(v21.cwise().inverse()).translate(-v20))).matrix().isIdentity(test_precision<Scalar>()) );
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// Transform - new API
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// 3D
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t0.setIdentity();
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t0.rotate(q1).scale(v0).translate(v0);
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// mat * scaling and mat * translation
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t1 = (Matrix3(q1) * Scaling3(v0)) * Translation3(v0);
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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// mat * transformation and scaling * translation
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t1 = Matrix3(q1) * (Scaling3(v0) * Translation3(v0));
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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t0.setIdentity();
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t0.prerotate(q1).prescale(v0).pretranslate(v0);
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// translation * scaling and transformation * mat
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t1 = (Translation3(v0) * Scaling3(v0)) * Matrix3(q1);
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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// scaling * mat and translation * mat
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t1 = Translation3(v0) * (Scaling3(v0) * Matrix3(q1));
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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t0.setIdentity();
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t0.scale(v0).translate(v0).rotate(q1);
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// translation * mat and scaling * transformation
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t1 = Scaling3(v0) * (Translation3(v0) * Matrix3(q1));
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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// transformation * scaling
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t0.scale(v0);
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t1 = t1 * Scaling3(v0);
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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// transformation * translation
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t0.translate(v0);
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t1 = t1 * Translation3(v0);
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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// translation * transformation
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t0.pretranslate(v0);
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t1 = Translation3(v0) * t1;
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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// transform * quaternion
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t0.rotate(q1);
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t1 = t1 * q1;
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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// translation * quaternion
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t0.translate(v1).rotate(q1);
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t1 = t1 * (Translation3(v1) * q1);
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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// scaling * quaternion
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t0.scale(v1).rotate(q1);
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t1 = t1 * (Scaling3(v1) * q1);
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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// quaternion * transform
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t0.prerotate(q1);
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t1 = q1 * t1;
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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// quaternion * translation
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t0.rotate(q1).translate(v1);
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t1 = t1 * (q1 * Translation3(v1));
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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// quaternion * scaling
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t0.rotate(q1).scale(v1);
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t1 = t1 * (q1 * Scaling3(v1));
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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|
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||
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// translation * vector
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t0.setIdentity();
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t0.translate(v0);
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VERIFY_IS_APPROX(t0 * v1, Translation3(v0) * v1);
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||
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// scaling * vector
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t0.setIdentity();
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t0.scale(v0);
