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- // This file is part of Eigen, a lightweight C++ template library
- // for linear algebra.
- //
- // Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.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 T>
- Matrix<T,2,1> angleToVec(T a)
- {
- return Matrix<T,2,1>(std::cos(a), std::sin(a));
- }
- // This permits to workaround a bug in clang/llvm code generation.
- template<typename T>
- EIGEN_DONT_INLINE
- void dont_over_optimize(T& x) { volatile typename T::Scalar tmp = x(0); x(0) = tmp; }
- template<typename Scalar, int Mode, int Options> void non_projective_only()
- {
- /* this test covers the following files:
- Cross.h Quaternion.h, Transform.cpp
- */
- typedef Matrix<Scalar,3,1> Vector3;
- typedef Quaternion<Scalar> Quaternionx;
- typedef AngleAxis<Scalar> AngleAxisx;
- typedef Transform<Scalar,3,Mode,Options> Transform3;
- typedef DiagonalMatrix<Scalar,3> AlignedScaling3;
- typedef Translation<Scalar,3> Translation3;
- Vector3 v0 = Vector3::Random(),
- v1 = Vector3::Random();
- Transform3 t0, t1, t2;
- Scalar a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI));
- Quaternionx q1, q2;
- q1 = AngleAxisx(a, v0.normalized());
- t0 = Transform3::Identity();
- VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());
- t0.linear() = q1.toRotationMatrix();
- v0 << 50, 2, 1;
- t0.scale(v0);
- VERIFY_IS_APPROX( (t0 * Vector3(1,0,0)).template head<3>().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.cwiseInverse());
- t1.translate(-v0);
- VERIFY((t0 * 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);
- // translation * vector
- t0.setIdentity();
- t0.translate(v0);
- VERIFY_IS_APPROX((t0 * v1).template head<3>(), Translation3(v0) * v1);
- // AlignedScaling * vector
- t0.setIdentity();
- t0.scale(v0);
- VERIFY_IS_APPROX((t0 * v1).template head<3>(), AlignedScaling3(v0) * v1);
- }
- template<typename Scalar, int Mode, int Options> void transformations()
- {
- /* this test covers the following files:
- Cross.h Quaternion.h, Transform.cpp
- */
- using std::cos;
- using std::abs;
- 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,Mode,Options> Transform2;
- typedef Transform<Scalar,3,Mode,Options> Transform3;
- typedef typename Transform3::MatrixType MatrixType;
- typedef DiagonalMatrix<Scalar,3> AlignedScaling3;
- typedef Translation<Scalar,2> Translation2;
- typedef Translation<Scalar,3> Translation3;
- Vector3 v0 = Vector3::Random(),
- v1 = Vector3::Random();
- Matrix3 matrot1, m;
- Scalar a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI));
- Scalar s0 = internal::random<Scalar>(), s1 = internal::random<Scalar>();
-
- while(v0.norm() < test_precision<Scalar>()) v0 = Vector3::Random();
- while(v1.norm() < test_precision<Scalar>()) v1 = Vector3::Random();
- VERIFY_IS_APPROX(v0, AngleAxisx(a, v0.normalized()) * v0);
- VERIFY_IS_APPROX(-v0, AngleAxisx(Scalar(EIGEN_PI), v0.unitOrthogonal()) * v0);
- if(abs(cos(a)) > test_precision<Scalar>())
- {
- VERIFY_IS_APPROX(cos(a)*v0.squaredNorm(), v0.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);
- Quaternionx q1, q2;
- q1 = AngleAxisx(a, v0.normalized());
- q2 = AngleAxisx(a, v1.normalized());
- // rotation matrix conversion
- 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 = AngleAxisx(q1);
- VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1);
-
- // The following test is stable only if 2*angle != angle and v1 is not colinear with axis
- if( (abs(aa.angle()) > test_precision<Scalar>()) && (abs(aa.axis().dot(v1.normalized()))<(Scalar(1)-Scalar(4)*test_precision<Scalar>())) )
- {
- VERIFY( !(q1 * v1).isApprox(Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1) );
- }
- aa.fromRotationMatrix(aa.toRotationMatrix());
- VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1);
- // The following test is stable only if 2*angle != angle and v1 is not colinear with axis
- if( (abs(aa.angle()) > test_precision<Scalar>()) && (abs(aa.axis().dot(v1.normalized()))<(Scalar(1)-Scalar(4)*test_precision<Scalar>())) )
- {
- VERIFY( !(q1 * v1).isApprox(Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * 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 (abs(a)<Scalar(0.1))
- a = internal::random<Scalar>(-Scalar(0.4)*Scalar(EIGEN_PI), Scalar(0.4)*Scalar(EIGEN_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.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.cwiseInverse());
- t1.translate(-v0);
- VERIFY((t0 * t1).matrix().isIdentity(test_precision<Scalar>()));
- t1.fromPositionOrientationScale(v0, q1, v1);
- VERIFY_IS_APPROX(t1.matrix(), t0.matrix());
- 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);
- if(Mode!=int(AffineCompact))
- tmat4.matrix()(3,3) = Scalar(1);
- VERIFY_IS_APPROX(tmat3.matrix(), tmat4.matrix());
- Scalar a3 = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_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(), MatrixType::Identity());
- t4 *= aa3;
- VERIFY_IS_APPROX(t3.matrix(), t4.matrix());
- do {
- v3 = Vector3::Random();
- dont_over_optimize(v3);
- } while (v3.cwiseAbs().minCoeff()<NumTraits<Scalar>::epsilon());
- Translation3 tv3(v3);
- Transform3 t5(tv3);
- t4 = tv3;
- VERIFY_IS_APPROX(t5.matrix(), t4.matrix());
- t4.translate((-v3).eval());
- VERIFY_IS_APPROX(t4.matrix(), MatrixType::Identity());
- t4 *= tv3;
- VERIFY_IS_APPROX(t5.matrix(), t4.matrix());
- AlignedScaling3 sv3(v3);
- Transform3 t6(sv3);
- t4 = sv3;
- VERIFY_IS_APPROX(t6.matrix(), t4.matrix());
- t4.scale(v3.cwiseInverse());
- VERIFY_IS_APPROX(t4.matrix(), MatrixType::Identity());
- t4 *= sv3;
- VERIFY_IS_APPROX(t6.matrix(), t4.matrix());
- // matrix * transform
- VERIFY_IS_APPROX((t3.matrix()*t4).matrix(), (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 (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.cwiseInverse()).translate(-v20))).matrix().isIdentity(test_precision<Scalar>()) );
- // Transform - new API
- // 3D
- t0.setIdentity();
- t0.rotate(q1).scale(v0).translate(v0);
- // mat * aligned scaling and mat * translation
- t1 = (Matrix3(q1) * AlignedScaling3(v0)) * Translation3(v0);
- VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
- t1 = (Matrix3(q1) * Eigen::Scaling(v0)) * Translation3(v0);
- VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
- t1 = (q1 * Eigen::Scaling(v0)) * Translation3(v0);
- VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
- // mat * transformation and aligned scaling * translation
- t1 = Matrix3(q1) * (AlignedScaling3(v0) * Translation3(v0));
- VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
