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#include "main.h" 11c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#include <Eigen/Geometry> 12c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#include <Eigen/LU> 13c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#include <Eigen/SVD> 14c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 15c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename Scalar> void geometry(void) 16c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 17c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /* this test covers the following files: 18c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Cross.h Quaternion.h, Transform.cpp 19c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 20c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 21c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar,2,2> Matrix2; 22c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar,3,3> Matrix3; 23c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar,4,4> Matrix4; 24c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar,2,1> Vector2; 25c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar,3,1> Vector3; 26c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar,4,1> Vector4; 27c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Quaternion<Scalar> Quaternionx; 28c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef AngleAxis<Scalar> AngleAxisx; 29c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Transform<Scalar,2> Transform2; 30c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Transform<Scalar,3> Transform3; 31c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Scaling<Scalar,2> Scaling2; 32c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Scaling<Scalar,3> Scaling3; 33c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Translation<Scalar,2> Translation2; 34c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Translation<Scalar,3> Translation3; 35c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 36c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scalar largeEps = test_precision<Scalar>(); 37c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (ei_is_same_type<Scalar,float>::ret) 38c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath largeEps = 1e-2f; 39c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 40c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Vector3 v0 = Vector3::Random(), 41c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath v1 = Vector3::Random(), 42c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath v2 = Vector3::Random(); 43c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Vector2 u0 = Vector2::Random(); 44c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Matrix3 matrot1; 45c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 46c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scalar a = ei_random<Scalar>(-Scalar(M_PI), Scalar(M_PI)); 47c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 48c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // cross product 49c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(v2).eigen2_dot(v1), Scalar(1)); 50c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Matrix3 m; 51c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m << v0.normalized(), 52c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath (v0.cross(v1)).normalized(), 53c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath (v0.cross(v1).cross(v0)).normalized(); 54c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY(m.isUnitary()); 55c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 56c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // Quaternion: Identity(), setIdentity(); 57c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Quaternionx q1, q2; 58c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath q2.setIdentity(); 59c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(Quaternionx(Quaternionx::Identity()).coeffs(), q2.coeffs()); 60c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath q1.coeffs().setRandom(); 61c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(q1.coeffs(), (q1*q2).coeffs()); 62c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 63c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // unitOrthogonal 64c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_MUCH_SMALLER_THAN(u0.unitOrthogonal().eigen2_dot(u0), Scalar(1)); 65c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_MUCH_SMALLER_THAN(v0.unitOrthogonal().eigen2_dot(v0), Scalar(1)); 66c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(u0.unitOrthogonal().norm(), Scalar(1)); 67c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(v0.unitOrthogonal().norm(), Scalar(1)); 68c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 69c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 70c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(v0, AngleAxisx(a, v0.normalized()) * v0); 71c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(-v0, AngleAxisx(Scalar(M_PI), v0.unitOrthogonal()) * v0); 72c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(ei_cos(a)*v0.squaredNorm(), v0.eigen2_dot(AngleAxisx(a, v0.unitOrthogonal()) * v0)); 73c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m = AngleAxisx(a, v0.normalized()).toRotationMatrix().adjoint(); 74c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(Matrix3::Identity(), m * AngleAxisx(a, v0.normalized())); 75c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(Matrix3::Identity(), AngleAxisx(a, v0.normalized()) * m); 76c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 77c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath q1 = AngleAxisx(a, v0.normalized()); 78c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath q2 = AngleAxisx(a, v1.normalized()); 79c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 80c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // angular distance 81c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scalar refangle = ei_abs(AngleAxisx(q1.inverse()*q2).angle()); 82c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (refangle>Scalar(M_PI)) 83c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath refangle = Scalar(2)*Scalar(M_PI) - refangle; 84c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 85c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if((q1.coeffs()-q2.coeffs()).norm() > 10*largeEps) 86c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 87c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY(ei_isApprox(q1.angularDistance(q2), refangle, largeEps)); 88c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 89c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 90c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // rotation matrix conversion 91c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(q1 * v2, q1.toRotationMatrix() * v2); 92c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(q1 * q2 * v2, 93c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath q1.toRotationMatrix() * q2.toRotationMatrix() * v2); 94c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 95c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY( (q2*q1).isApprox(q1*q2, largeEps) || !