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VERIFY_IS_APPROX(t0 * v1, Scaling3(v0) * v1);
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|
|
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||
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// test transform inversion
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t0.setIdentity();
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|
t0.translate(v0);
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|
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t0.linear().setRandom();
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|
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VERIFY_IS_APPROX(t0.inverse(Affine), t0.matrix().inverse());
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||
|
|
t0.setIdentity();
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||
|
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t0.translate(v0).rotate(q1);
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|
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VERIFY_IS_APPROX(t0.inverse(Isometry), t0.matrix().inverse());
|
||
|
|
|
||
|
|
// test extract rotation and scaling
|
||
|
|
t0.setIdentity();
|
||
|
|
t0.translate(v0).rotate(q1).scale(v1);
|
||
|
|
VERIFY_IS_APPROX(t0.rotation() * v1, Matrix3(q1) * v1);
|
||
|
|
|
||
|
|
Matrix3 mat_rotation, mat_scaling;
|
||
|
|
t0.setIdentity();
|
||
|
|
t0.translate(v0).rotate(q1).scale(v1);
|
||
|
|
t0.computeRotationScaling(&mat_rotation, &mat_scaling);
|
||
|
|
VERIFY_IS_APPROX(t0.linear(), mat_rotation * mat_scaling);
|
||
|
|
VERIFY_IS_APPROX(mat_rotation*mat_rotation.adjoint(), Matrix3::Identity());
|
||
|
|
VERIFY_IS_APPROX(mat_rotation.determinant(), Scalar(1));
|
||
|
|
t0.computeScalingRotation(&mat_scaling, &mat_rotation);
|
||
|
|
VERIFY_IS_APPROX(t0.linear(), mat_scaling * mat_rotation);
|
||
|
|
VERIFY_IS_APPROX(mat_rotation*mat_rotation.adjoint(), Matrix3::Identity());
|
||
|
|
VERIFY_IS_APPROX(mat_rotation.determinant(), Scalar(1));
|
||
|
|
|
||
|
|
// test casting
|
||
|
|
Transform<float,3> t1f = t1.template cast<float>();
|
||
|
|
VERIFY_IS_APPROX(t1f.template cast<Scalar>(),t1);
|
||
|
|
Transform<double,3> t1d = t1.template cast<double>();
|
||
|
|
VERIFY_IS_APPROX(t1d.template cast<Scalar>(),t1);
|
||
|
|
|
||
|
|
Translation3 tr1(v0);
|
||
|
|
Translation<float,3> tr1f = tr1.template cast<float>();
|
||
|
|
VERIFY_IS_APPROX(tr1f.template cast<Scalar>(),tr1);
|
||
|
|
Translation<double,3> tr1d = tr1.template cast<double>();
|
||
|
|
VERIFY_IS_APPROX(tr1d.template cast<Scalar>(),tr1);
|
||
|
|
|
||
|
|
Scaling3 sc1(v0);
|
||
|
|
Scaling<float,3> sc1f = sc1.template cast<float>();
|
||
|
|
VERIFY_IS_APPROX(sc1f.template cast<Scalar>(),sc1);
|
||
|
|
Scaling<double,3> sc1d = sc1.template cast<double>();
|
||
|
|
VERIFY_IS_APPROX(sc1d.template cast<Scalar>(),sc1);
|
||
|
|
|
||
|
|
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);
|
||
|
|
|
||
|
|
AngleAxis<float> aa1f = aa1.template cast<float>();
|
||
|
|
VERIFY_IS_APPROX(aa1f.template cast<Scalar>(),aa1);
|
||
|
|
AngleAxis<double> aa1d = aa1.template cast<double>();
|
||
|
|
VERIFY_IS_APPROX(aa1d.template cast<Scalar>(),aa1);
|
||
|
|
|
||
|
|
Rotation2D<Scalar> r2d1(ei_random<Scalar>());
|
||
|
|
Rotation2D<float> r2d1f = r2d1.template cast<float>();
|
||
|
|
VERIFY_IS_APPROX(r2d1f.template cast<Scalar>(),r2d1);
|
||
|
|
Rotation2D<double> r2d1d = r2d1.template cast<double>();
|
||
|
|
VERIFY_IS_APPROX(r2d1d.template cast<Scalar>(),r2d1);
|
||
|
|
|
||
|
|
m = q1;
|
||
|
|
// m.col(1) = Vector3(0,ei_random<Scalar>(),ei_random<Scalar>()).normalized();
|
||
|
|
// m.col(0) = Vector3(-1,0,0).normalized();
|
||
|
|
// m.col(2) = m.col(0).cross(m.col(1));
|
||
|
|
#define VERIFY_EULER(I,J,K, X,Y,Z) { \
|
||
|
|
Vector3 ea = m.eulerAngles(I,J,K); \
|
||
|
|
Matrix3 m1 = Matrix3(AngleAxisx(ea[0], Vector3::Unit##X()) * AngleAxisx(ea[1], Vector3::Unit##Y()) * AngleAxisx(ea[2], Vector3::Unit##Z())); \
|
||
|
|
VERIFY_IS_APPROX(m, m1); \
|
||
|
|
VERIFY_IS_APPROX(m, Matrix3(AngleAxisx(ea[0], Vector3::Unit##X()) * AngleAxisx(ea[1], Vector3::Unit##Y()) * AngleAxisx(ea[2], Vector3::Unit##Z()))); \
|
||
|
|
}
|
||
|
|
VERIFY_EULER(0,1,2, X,Y,Z);
|
||
|
|
VERIFY_EULER(0,1,0, X,Y,X);
|
||
|
|
VERIFY_EULER(0,2,1, X,Z,Y);
|
||
|
|
VERIFY_EULER(0,2,0, X,Z,X);
|
||
|
|
|
||
|
|
VERIFY_EULER(1,2,0, Y,Z,X);
|
||
|
|
VERIFY_EULER(1,2,1, Y,Z,Y);
|
||
|
|
VERIFY_EULER(1,0,2, Y,X,Z);
|
||
|
|
VERIFY_EULER(1,0,1, Y,X,Y);
|
||
|
|
|
||
|
|
VERIFY_EULER(2,0,1, Z,X,Y);
|
||
|
|
VERIFY_EULER(2,0,2, Z,X,Z);
|
||
|
|
VERIFY_EULER(2,1,0, Z,Y,X);
|
||
|
|
VERIFY_EULER(2,1,2, Z,Y,Z);
|
||
|
|
|
||
|
|
// colwise/rowwise cross product
|
||
|
|
mat3.setRandom();
|
||
|
|
Vector3 vec3 = Vector3::Random();
|
||
|
|
Matrix3 mcross;
|
||
|
|
int i = ei_random<int>(0,2);
|
||
|
|
mcross = mat3.colwise().cross(vec3);
|
||
|
|
VERIFY_IS_APPROX(mcross.col(i), mat3.col(i).cross(vec3));
|
||
|
|
mcross = mat3.rowwise().cross(vec3);
|
||
|
|
VERIFY_IS_APPROX(mcross.row(i), mat3.row(i).cross(vec3));
|
||
|
|
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
void test_eigen2_geometry()
|
||
|
|
{
|
||
|
|
for(int i = 0; i < g_repeat; i++) {
|
||
|
|
CALL_SUBTEST_1( geometry<float>() );
|
||
|
|
CALL_SUBTEST_2( geometry<double>() );
|
||
|
|
}
|
||
|
|
}
|