+// This file is part of Eigen, a lightweight C++ template library

+// for linear algebra. Eigen itself is part of the KDE project.

+//

+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>

+//

+// This Source Code Form is subject to the terms of the Mozilla

+// Public License v. 2.0. If a copy of the MPL was not distributed

+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

+

+#include "main.h"

+#include <Eigen/Geometry>

+#include <Eigen/LU>

+#include <Eigen/SVD>

+

+template<typename Scalar> void geometry(void)

+{

+ /* this test covers the following files:

+ Cross.h Quaternion.h, Transform.cpp

+ */

+

+ typedef Matrix<Scalar,2,2> Matrix2;

+ typedef Matrix<Scalar,3,3> Matrix3;

+ typedef Matrix<Scalar,4,4> Matrix4;

+ typedef Matrix<Scalar,2,1> Vector2;

+ typedef Matrix<Scalar,3,1> Vector3;

+ typedef Matrix<Scalar,4,1> Vector4;

+ typedef Quaternion<Scalar> Quaternionx;

+ typedef AngleAxis<Scalar> AngleAxisx;

+ typedef Transform<Scalar,2> Transform2;

+ typedef Transform<Scalar,3> Transform3;

+ typedef Scaling<Scalar,2> Scaling2;

+ typedef Scaling<Scalar,3> Scaling3;

+ typedef Translation<Scalar,2> Translation2;

+ typedef Translation<Scalar,3> Translation3;

+

+ Scalar largeEps = test_precision<Scalar>();

+ if (ei_is_same_type<Scalar,float>::ret)

+ largeEps = 1e-2f;

+

+ Vector3 v0 = Vector3::Random(),

+ v1 = Vector3::Random(),

+ v2 = Vector3::Random();

+ Vector2 u0 = Vector2::Random();

+ Matrix3 matrot1;

+

+ Scalar a = ei_random<Scalar>(-Scalar(M_PI), Scalar(M_PI));

+

+ // cross product

+ VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(v2).eigen2_dot(v1), Scalar(1));

+ Matrix3 m;

+ m << v0.normalized(),

+ (v0.cross(v1)).normalized(),

+ (v0.cross(v1).cross(v0)).normalized();

+ VERIFY(m.isUnitary());

+

+ // Quaternion: Identity(), setIdentity();

+ Quaternionx q1, q2;

+ q2.setIdentity();

+ VERIFY_IS_APPROX(Quaternionx(Quaternionx::Identity()).coeffs(), q2.coeffs());

+ q1.coeffs().setRandom();

+ VERIFY_IS_APPROX(q1.coeffs(), (q1*q2).coeffs());

+

+ // unitOrthogonal

+ VERIFY_IS_MUCH_SMALLER_THAN(u0.unitOrthogonal().eigen2_dot(u0), Scalar(1));

+ VERIFY_IS_MUCH_SMALLER_THAN(v0.unitOrthogonal().eigen2_dot(v0), Scalar(1));

+ VERIFY_IS_APPROX(u0.unitOrthogonal().norm(), Scalar(1));

+ VERIFY_IS_APPROX(v0.unitOrthogonal().norm(), Scalar(1));

+

+

+ VERIFY_IS_APPROX(v0, AngleAxisx(a, v0.normalized()) * v0);

+ VERIFY_IS_APPROX(-v0, AngleAxisx(Scalar(M_PI), v0.unitOrthogonal()) * v0);

+ VERIFY_IS_APPROX(ei_cos(a)*v0.squaredNorm(), v0.eigen2_dot(AngleAxisx(a, v0.unitOrthogonal()) * v0));

+ m = AngleAxisx(a, v0.normalized()).toRotationMatrix().adjoint();

+ VERIFY_IS_APPROX(Matrix3::Identity(), m * AngleAxisx(a, v0.normalized()));

+ VERIFY_IS_APPROX(Matrix3::Identity(), AngleAxisx(a, v0.normalized()) * m);