(q2 * q1 * v2).isApprox( 96c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath q1.toRotationMatrix() * q2.toRotationMatrix() * v2)); 97c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 98c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath q2 = q1.toRotationMatrix(); 99c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(q1*v1,q2*v1); 100c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 101c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath matrot1 = AngleAxisx(Scalar(0.1), Vector3::UnitX()) 102c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * AngleAxisx(Scalar(0.2), Vector3::UnitY()) 103c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * AngleAxisx(Scalar(0.3), Vector3::UnitZ()); 104c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(matrot1 * v1, 105c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath AngleAxisx(Scalar(0.1), Vector3(1,0,0)).toRotationMatrix() 106c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * (AngleAxisx(Scalar(0.2), Vector3(0,1,0)).toRotationMatrix() 107c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * (AngleAxisx(Scalar(0.3), Vector3(0,0,1)).toRotationMatrix() * v1))); 108c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 109c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // angle-axis conversion 110c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath AngleAxisx aa = q1; 111c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1); 112c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_NOT_APPROX(q1 * v1, Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1); 113c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 114c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // from two vector creation 115c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(v2.normalized(),(q2.setFromTwoVectors(v1,v2)*v1).normalized()); 116c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(v2.normalized(),(q2.setFromTwoVectors(v1,v2)*v1).normalized()); 117c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 118c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // inverse and conjugate 119c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(q1 * (q1.inverse() * v1), v1); 120c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(q1 * (q1.conjugate() * v1), v1); 121c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 122c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // AngleAxis 123c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(AngleAxisx(a,v1.normalized()).toRotationMatrix(), 124c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Quaternionx(AngleAxisx(a,v1.normalized())).toRotationMatrix()); 125c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 126c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath AngleAxisx aa1; 127c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m = q1.toRotationMatrix(); 128c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath aa1 = m; 129c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(AngleAxisx(m).toRotationMatrix(), 130c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Quaternionx(m).toRotationMatrix()); 131c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 132c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // Transform 133c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // TODO complete the tests ! 134c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath a = 0; 135c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath while (ei_abs(a)<Scalar(0.1)) 136c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath a = ei_random<Scalar>(-Scalar(0.4)*Scalar(M_PI), Scalar(0.4)*Scalar(M_PI)); 137c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath q1 = AngleAxisx(a, v0.normalized()); 138c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Transform3 t0, t1, t2; 139c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // first test setIdentity() and Identity() 140c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.setIdentity(); 141c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity()); 142c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.matrix().setZero(); 143c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0 = Transform3::Identity(); 144c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity()); 145c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 146c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.linear() = q1.toRotationMatrix(); 147c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1.setIdentity(); 148c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1.linear() = q1.toRotationMatrix(); 149c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 150c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath v0 << 50, 2, 1;//= ei_random_matrix<Vector3>().cwiseProduct(Vector3(10,2,0.5)); 151c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.scale(v0); 152c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1.prescale(v0); 153c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 154c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX( (t0 * Vector3(1,0,0)).norm(), v0.x()); 155c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath //VERIFY(!ei_isApprox((t1 * Vector3(1,0,0)).norm(), v0.x())); 156c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 157c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.setIdentity(); 158c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1.setIdentity(); 159c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath v1 << 1, 2, 3; 160c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.linear() = q1.toRotationMatrix(); 161c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.pretranslate(v0); 162c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.scale(v1); 163c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1.linear() = q1.conjugate().toRotationMatrix(); 164c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1.prescale(v1.cwise().inverse()); 165c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1.translate(-v0); 166c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 167c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY((t0.matrix() * t1.matrix()).isIdentity(test_precision<Scalar>())); 168c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 169c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1.fromPositionOrientationScale(v0, q1, v1); 170c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t1.matrix(), t0.matrix()); 171c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t1*v1, t0*v1); 172c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 173c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.setIdentity(); t0.scale(v0).rotate(q1.toRotationMatrix()); 174c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1.setIdentity(); t1.scale(v0).rotate(q1); 175c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); 176c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 177c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.setIdentity(); t0.scale(v0).rotate(AngleAxisx(q1)); 