1c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// This file is part of Eigen, a lightweight C++ template library 2c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// for linear algebra. Eigen itself is part of the KDE project. 3c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// 4c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr> 5c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// 6c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// This Source Code Form is subject to the terms of the Mozilla 7c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Public License v. 2.0. If a copy of the MPL was not distributed 8c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 9c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 10c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#define EIGEN2_SUPPORT_STAGE15_RESOLVE_API_CONFLICTS_WARN 11c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 12c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#include "main.h" 13c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#include <Eigen/Geometry> 14c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#include <Eigen/LU> 15c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#include <Eigen/SVD> 16c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 17c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename Scalar> void geometry(void) 18c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 19c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /* this test covers the following files: 20c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Cross.h Quaternion.h, Transform.cpp 21c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 22c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 23c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar,2,2> Matrix2; 24c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar,3,3> Matrix3; 25c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar,4,4> Matrix4; 26c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar,2,1> Vector2; 27c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar,3,1> Vector3; 28c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar,4,1> Vector4; 29c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef eigen2_Quaternion<Scalar> Quaternionx; 30c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef eigen2_AngleAxis<Scalar> AngleAxisx; 31c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef eigen2_Transform<Scalar,2> Transform2; 32c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef eigen2_Transform<Scalar,3> Transform3; 33c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef eigen2_Scaling<Scalar,2> Scaling2; 34c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef eigen2_Scaling<Scalar,3> Scaling3; 35c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef eigen2_Translation<Scalar,2> Translation2; 36c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef eigen2_Translation<Scalar,3> Translation3; 37c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 38c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scalar largeEps = test_precision<Scalar>(); 39c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (ei_is_same_type<Scalar,float>::ret) 40c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath largeEps = 1e-2f; 41c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 42c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Vector3 v0 = Vector3::Random(), 43c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath v1 = Vector3::Random(), 44c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath v2 = Vector3::Random(); 45c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Vector2 u0 = Vector2::Random(); 46c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Matrix3 matrot1; 47c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 48c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scalar a = ei_random<Scalar>(-Scalar(M_PI), Scalar(M_PI)); 49c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 50c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // cross product 51c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(v2).eigen2_dot(v1), Scalar(1)); 52c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Matrix3 m; 53c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m << v0.normalized(), 54c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath (v0.cross(v1)).normalized(), 55c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath (v0.cross(v1).cross(v0)).normalized(); 56c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY(m.isUnitary()); 57c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 58c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // Quaternion: Identity(), setIdentity(); 59c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Quaternionx q1, q2; 60c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath q2.setIdentity(); 61c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(Quaternionx(Quaternionx::Identity()).coeffs(), q2.coeffs()); 62c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath q1.coeffs().setRandom(); 63c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(q1.coeffs(), (q1*q2).coeffs()); 64c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 65c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // unitOrthogonal 66c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_MUCH_SMALLER_THAN(u0.unitOrthogonal().eigen2_dot(u0), Scalar(1)); 67c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_MUCH_SMALLER_THAN(v0.unitOrthogonal().eigen2_dot(v0), Scalar(1)); 68c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(u0.unitOrthogonal().norm(), Scalar(1)); 69c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(v0.unitOrthogonal().norm(), Scalar(1)); 70c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 71c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 72c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(v0, AngleAxisx(a, v0.normalized()) * v0); 73c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(-v0, AngleAxisx(Scalar(M_PI), v0.unitOrthogonal()) * v0); 74c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(ei_cos(a)*v0.squaredNorm(), v0.eigen2_dot(AngleAxisx(a, v0.unitOrthogonal()) * v0)); 75c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m = AngleAxisx(a, v0.normalized()).toRotationMatrix().adjoint(); 76c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(Matrix3::Identity(), m * AngleAxisx(a, v0.normalized())); 77c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(Matrix3::Identity(), AngleAxisx(a, v0.normalized()) * m); 78c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 79c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath q1 = AngleAxisx(a, v0.normalized()); 80c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath q2 = AngleAxisx(a, v1.normalized()); 81c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 82c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // angular distance 83c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scalar refangle = ei_abs(AngleAxisx(q1.inverse()*q2).angle()); 84c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (refangle>Scalar(M_PI)) 85c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath refangle = Scalar(2)*Scalar(M_PI) - refangle; 86c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 87c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if((q1.coeffs()-q2.coeffs()).norm() > 10*largeEps) 88c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 89c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY(ei_isApprox(q1.angularDistance(q2), refangle, largeEps)); 90c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 91c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 92c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // rotation matrix conversion 93c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(q1 * v2, q1.toRotationMatrix() * v2); 94c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(q1 * q2 * v2, 95c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath q1.toRotationMatrix() * q2.toRotationMatrix() * v2); 96c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 97c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY( (q2*q1).isApprox(q1*q2, largeEps) || !