+

+ q1 = AngleAxisx(a, v0.normalized());

+ q2 = AngleAxisx(a, v1.normalized());

+

+ // angular distance

+ Scalar refangle = ei_abs(AngleAxisx(q1.inverse()*q2).angle());

+ if (refangle>Scalar(M_PI))

+ refangle = Scalar(2)*Scalar(M_PI) - refangle;

+

+ if((q1.coeffs()-q2.coeffs()).norm() > 10*largeEps)

+ {

+ VERIFY(ei_isApprox(q1.angularDistance(q2), refangle, largeEps));

+ }

+

+ // rotation matrix conversion

+ VERIFY_IS_APPROX(q1 * v2, q1.toRotationMatrix() * v2);

+ VERIFY_IS_APPROX(q1 * q2 * v2,

+ q1.toRotationMatrix() * q2.toRotationMatrix() * v2);

+

+ VERIFY( (q2*q1).isApprox(q1*q2, largeEps) || !(q2 * q1 * v2).isApprox(

+ q1.toRotationMatrix() * q2.toRotationMatrix() * v2));

+

+ q2 = q1.toRotationMatrix();

+ VERIFY_IS_APPROX(q1*v1,q2*v1);

+

+ matrot1 = AngleAxisx(Scalar(0.1), Vector3::UnitX())

+ * AngleAxisx(Scalar(0.2), Vector3::UnitY())

+ * AngleAxisx(Scalar(0.3), Vector3::UnitZ());

+ VERIFY_IS_APPROX(matrot1 * v1,

+ AngleAxisx(Scalar(0.1), Vector3(1,0,0)).toRotationMatrix()

+ * (AngleAxisx(Scalar(0.2), Vector3(0,1,0)).toRotationMatrix()

+ * (AngleAxisx(Scalar(0.3), Vector3(0,0,1)).toRotationMatrix() * v1)));

+

+ // angle-axis conversion

+ AngleAxisx aa = q1;

+ VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1);

+ VERIFY_IS_NOT_APPROX(q1 * v1, Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1);

+

+ // from two vector creation

+ VERIFY_IS_APPROX(v2.normalized(),(q2.setFromTwoVectors(v1,v2)*v1).normalized());

+ VERIFY_IS_APPROX(v2.normalized(),(q2.setFromTwoVectors(v1,v2)*v1).normalized());

+

+ // inverse and conjugate

+ VERIFY_IS_APPROX(q1 * (q1.inverse() * v1), v1);

+ VERIFY_IS_APPROX(q1 * (q1.conjugate() * v1), v1);

+

+ // AngleAxis

+ VERIFY_IS_APPROX(AngleAxisx(a,v1.normalized()).toRotationMatrix(),

+ Quaternionx(AngleAxisx(a,v1.normalized())).toRotationMatrix());

+

+ AngleAxisx aa1;

+ m = q1.toRotationMatrix();

+ aa1 = m;

+ VERIFY_IS_APPROX(AngleAxisx(m).toRotationMatrix(),

+ Quaternionx(m).toRotationMatrix());

+

+ // Transform

+ // TODO complete the tests !

+ a = 0;

+ while (ei_abs(a)<Scalar(0.1))

+ a = ei_random<Scalar>(-Scalar(0.4)*Scalar(M_PI), Scalar(0.4)*Scalar(M_PI));

+ q1 = AngleAxisx(a, v0.normalized());

+ Transform3 t0, t1, t2;

+ // first test setIdentity() and Identity()

+ t0.setIdentity();

+ VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());

+ t0.matrix().setZero();

+ t0 = Transform3::Identity();

+ VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());

+

+ t0.linear() = q1.toRotationMatrix();

+ t1.setIdentity();

+ t1.linear() = q1.toRotationMatrix();

+

+ v0 << 50, 2, 1;//= ei_random_matrix<Vector3>().cwiseProduct(Vector3(10,2,0.5));

+ t0.scale(v0);

+ t1.prescale(v0);