178c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); 179c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 180c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.scale(a).matrix(), t1.scale(Vector3::Constant(a)).matrix()); 181c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.prescale(a).matrix(), t1.prescale(Vector3::Constant(a)).matrix()); 182c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 183c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // More transform constructors, operator=, operator*= 184c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 185c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Matrix3 mat3 = Matrix3::Random(); 186c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Matrix4 mat4; 187c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath mat4 << mat3 , Vector3::Zero() , Vector4::Zero().transpose(); 188c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Transform3 tmat3(mat3), tmat4(mat4); 189c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath tmat4.matrix()(3,3) = Scalar(1); 190c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(tmat3.matrix(), tmat4.matrix()); 191c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 192c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scalar a3 = ei_random<Scalar>(-Scalar(M_PI), Scalar(M_PI)); 193c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Vector3 v3 = Vector3::Random().normalized(); 194c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath AngleAxisx aa3(a3, v3); 195c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Transform3 t3(aa3); 196c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Transform3 t4; 197c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t4 = aa3; 198c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t3.matrix(), t4.matrix()); 199c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t4.rotate(AngleAxisx(-a3,v3)); 200c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t4.matrix(), Matrix4::Identity()); 201c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t4 *= aa3; 202c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t3.matrix(), t4.matrix()); 203c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 204c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath v3 = Vector3::Random(); 205c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Translation3 tv3(v3); 206c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Transform3 t5(tv3); 207c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t4 = tv3; 208c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t5.matrix(), t4.matrix()); 209c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t4.translate(-v3); 210c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t4.matrix(), Matrix4::Identity()); 211c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t4 *= tv3; 212c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t5.matrix(), t4.matrix()); 213c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 214c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scaling3 sv3(v3); 215c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Transform3 t6(sv3); 216c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t4 = sv3; 217c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t6.matrix(), t4.matrix()); 218c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t4.scale(v3.cwise().inverse()); 219c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t4.matrix(), Matrix4::Identity()); 220c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t4 *= sv3; 221c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t6.matrix(), t4.matrix()); 222c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 223c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // matrix * transform 224c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(Transform3(t3.matrix()*t4).matrix(), Transform3(t3*t4).matrix()); 225c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 226c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // chained Transform product 227c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(((t3*t4)*t5).matrix(), (t3*(t4*t5)).matrix()); 228c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 229c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // check that Transform product doesn't have aliasing problems 230c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t5 = t4; 231c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t5 = t5*t5; 232c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t5, t4*t4); 233c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 234c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // 2D transformation 235c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Transform2 t20, t21; 236c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Vector2 v20 = Vector2::Random(); 237c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Vector2 v21 = Vector2::Random(); 238c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath for (int k=0; k<2; ++k) 239c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (ei_abs(v21[k])<Scalar(1e-3)) v21[k] = Scalar(1e-3); 240c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t21.setIdentity(); 241c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t21.linear() = Rotation2D<Scalar>(a).toRotationMatrix(); 242c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t20.fromPositionOrientationScale(v20,a,v21).matrix(), 243c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t21.pretranslate(v20).scale(v21).matrix()); 244c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 245c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t21.setIdentity(); 246c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t21.linear() = Rotation2D<Scalar>(-a).toRotationMatrix(); 247c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY( (t20.fromPositionOrientationScale(v20,a,v21) 248c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath * (t21.prescale(v21.cwise().inverse()).translate(-v20))).matrix().isIdentity(test_precision<Scalar>()) ); 249c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 250c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // Transform - new API 251c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // 3D 252c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.setIdentity(); 253c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.rotate(q1).scale(v0).translate(v0); 254c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // mat * scaling and mat * translation 255c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1 = (Matrix3(q1) * Scaling3(v0)) * Translation3(v0); 256c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); 257c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // mat * transformation and scaling * translation 258c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1 = Matrix3(q1) * (Scaling3(v0) * Translation3(v0)); 259c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); 260c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 261c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.setIdentity(); 262c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.prerotate(q1).prescale(v0).pretranslate(v0); 