(q2 * q1 * v2).isApprox( 98c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath q1.toRotationMatrix() * q2.toRotationMatrix() * v2)); 99c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 100c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath q2 = q1.toRotationMatrix(); 101c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(q1*v1,q2*v1); 102c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 103c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath matrot1 = AngleAxisx(Scalar(0.1), Vector3::UnitX()) 104c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * AngleAxisx(Scalar(0.2), Vector3::UnitY()) 105c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * AngleAxisx(Scalar(0.3), Vector3::UnitZ()); 106c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(matrot1 * v1, 107c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath AngleAxisx(Scalar(0.1), Vector3(1,0,0)).toRotationMatrix() 108c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * (AngleAxisx(Scalar(0.2), Vector3(0,1,0)).toRotationMatrix() 109c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * (AngleAxisx(Scalar(0.3), Vector3(0,0,1)).toRotationMatrix() * v1))); 110c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 111c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // angle-axis conversion 112c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath AngleAxisx aa = q1; 113c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1); 114c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_NOT_APPROX(q1 * v1, Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1); 115c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 116c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // from two vector creation 117c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(v2.normalized(),(q2.setFromTwoVectors(v1,v2)*v1).normalized()); 118c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(v2.normalized(),(q2.setFromTwoVectors(v1,v2)*v1).normalized()); 119c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 120c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // inverse and conjugate 121c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(q1 * (q1.inverse() * v1), v1); 122c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(q1 * (q1.conjugate() * v1), v1); 123c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 124c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // AngleAxis 125c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(AngleAxisx(a,v1.normalized()).toRotationMatrix(), 126c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Quaternionx(AngleAxisx(a,v1.normalized())).toRotationMatrix()); 127c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 128c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath AngleAxisx aa1; 129c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m = q1.toRotationMatrix(); 130c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath aa1 = m; 131c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(AngleAxisx(m).toRotationMatrix(), 132c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Quaternionx(m).toRotationMatrix()); 133c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 134c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // Transform 135c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // TODO complete the tests ! 136c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath a = 0; 137c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath while (ei_abs(a)<Scalar(0.1)) 138c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath a = ei_random<Scalar>(-Scalar(0.4)*Scalar(M_PI), Scalar(0.4)*Scalar(M_PI)); 139c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath q1 = AngleAxisx(a, v0.normalized()); 140c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Transform3 t0, t1, t2; 141c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // first test setIdentity() and Identity() 142c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.setIdentity(); 143c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity()); 144c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.matrix().setZero(); 145c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0 = Transform3::Identity(); 146c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity()); 147c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 148c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.linear() = q1.toRotationMatrix(); 149c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1.setIdentity(); 150c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1.linear() = q1.toRotationMatrix(); 151c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 152c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath v0 << 50, 2, 1;//= ei_random_matrix<Vector3>().cwiseProduct(Vector3(10,2,0.5)); 153c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.scale(v0); 154c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1.prescale(v0); 155c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 156c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX( (t0 * Vector3(1,0,0)).norm(), v0.x()); 157c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath //VERIFY(!ei_isApprox((t1 * Vector3(1,0,0)).norm(), v0.x())); 158c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 159c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.setIdentity(); 160c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1.setIdentity(); 161c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath v1 << 1, 2, 3; 162c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.linear() = q1.toRotationMatrix(); 163c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.pretranslate(v0); 164c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.scale(v1); 165c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1.linear() = q1.conjugate().toRotationMatrix(); 166c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1.prescale(v1.cwise().inverse()); 167c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1.translate(-v0); 168c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 169c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY((t0.matrix() * t1.matrix()).isIdentity(test_precision<Scalar>())); 170c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 171c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1.fromPositionOrientationScale(v0, q1, v1); 172c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t1.matrix(), t0.matrix()); 