- t0.setIdentity();
- t0.scale(s0).translate(v0);
- t1 = Eigen::Scaling(s0) * Translation3(v0);
- VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
- t0.prescale(s0);
- t1 = Eigen::Scaling(s0) * t1;
- VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
-
- t0 = t3;
- t0.scale(s0);
- t1 = t3 * Eigen::Scaling(s0,s0,s0);
- VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
- t0.prescale(s0);
- t1 = Eigen::Scaling(s0,s0,s0) * t1;
- VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
- t0 = t3;
- t0.scale(s0);
- t1 = t3 * Eigen::Scaling(s0);
- VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
- t0.prescale(s0);
- t1 = Eigen::Scaling(s0) * t1;
- VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
- t0.setIdentity();
- t0.prerotate(q1).prescale(v0).pretranslate(v0);
- // translation * aligned scaling and transformation * mat
- t1 = (Translation3(v0) * AlignedScaling3(v0)) * Transform3(q1);
- VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
- // scaling * mat and translation * mat
- t1 = Translation3(v0) * (AlignedScaling3(v0) * Transform3(q1));
- VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
- t0.setIdentity();
- t0.scale(v0).translate(v0).rotate(q1);
- // translation * mat and aligned scaling * transformation
- t1 = AlignedScaling3(v0) * (Translation3(v0) * Transform3(q1));
- VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
- // transformation * aligned scaling
- t0.scale(v0);
- t1 *= AlignedScaling3(v0);
- VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
- t1 = AlignedScaling3(v0) * (Translation3(v0) * Transform3(q1));
- t1 = t1 * v0.asDiagonal();
- 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());
- // aligned scaling * quaternion
- t0.scale(v1).rotate(q1);
- t1 = t1 * (AlignedScaling3(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 * aligned scaling
- t0.rotate(q1).scale(v1);
- t1 = t1 * (q1 * AlignedScaling3(v1));
- VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
- // test transform inversion
- t0.setIdentity();
- t0.translate(v0);
- do {
- t0.linear().setRandom();
- } while(t0.linear().jacobiSvd().singularValues()(2)<test_precision<Scalar>());
- Matrix4 t044 = Matrix4::Zero();
- t044(3,3) = 1;
- t044.block(0,0,t0.matrix().rows(),4) = t0.matrix();
- VERIFY_IS_APPROX(t0.inverse(Affine).matrix(), t044.inverse().block(0,0,t0.matrix().rows(),4));
- t0.setIdentity();
- t0.translate(v0).rotate(q1);
- t044 = Matrix4::Zero();
- t044(3,3) = 1;
- t044.block(0,0,t0.matrix().rows(),4) = t0.matrix();
- VERIFY_IS_APPROX(t0.inverse(Isometry).matrix(), t044.inverse().block(0,0,t0.matrix().rows(),4));
- 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,Mode> t1f = t1.template cast<float>();
- VERIFY_IS_APPROX(t1f.template cast<Scalar>(),t1);
- Transform<double,3,Mode> 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);
- 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(internal::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);
-
- for(int k=0; k<100; ++k)
- {
- Scalar angle = internal::random<Scalar>(-100,100);
- Rotation2D<Scalar> rot2(angle);
- VERIFY( rot2.smallestPositiveAngle() >= 0 );
- VERIFY( rot2.smallestPositiveAngle() <= Scalar(2)*Scalar(EIGEN_PI) );
- VERIFY_IS_APPROX( angleToVec(rot2.smallestPositiveAngle()), angleToVec(rot2.angle()) );