263c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // translation * scaling and transformation * mat 264c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1 = (Translation3(v0) * Scaling3(v0)) * Matrix3(q1); 265c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); 266c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // scaling * mat and translation * mat 267c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1 = Translation3(v0) * (Scaling3(v0) * Matrix3(q1)); 268c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); 269c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 270c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.setIdentity(); 271c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.scale(v0).translate(v0).rotate(q1); 272c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // translation * mat and scaling * transformation 273c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1 = Scaling3(v0) * (Translation3(v0) * Matrix3(q1)); 274c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); 275c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // transformation * scaling 276c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.scale(v0); 277c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1 = t1 * Scaling3(v0); 278c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); 279c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // transformation * translation 280c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.translate(v0); 281c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1 = t1 * Translation3(v0); 282c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); 283c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // translation * transformation 284c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.pretranslate(v0); 285c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1 = Translation3(v0) * t1; 286c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); 287c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 288c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // transform * quaternion 289c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.rotate(q1); 290c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1 = t1 * q1; 291c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); 292c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 293c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // translation * quaternion 294c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.translate(v1).rotate(q1); 295c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1 = t1 * (Translation3(v1) * q1); 296c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); 297c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 298c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // scaling * quaternion 299c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.scale(v1).rotate(q1); 300c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1 = t1 * (Scaling3(v1) * q1); 301c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); 302c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 303c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // quaternion * transform 304c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.prerotate(q1); 305c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1 = q1 * t1; 306c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); 307c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 308c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // quaternion * translation 309c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.rotate(q1).translate(v1); 310c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1 = t1 * (q1 * Translation3(v1)); 311c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); 312c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 313c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // quaternion * scaling 314c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.rotate(q1).scale(v1); 315c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t1 = t1 * (q1 * Scaling3(v1)); 316c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); 317c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 318c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // translation * vector 319c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.setIdentity(); 320c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.translate(v0); 321c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0 * v1, Translation3(v0) * v1); 322c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 323c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // scaling * vector 324c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.setIdentity(); 325c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.scale(v0); 326c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0 * v1, Scaling3(v0) * v1); 327c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 328c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // test transform inversion 329c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.setIdentity(); 330c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.translate(v0); 331c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.linear().setRandom(); 332c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.inverse(Affine), t0.matrix().inverse()); 333c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.setIdentity(); 334c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.translate(v0).rotate(q1); 335c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.inverse(Isometry), t0.matrix().inverse()); 336c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 337c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // test extract rotation and scaling 338c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.setIdentity(); 339c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.translate(v0).rotate(q1).scale(v1); 340c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.rotation() * v1, Matrix3(q1) * v1); 341c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 342c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Matrix3 mat_rotation, mat_scaling; 343c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.setIdentity(); 344c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.translate(v0).rotate(q1).scale(v1); 345c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.computeRotationScaling(&mat_rotation, &mat_scaling); 346c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.linear(), mat_rotation * mat_scaling); 347c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(mat_rotation*mat_rotation.adjoint(), Matrix3::Identity()); 348c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(mat_rotation.determinant(), Scalar(1)); 349c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath t0.computeScalingRotation(&mat_scaling, &mat_rotation); 350c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t0.linear(), mat_scaling * mat_rotation); 351c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(mat_rotation*mat_rotation.adjoint(), Matrix3::Identity()); 