173c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t1*v1, t0*v1); 174c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 175c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.setIdentity(); t0.scale(v0).rotate(q1.toRotationMatrix()); 176c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1.setIdentity(); t1.scale(v0).rotate(q1); 177c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); 178c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 179c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.setIdentity(); t0.scale(v0).rotate(AngleAxisx(q1)); 180c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); 181c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 182c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.scale(a).matrix(), t1.scale(Vector3::Constant(a)).matrix()); 183c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.prescale(a).matrix(), t1.prescale(Vector3::Constant(a)).matrix()); 184c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 185c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // More transform constructors, operator=, operator*= 186c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 187c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Matrix3 mat3 = Matrix3::Random(); 188c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Matrix4 mat4; 189c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath mat4 << mat3 , Vector3::Zero() , Vector4::Zero().transpose(); 190c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Transform3 tmat3(mat3), tmat4(mat4); 191c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath tmat4.matrix()(3,3) = Scalar(1); 192c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(tmat3.matrix(), tmat4.matrix()); 193c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 194c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scalar a3 = ei_random<Scalar>(-Scalar(M_PI), Scalar(M_PI)); 195c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Vector3 v3 = Vector3::Random().normalized(); 196c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath AngleAxisx aa3(a3, v3); 197c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Transform3 t3(aa3); 198c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Transform3 t4; 199c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t4 = aa3; 200c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t3.matrix(), t4.matrix()); 201c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t4.rotate(AngleAxisx(-a3,v3)); 202c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t4.matrix(), Matrix4::Identity()); 203c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t4 *= aa3; 204c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t3.matrix(), t4.matrix()); 205c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 206c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath v3 = Vector3::Random(); 207c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Translation3 tv3(v3); 208c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Transform3 t5(tv3); 209c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t4 = tv3; 210c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t5.matrix(), t4.matrix()); 211c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t4.translate(-v3); 212c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t4.matrix(), Matrix4::Identity()); 213c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t4 *= tv3; 214c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t5.matrix(), t4.matrix()); 215c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 216c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scaling3 sv3(v3); 217c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Transform3 t6(sv3); 218c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t4 = sv3; 219c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t6.matrix(), t4.matrix()); 220c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t4.scale(v3.cwise().inverse()); 221c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t4.matrix(), Matrix4::Identity()); 222c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t4 *= sv3; 223c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t6.matrix(), t4.matrix()); 224c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 225c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // matrix * transform 226c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(Transform3(t3.matrix()*t4).matrix(), Transform3(t3*t4).matrix()); 227c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 228c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // chained Transform product 229c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(((t3*t4)*t5).matrix(), (t3*(t4*t5)).matrix()); 230c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 231c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // check that Transform product doesn't have aliasing problems 232c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t5 = t4; 233c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t5 = t5*t5; 234c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t5, t4*t4); 235c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 236c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // 2D transformation 237c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Transform2 t20, t21; 238c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Vector2 v20 = Vector2::Random(); 239c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Vector2 v21 = Vector2::Random(); 240c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath for (int k=0; k<2; ++k) 241c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (ei_abs(v21[k])<Scalar(1e-3)) v21[k] = Scalar(1e-3); 242c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t21.setIdentity(); 243c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t21.linear() = Rotation2D<Scalar>(a).toRotationMatrix(); 244c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t20.fromPositionOrientationScale(v20,a,v21).matrix(), 245c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t21.pretranslate(v20).scale(v21).matrix()); 246c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 247c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t21.setIdentity(); 248c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t21.linear() = Rotation2D<Scalar>(-a).toRotationMatrix(); 249c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY( (t20.fromPositionOrientationScale(v20,a,v21) 250c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * (t21.prescale(v21.cwise().inverse()).translate(-v20))).matrix().isIdentity(test_precision<Scalar>()) ); 251c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 252c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // Transform - new API 253c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // 3D 254c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.setIdentity(); 255c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.rotate(q1).scale(v0).translate(v0); 256c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // mat * scaling and mat * translation 257c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1 = (Matrix3(q1) * Scaling3(v0)) * Translation3(v0); 258c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); 259c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // mat * transformation and scaling * translation 260c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1 = Matrix3(q1) * (Scaling3(v0) * Translation3(v0)); 261c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); 262c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 263c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.setIdentity(); 264c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.prerotate(q1).prescale(v0).pretranslate(v0); 265c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // translation * scaling and transformation * mat 266c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1 = (Translation3(v0) * Scaling3(v0)) * Matrix3(q1); 267c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); 268c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // scaling * mat and translation * mat 269c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1 = Translation3(v0) * (Scaling3(v0) * Matrix3(q1)); 270c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); 271c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 272c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.setIdentity(); 273c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.scale(v0).translate(v0).rotate(q1); 274c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // translation * mat and scaling * transformation 275c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1 = Scaling3(v0) * (Translation3(v0) * Matrix3(q1)); 276c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); 277c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // transformation * scaling 278c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.scale(v0); 279c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1 = t1 * Scaling3(v0); 280c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); 281c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // transformation * translation 282c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.translate(v0); 283c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1 = t1 * Translation3(v0); 284c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); 285c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // translation * transformation 286c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.pretranslate(v0); 287c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1 = Translation3(v0) * t1; 288c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); 289c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 290c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // transform * quaternion 291c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.rotate(q1); 292c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1 = t1 * q1; 293c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); 294c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 295c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // translation * quaternion 296c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.translate(v1).rotate(q1); 297c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1 = t1 * (Translation3(v1) * q1); 298c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); 299c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 300c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // scaling * quaternion 301c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.scale(v1).rotate(q1); 302c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1 = t1 * (Scaling3(v1) * q1); 303c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); 304c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 305c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // quaternion * transform 306c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.prerotate(q1); 307c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1 = q1 * t1; 308c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); 309c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 310c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // quaternion * translation 311c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.rotate(q1).translate(v1); 312c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1 = t1 * (q1 * Translation3(v1)); 313c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); 314c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 315c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // quaternion * scaling 316c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.rotate(q1).scale(v1); 317c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1 = t1 * (q1 * Scaling3(v1)); 318c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); 319c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 320c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // translation * vector 321c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.setIdentity(); 322c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.translate(v0); 323c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0 * v1, Translation3(v0) * v1); 324c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 325c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // scaling * vector 326c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.setIdentity(); 327c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.scale(v0); 328c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0 * v1, Scaling3(v0) * v1); 329c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 330c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // test transform inversion 331c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.setIdentity(); 332c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.translate(v0); 333c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.linear().setRandom(); 334c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.inverse(Affine), t0.matrix().inverse()); 335c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.setIdentity(); 336c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.translate(v0).rotate(q1); 337c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.inverse(Isometry), t0.matrix().inverse()); 338c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 339c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // test extract rotation and scaling 340c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.setIdentity(); 341c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.translate(v0).rotate(q1).scale(v1); 342c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.rotation() * v1, Matrix3(q1) * v1); 343c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 344c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Matrix3 mat_rotation, mat_scaling; 345c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.setIdentity(); 346c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.translate(v0).rotate(q1).scale(v1); 347c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.computeRotationScaling(&mat_rotation, &mat_scaling); 348c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.linear(), mat_rotation * mat_scaling); 349c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(mat_rotation*mat_rotation.adjoint(), Matrix3::Identity()); 350c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(mat_rotation.determinant(), Scalar(1)); 351c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.computeScalingRotation(&mat_scaling, &mat_rotation); 352c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.linear(), mat_scaling * mat_rotation); 