-
- VERIFY( rot2.smallestAngle() >= -Scalar(EIGEN_PI) );
- VERIFY( rot2.smallestAngle() <= Scalar(EIGEN_PI) );
- VERIFY_IS_APPROX( angleToVec(rot2.smallestAngle()), angleToVec(rot2.angle()) );
- Matrix<Scalar,2,2> rot2_as_mat(rot2);
- Rotation2D<Scalar> rot3(rot2_as_mat);
- VERIFY_IS_APPROX( angleToVec(rot2.smallestAngle()), angleToVec(rot3.angle()) );
- }
- s0 = internal::random<Scalar>(-100,100);
- s1 = internal::random<Scalar>(-100,100);
- Rotation2D<Scalar> R0(s0), R1(s1);
-
- t20 = Translation2(v20) * (R0 * Eigen::Scaling(s0));
- t21 = Translation2(v20) * R0 * Eigen::Scaling(s0);
- VERIFY_IS_APPROX(t20,t21);
-
- t20 = Translation2(v20) * (R0 * R0.inverse() * Eigen::Scaling(s0));
- t21 = Translation2(v20) * Eigen::Scaling(s0);
- VERIFY_IS_APPROX(t20,t21);
-
- VERIFY_IS_APPROX(s0, (R0.slerp(0, R1)).angle());
- VERIFY_IS_APPROX( angleToVec(R1.smallestPositiveAngle()), angleToVec((R0.slerp(1, R1)).smallestPositiveAngle()) );
- VERIFY_IS_APPROX(R0.smallestPositiveAngle(), (R0.slerp(0.5, R0)).smallestPositiveAngle());
- if(std::cos(s0)>0)
- VERIFY_IS_MUCH_SMALLER_THAN((R0.slerp(0.5, R0.inverse())).smallestAngle(), Scalar(1));
- else
- VERIFY_IS_APPROX(Scalar(EIGEN_PI), (R0.slerp(0.5, R0.inverse())).smallestPositiveAngle());
-
- // Check path length
- Scalar l = 0;
- int path_steps = 100;
- for(int k=0; k<path_steps; ++k)
- {
- Scalar a1 = R0.slerp(Scalar(k)/Scalar(path_steps), R1).angle();
- Scalar a2 = R0.slerp(Scalar(k+1)/Scalar(path_steps), R1).angle();
- l += std::abs(a2-a1);
- }
- VERIFY(l<=Scalar(EIGEN_PI)*(Scalar(1)+NumTraits<Scalar>::epsilon()*Scalar(path_steps/2)));
-
- // check basic features
- {
- Rotation2D<Scalar> r1; // default ctor
- r1 = Rotation2D<Scalar>(s0); // copy assignment
- VERIFY_IS_APPROX(r1.angle(),s0);
- Rotation2D<Scalar> r2(r1); // copy ctor
- VERIFY_IS_APPROX(r2.angle(),s0);
- }
- {
- Transform3 t32(Matrix4::Random()), t33, t34;
- t34 = t33 = t32;
- t32.scale(v0);
- t33*=AlignedScaling3(v0);
- VERIFY_IS_APPROX(t32.matrix(), t33.matrix());
- t33 = t34 * AlignedScaling3(v0);
- VERIFY_IS_APPROX(t32.matrix(), t33.matrix());
- }
- }
- template<typename A1, typename A2, typename P, typename Q, typename V, typename H>
- void transform_associativity_left(const A1& a1, const A2& a2, const P& p, const Q& q, const V& v, const H& h)
- {
- VERIFY_IS_APPROX( q*(a1*v), (q*a1)*v );
- VERIFY_IS_APPROX( q*(a2*v), (q*a2)*v );
- VERIFY_IS_APPROX( q*(p*h).hnormalized(), ((q*p)*h).hnormalized() );
- }
- template<typename A1, typename A2, typename P, typename Q, typename V, typename H>
- void transform_associativity2(const A1& a1, const A2& a2, const P& p, const Q& q, const V& v, const H& h)
- {
- VERIFY_IS_APPROX( a1*(q*v), (a1*q)*v );
- VERIFY_IS_APPROX( a2*(q*v), (a2*q)*v );
- VERIFY_IS_APPROX( p *(q*v).homogeneous(), (p *q)*v.homogeneous() );
- transform_associativity_left(a1, a2,p, q, v, h);
- }
- template<typename Scalar, int Dim, int Options,typename RotationType>
- void transform_associativity(const RotationType& R)
- {
- typedef Matrix<Scalar,Dim,1> VectorType;
- typedef Matrix<Scalar,Dim+1,1> HVectorType;
- typedef Matrix<Scalar,Dim,Dim> LinearType;
- typedef Matrix<Scalar,Dim+1,Dim+1> MatrixType;
- typedef Transform<Scalar,Dim,AffineCompact,Options> AffineCompactType;