352c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(mat_rotation.determinant(), Scalar(1)); 353c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 354c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // test casting 355c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Transform<float,3> t1f = t1.template cast<float>(); 356c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t1f.template cast<Scalar>(),t1); 357c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Transform<double,3> t1d = t1.template cast<double>(); 358c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(t1d.template cast<Scalar>(),t1); 359c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 360c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Translation3 tr1(v0); 361c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Translation<float,3> tr1f = tr1.template cast<float>(); 362c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(tr1f.template cast<Scalar>(),tr1); 363c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Translation<double,3> tr1d = tr1.template cast<double>(); 364c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(tr1d.template cast<Scalar>(),tr1); 365c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 366c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scaling3 sc1(v0); 367c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scaling<float,3> sc1f = sc1.template cast<float>(); 368c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(sc1f.template cast<Scalar>(),sc1); 369c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scaling<double,3> sc1d = sc1.template cast<double>(); 370c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(sc1d.template cast<Scalar>(),sc1); 371c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 372c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Quaternion<float> q1f = q1.template cast<float>(); 373c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(q1f.template cast<Scalar>(),q1); 374c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Quaternion<double> q1d = q1.template cast<double>(); 375c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(q1d.template cast<Scalar>(),q1); 376c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 377c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath AngleAxis<float> aa1f = aa1.template cast<float>(); 378c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(aa1f.template cast<Scalar>(),aa1); 379c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath AngleAxis<double> aa1d = aa1.template cast<double>(); 380c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(aa1d.template cast<Scalar>(),aa1); 381c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 382c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Rotation2D<Scalar> r2d1(ei_random<Scalar>()); 383c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Rotation2D<float> r2d1f = r2d1.template cast<float>(); 384c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(r2d1f.template cast<Scalar>(),r2d1); 385c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Rotation2D<double> r2d1d = r2d1.template cast<double>(); 386c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(r2d1d.template cast<Scalar>(),r2d1); 387c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 388c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath m = q1; 389c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// m.col(1) = Vector3(0,ei_random<Scalar>(),ei_random<Scalar>()).normalized(); 390c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// m.col(0) = Vector3(-1,0,0).normalized(); 391c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// m.col(2) = m.col(0).cross(m.col(1)); 392c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath #define VERIFY_EULER(I,J,K, X,Y,Z) { \ 393c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Vector3 ea = m.eulerAngles(I,J,K); \ 394c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Matrix3 m1 = Matrix3(AngleAxisx(ea[0], Vector3::Unit##X()) * AngleAxisx(ea[1], Vector3::Unit##Y()) * AngleAxisx(ea[2], Vector3::Unit##Z())); \ 395615d816d068b4d0f5e8df601930b5f160bf7eda1Tim Murray VERIFY_IS_APPROX(m, m1); \ 396c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(m, Matrix3(AngleAxisx(ea[0], Vector3::Unit##X()) * AngleAxisx(ea[1], Vector3::Unit##Y()) * AngleAxisx(ea[2], Vector3::Unit##Z()))); \ 397c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 398c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_EULER(0,1,2, X,Y,Z); 399c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_EULER(0,1,0, X,Y,X); 400c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_EULER(0,2,1, X,Z,Y); 401c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_EULER(0,2,0, X,Z,X); 402c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 403c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_EULER(1,2,0, Y,Z,X); 404c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_EULER(1,2,1, Y,Z,Y); 405c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_EULER(1,0,2, Y,X,Z); 406c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_EULER(1,0,1, Y,X,Y); 407c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 408c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_EULER(2,0,1, Z,X,Y); 409c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_EULER(2,0,2, Z,X,Z); 410c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_EULER(2,1,0, Z,Y,X); 411c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_EULER(2,1,2, Z,Y,Z); 412c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 413c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // colwise/rowwise cross product 414c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath mat3.setRandom(); 415c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Vector3 vec3 = Vector3::Random(); 416c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Matrix3 mcross; 417c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath int i = ei_random<int>(0,2); 418c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath mcross = mat3.colwise().cross(vec3); 419c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(mcross.col(i), mat3.col(i).cross(vec3)); 420c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath mcross = mat3.rowwise().cross(vec3); 421c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(mcross.row(i), mat3.row(i).cross(vec3)); 422c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 423c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 424c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 425c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 426c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathvoid test_eigen2_geometry() 427c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 428c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath for(int i = 0; i < g_repeat; i++) { 429c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_1( geometry<float>() ); 430c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_2( geometry<double>() ); 431c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 432c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 433