353c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(mat_rotation*mat_rotation.adjoint(), Matrix3::Identity()); 354c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(mat_rotation.determinant(), Scalar(1)); 355c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 356c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // test casting 357c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eigen2_Transform<float,3> t1f = t1.template cast<float>(); 358c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t1f.template cast<Scalar>(),t1); 359c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eigen2_Transform<double,3> t1d = t1.template cast<double>(); 360c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t1d.template cast<Scalar>(),t1); 361c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 362c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Translation3 tr1(v0); 363c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eigen2_Translation<float,3> tr1f = tr1.template cast<float>(); 364c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(tr1f.template cast<Scalar>(),tr1); 365c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eigen2_Translation<double,3> tr1d = tr1.template cast<double>(); 366c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(tr1d.template cast<Scalar>(),tr1); 367c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 368c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scaling3 sc1(v0); 369c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eigen2_Scaling<float,3> sc1f = sc1.template cast<float>(); 370c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(sc1f.template cast<Scalar>(),sc1); 371c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eigen2_Scaling<double,3> sc1d = sc1.template cast<double>(); 372c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(sc1d.template cast<Scalar>(),sc1); 373c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 374c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eigen2_Quaternion<float> q1f = q1.template cast<float>(); 375c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(q1f.template cast<Scalar>(),q1); 376c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eigen2_Quaternion<double> q1d = q1.template cast<double>(); 377c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(q1d.template cast<Scalar>(),q1); 378c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 379c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eigen2_AngleAxis<float> aa1f = aa1.template cast<float>(); 380c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(aa1f.template cast<Scalar>(),aa1); 381c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eigen2_AngleAxis<double> aa1d = aa1.template cast<double>(); 382c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(aa1d.template cast<Scalar>(),aa1); 383c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 384c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eigen2_Rotation2D<Scalar> r2d1(ei_random<Scalar>()); 385c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eigen2_Rotation2D<float> r2d1f = r2d1.template cast<float>(); 386c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(r2d1f.template cast<Scalar>(),r2d1); 387c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath eigen2_Rotation2D<double> r2d1d = r2d1.template cast<double>(); 388c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(r2d1d.template cast<Scalar>(),r2d1); 389c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 390c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m = q1; 391c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// m.col(1) = Vector3(0,ei_random<Scalar>(),ei_random<Scalar>()).normalized(); 392c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// m.col(0) = Vector3(-1,0,0).normalized(); 393c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// m.col(2) = m.col(0).cross(m.col(1)); 394c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath #define VERIFY_EULER(I,J,K, X,Y,Z) { \ 395c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Vector3 ea = m.eulerAngles(I,J,K); \ 396c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Matrix3 m1 = Matrix3(AngleAxisx(ea[0], Vector3::Unit##X()) * AngleAxisx(ea[1], Vector3::Unit##Y()) * AngleAxisx(ea[2], Vector3::Unit##Z())); \ 397c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(m, Matrix3(AngleAxisx(ea[0], Vector3::Unit##X()) * AngleAxisx(ea[1], Vector3::Unit##Y()) * AngleAxisx(ea[2], Vector3::Unit##Z()))); \ 398c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 399c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_EULER(0,1,2, X,Y,Z); 400c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_EULER(0,1,0, X,Y,X); 401c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_EULER(0,2,1, X,Z,Y); 402c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_EULER(0,2,0, X,Z,X); 403c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 404c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_EULER(1,2,0, Y,Z,X); 405c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_EULER(1,2,1, Y,Z,Y); 406c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_EULER(1,0,2, Y,X,Z); 407c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_EULER(1,0,1, Y,X,Y); 408c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 409c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_EULER(2,0,1, Z,X,Y); 410c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_EULER(2,0,2, Z,X,Z); 411c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_EULER(2,1,0, Z,Y,X); 412c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_EULER(2,1,2, Z,Y,Z); 413c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 414c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // colwise/rowwise cross product 415c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath mat3.setRandom(); 416c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Vector3 vec3 = Vector3::Random(); 417c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Matrix3 mcross; 418c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath int i = ei_random<int>(0,2); 419c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath mcross = mat3.colwise().cross(vec3); 420c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(mcross.col(i), mat3.col(i).cross(vec3)); 421c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath mcross = mat3.rowwise().cross(vec3); 422c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(mcross.row(i), mat3.row(i).cross(vec3)); 423c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 424c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 425c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 426c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 427c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathvoid test_eigen2_geometry_with_eigen2_prefix() 428c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 429c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath std::cout << "eigen2 support: " << EIGEN2_SUPPORT_STAGE << std::endl; 430c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath for(int i = 0; i < g_repeat; i++) { 431c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_1( geometry<float>() ); 432c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_2( geometry<double>() ); 433c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 434c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 435