- typedef Transform<Scalar,Dim,Affine,Options> AffineType;
- typedef Transform<Scalar,Dim,Projective,Options> ProjectiveType;
- typedef DiagonalMatrix<Scalar,Dim> ScalingType;
- typedef Translation<Scalar,Dim> TranslationType;
- AffineCompactType A1c; A1c.matrix().setRandom();
- AffineCompactType A2c; A2c.matrix().setRandom();
- AffineType A1(A1c);
- AffineType A2(A2c);
- ProjectiveType P1; P1.matrix().setRandom();
- VectorType v1 = VectorType::Random();
- VectorType v2 = VectorType::Random();
- HVectorType h1 = HVectorType::Random();
- Scalar s1 = internal::random<Scalar>();
- LinearType L = LinearType::Random();
- MatrixType M = MatrixType::Random();
- CALL_SUBTEST( transform_associativity2(A1c, A1, P1, A2, v2, h1) );
- CALL_SUBTEST( transform_associativity2(A1c, A1, P1, A2c, v2, h1) );
- CALL_SUBTEST( transform_associativity2(A1c, A1, P1, v1.asDiagonal(), v2, h1) );
- CALL_SUBTEST( transform_associativity2(A1c, A1, P1, ScalingType(v1), v2, h1) );
- CALL_SUBTEST( transform_associativity2(A1c, A1, P1, Scaling(v1), v2, h1) );
- CALL_SUBTEST( transform_associativity2(A1c, A1, P1, Scaling(s1), v2, h1) );
- CALL_SUBTEST( transform_associativity2(A1c, A1, P1, TranslationType(v1), v2, h1) );
- CALL_SUBTEST( transform_associativity_left(A1c, A1, P1, L, v2, h1) );
- CALL_SUBTEST( transform_associativity2(A1c, A1, P1, R, v2, h1) );
- VERIFY_IS_APPROX( A1*(M*h1), (A1*M)*h1 );
- VERIFY_IS_APPROX( A1c*(M*h1), (A1c*M)*h1 );
- VERIFY_IS_APPROX( P1*(M*h1), (P1*M)*h1 );
- VERIFY_IS_APPROX( M*(A1*h1), (M*A1)*h1 );
- VERIFY_IS_APPROX( M*(A1c*h1), (M*A1c)*h1 );
- VERIFY_IS_APPROX( M*(P1*h1), ((M*P1)*h1) );
- }
- template<typename Scalar> void transform_alignment()
- {
- typedef Transform<Scalar,3,Projective,AutoAlign> Projective3a;
- typedef Transform<Scalar,3,Projective,DontAlign> Projective3u;
- EIGEN_ALIGN_MAX Scalar array1[16];
- EIGEN_ALIGN_MAX Scalar array2[16];
- EIGEN_ALIGN_MAX Scalar array3[16+1];
- Scalar* array3u = array3+1;
- Projective3a *p1 = ::new(reinterpret_cast<void*>(array1)) Projective3a;
- Projective3u *p2 = ::new(reinterpret_cast<void*>(array2)) Projective3u;
- Projective3u *p3 = ::new(reinterpret_cast<void*>(array3u)) Projective3u;
-
- p1->matrix().setRandom();
- *p2 = *p1;
- *p3 = *p1;
- VERIFY_IS_APPROX(p1->matrix(), p2->matrix());
- VERIFY_IS_APPROX(p1->matrix(), p3->matrix());
-
- VERIFY_IS_APPROX( (*p1) * (*p1), (*p2)*(*p3));
-
- #if defined(EIGEN_VECTORIZE) && EIGEN_MAX_STATIC_ALIGN_BYTES>0
- if(internal::packet_traits<Scalar>::Vectorizable)
- VERIFY_RAISES_ASSERT((::new(reinterpret_cast<void*>(array3u)) Projective3a));
- #endif
- }
- template<typename Scalar, int Dim, int Options> void transform_products()
- {
- typedef Matrix<Scalar,Dim+1,Dim+1> Mat;
- typedef Transform<Scalar,Dim,Projective,Options> Proj;
- typedef Transform<Scalar,Dim,Affine,Options> Aff;
- typedef Transform<Scalar,Dim,AffineCompact,Options> AffC;
- Proj p; p.matrix().setRandom();
- Aff a; a.linear().setRandom(); a.translation().setRandom();
- AffC ac = a;
- Mat p_m(p.matrix()), a_m(a.matrix());
- VERIFY_IS_APPROX((p*p).matrix(), p_m*p_m);
- VERIFY_IS_APPROX((a*a).matrix(), a_m*a_m);
- VERIFY_IS_APPROX((p*a).matrix(), p_m*a_m);
- VERIFY_IS_APPROX((a*p).matrix(), a_m*p_m);
- VERIFY_IS_APPROX((ac*a).matrix(), a_m*a_m);