+

+ VERIFY_IS_APPROX( (t0 * Vector3(1,0,0)).norm(), v0.x());

+ //VERIFY(!ei_isApprox((t1 * Vector3(1,0,0)).norm(), v0.x()));

+

+ t0.setIdentity();

+ t1.setIdentity();

+ v1 << 1, 2, 3;

+ t0.linear() = q1.toRotationMatrix();

+ t0.pretranslate(v0);

+ t0.scale(v1);

+ t1.linear() = q1.conjugate().toRotationMatrix();

+ t1.prescale(v1.cwise().inverse());

+ t1.translate(-v0);

+

+ VERIFY((t0.matrix() * t1.matrix()).isIdentity(test_precision<Scalar>()));

+

+ t1.fromPositionOrientationScale(v0, q1, v1);

+ VERIFY_IS_APPROX(t1.matrix(), t0.matrix());

+ VERIFY_IS_APPROX(t1*v1, t0*v1);

+

+ t0.setIdentity(); t0.scale(v0).rotate(q1.toRotationMatrix());

+ t1.setIdentity(); t1.scale(v0).rotate(q1);

+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());

+

+ t0.setIdentity(); t0.scale(v0).rotate(AngleAxisx(q1));

+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());

+

+ VERIFY_IS_APPROX(t0.scale(a).matrix(), t1.scale(Vector3::Constant(a)).matrix());

+ VERIFY_IS_APPROX(t0.prescale(a).matrix(), t1.prescale(Vector3::Constant(a)).matrix());

+

+ // More transform constructors, operator=, operator*=

+

+ Matrix3 mat3 = Matrix3::Random();

+ Matrix4 mat4;

+ mat4 << mat3 , Vector3::Zero() , Vector4::Zero().transpose();

+ Transform3 tmat3(mat3), tmat4(mat4);

+ tmat4.matrix()(3,3) = Scalar(1);

+ VERIFY_IS_APPROX(tmat3.matrix(), tmat4.matrix());

+

+ Scalar a3 = ei_random<Scalar>(-Scalar(M_PI), Scalar(M_PI));

+ Vector3 v3 = Vector3::Random().normalized();

+ AngleAxisx aa3(a3, v3);

+ Transform3 t3(aa3);

+ Transform3 t4;

+ t4 = aa3;

+ VERIFY_IS_APPROX(t3.matrix(), t4.matrix());

+ t4.rotate(AngleAxisx(-a3,v3));

+ VERIFY_IS_APPROX(t4.matrix(), Matrix4::Identity());

+ t4 *= aa3;

+ VERIFY_IS_APPROX(t3.matrix(), t4.matrix());

+

+ v3 = Vector3::Random();

+ Translation3 tv3(v3);

+ Transform3 t5(tv3);

+ t4 = tv3;

+ VERIFY_IS_APPROX(t5.matrix(), t4.matrix());

+ t4.translate(-v3);

+ VERIFY_IS_APPROX(t4.matrix(), Matrix4::Identity());

+ t4 *= tv3;

+ VERIFY_IS_APPROX(t5.matrix(), t4.matrix());

+

+ Scaling3 sv3(v3);

+ Transform3 t6(sv3);

+ t4 = sv3;

+ VERIFY_IS_APPROX(t6.matrix(), t4.matrix());

+ t4.scale(v3.cwise().inverse());

+ VERIFY_IS_APPROX(t4.matrix(), Matrix4::Identity());

+ t4 *= sv3;

+ VERIFY_IS_APPROX(t6.matrix(), t4.matrix());

+

+ // matrix * transform

+ VERIFY_IS_APPROX(Transform3(t3.matrix()*t4).matrix(), Transform3(t3*t4).matrix());

+

+ // chained Transform product

+ VERIFY_IS_APPROX(((t3*t4)*t5).matrix(), (t3*(t4*t5)).matrix());

+

+ // check that Transform product doesn't have aliasing problems

+ t5 = t4;

+ t5 = t5*t5;