- VERIFY_IS_APPROX((a*ac).matrix(), a_m*a_m);
- VERIFY_IS_APPROX((p*ac).matrix(), p_m*a_m);
- VERIFY_IS_APPROX((ac*p).matrix(), a_m*p_m);
- }
- template<typename Scalar, int Mode, int Options> void transformations_no_scale()
- {
- /* this test covers the following files:
- Cross.h Quaternion.h, Transform.h
- */
- typedef Matrix<Scalar,3,1> Vector3;
- typedef Matrix<Scalar,4,1> Vector4;
- typedef Quaternion<Scalar> Quaternionx;
- typedef AngleAxis<Scalar> AngleAxisx;
- typedef Transform<Scalar,3,Mode,Options> Transform3;
- typedef Translation<Scalar,3> Translation3;
- typedef Matrix<Scalar,4,4> Matrix4;
- Vector3 v0 = Vector3::Random(),
- v1 = Vector3::Random();
- Transform3 t0, t1, t2;
- Scalar a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI));
- Quaternionx q1, q2;
- q1 = AngleAxisx(a, v0.normalized());
- t0 = Transform3::Identity();
- VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());
- t0.setIdentity();
- t1.setIdentity();
- v1 = Vector3::Ones();
- t0.linear() = q1.toRotationMatrix();
- t0.pretranslate(v0);
- t1.linear() = q1.conjugate().toRotationMatrix();
- t1.translate(-v0);
- VERIFY((t0 * 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);
- // translation * vector
- t0.setIdentity();
- t0.translate(v0);
- VERIFY_IS_APPROX((t0 * v1).template head<3>(), Translation3(v0) * v1);
- // Conversion to matrix.
- Transform3 t3;
- t3.linear() = q1.toRotationMatrix();
- t3.translation() = v1;
- Matrix4 m3 = t3.matrix();
- VERIFY((m3 * m3.inverse()).isIdentity(test_precision<Scalar>()));
- // Verify implicit last row is initialized.
- VERIFY_IS_APPROX(Vector4(m3.row(3)), Vector4(0.0, 0.0, 0.0, 1.0));
- }
- void test_geo_transformations()
- {
- for(int i = 0; i < g_repeat; i++) {
- CALL_SUBTEST_1(( transformations<double,Affine,AutoAlign>() ));
- CALL_SUBTEST_1(( non_projective_only<double,Affine,AutoAlign>() ));
-
- CALL_SUBTEST_2(( transformations<float,AffineCompact,AutoAlign>() ));
- CALL_SUBTEST_2(( non_projective_only<float,AffineCompact,AutoAlign>() ));
- CALL_SUBTEST_2(( transform_alignment<float>() ));
-
- CALL_SUBTEST_3(( transformations<double,Projective,AutoAlign>() ));
- CALL_SUBTEST_3(( transformations<double,Projective,DontAlign>() ));
- CALL_SUBTEST_3(( transform_alignment<double>() ));
- CALL_SUBTEST_4(( transformations<float,Affine,RowMajor|AutoAlign>() ));
- CALL_SUBTEST_4(( non_projective_only<float,Affine,RowMajor>() ));
-
- CALL_SUBTEST_5(( transformations<double,AffineCompact,RowMajor|AutoAlign>() ));
- CALL_SUBTEST_5(( non_projective_only<double,AffineCompact,RowMajor>() ));
- CALL_SUBTEST_6(( transformations<double,Projective,RowMajor|AutoAlign>() ));
- CALL_SUBTEST_6(( transformations<double,Projective,RowMajor|DontAlign>() ));
- CALL_SUBTEST_7(( transform_products<double,3,RowMajor|AutoAlign>() ));
- CALL_SUBTEST_7(( transform_products<float,2,AutoAlign>() ));
- CALL_SUBTEST_8(( transform_associativity<double,2,ColMajor>(Rotation2D<double>(internal::random<double>()*double(EIGEN_PI))) ));
- CALL_SUBTEST_8(( transform_associativity<double,3,ColMajor>(Quaterniond::UnitRandom()) ));
- CALL_SUBTEST_9(( transformations_no_scale<double,Affine,AutoAlign>() ));
- CALL_SUBTEST_9(( transformations_no_scale<double,Isometry,AutoAlign>() ));
- }
- }
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