+ VERIFY_IS_APPROX(t5, t4*t4);

+

+ // 2D transformation

+ Transform2 t20, t21;

+ Vector2 v20 = Vector2::Random();

+ Vector2 v21 = Vector2::Random();

+ for (int k=0; k<2; ++k)

+ if (ei_abs(v21[k])<Scalar(1e-3)) v21[k] = Scalar(1e-3);

+ t21.setIdentity();

+ t21.linear() = Rotation2D<Scalar>(a).toRotationMatrix();

+ VERIFY_IS_APPROX(t20.fromPositionOrientationScale(v20,a,v21).matrix(),

+ t21.pretranslate(v20).scale(v21).matrix());

+

+ t21.setIdentity();

+ t21.linear() = Rotation2D<Scalar>(-a).toRotationMatrix();

+ VERIFY( (t20.fromPositionOrientationScale(v20,a,v21)

+ * (t21.prescale(v21.cwise().inverse()).translate(-v20))).matrix().isIdentity(test_precision<Scalar>()) );

+

+ // Transform - new API

+ // 3D

+ t0.setIdentity();

+ t0.rotate(q1).scale(v0).translate(v0);

+ // mat * scaling and mat * translation

+ t1 = (Matrix3(q1) * Scaling3(v0)) * Translation3(v0);

+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());

+ // mat * transformation and scaling * translation

+ t1 = Matrix3(q1) * (Scaling3(v0) * Translation3(v0));

+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());

+

+ t0.setIdentity();

+ t0.prerotate(q1).prescale(v0).pretranslate(v0);

+ // translation * scaling and transformation * mat

+ t1 = (Translation3(v0) * Scaling3(v0)) * Matrix3(q1);

+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());

+ // scaling * mat and translation * mat

+ t1 = Translation3(v0) * (Scaling3(v0) * Matrix3(q1));

+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());

+

+ t0.setIdentity();

+ t0.scale(v0).translate(v0).rotate(q1);

+ // translation * mat and scaling * transformation

+ t1 = Scaling3(v0) * (Translation3(v0) * Matrix3(q1));

+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());

+ // transformation * scaling

+ t0.scale(v0);

+ t1 = t1 * Scaling3(v0);

+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());

+ // transformation * translation

+ t0.translate(v0);

+ t1 = t1 * Translation3(v0);

+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());

+ // translation * transformation

+ t0.pretranslate(v0);

+ t1 = Translation3(v0) * t1;

+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());

+

+ // transform * quaternion

+ t0.rotate(q1);

+ t1 = t1 * q1;

+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());

+

+ // translation * quaternion

+ t0.translate(v1).rotate(q1);

+ t1 = t1 * (Translation3(v1) * q1);

+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());

+

+ // scaling * quaternion

+ t0.scale(v1).rotate(q1);

+ t1 = t1 * (Scaling3(v1) * q1);

+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());

+

+ // quaternion * transform

+ t0.prerotate(q1);

+ t1 = q1 * t1;

+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());

+

+ // quaternion * translation

+ t0.rotate(q1).translate(v1);

+ t1 = t1 * (q1 * Translation3(v1));

+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());

+

+ // quaternion * scaling

+ t0.rotate(q1).scale(v1);

+ t1 = t1 * (q1 * Scaling3(v1));

+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());

+

+ // translation * vector

+ t0.setIdentity();

+ t0.translate(v0);

+ VERIFY_IS_APPROX(t0 * v1, Translation3(v0) * v1);

+

+ // scaling * vector

+ t0.setIdentity();

+ t0.scale(v0);

+ VERIFY_IS_APPROX(t0 * v1, Scaling3(v0) * v1);

+

+ // test transform inversion

+ t0.setIdentity();

+ t0.translate(v0);

+ t0.linear().setRandom();

+ VERIFY_IS_APPROX(t0.inverse(Affine), t0.matrix().inverse());

+ t0.setIdentity();

+ t0.translate(v0).rotate(q1);

+ 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>() );

+ }

+}