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487 lines
17 KiB
487 lines
17 KiB
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#include "main.h"
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#include <Eigen/Geometry>
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#include <Eigen/LU>
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#include <Eigen/SVD>
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template<typename Scalar, int Mode, int Options> void non_projective_only()
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{
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/* this test covers the following files:
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Cross.h Quaternion.h, Transform.cpp
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*/
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typedef Matrix<Scalar,2,2> Matrix2;
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typedef Matrix<Scalar,3,3> Matrix3;
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typedef Matrix<Scalar,4,4> Matrix4;
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typedef Matrix<Scalar,2,1> Vector2;
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typedef Matrix<Scalar,3,1> Vector3;
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typedef Matrix<Scalar,4,1> Vector4;
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typedef Quaternion<Scalar> Quaternionx;
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typedef AngleAxis<Scalar> AngleAxisx;
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typedef Transform<Scalar,2,Mode,Options> Transform2;
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typedef Transform<Scalar,3,Mode,Options> Transform3;
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typedef Transform<Scalar,2,Isometry,Options> Isometry2;
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typedef Transform<Scalar,3,Isometry,Options> Isometry3;
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typedef typename Transform3::MatrixType MatrixType;
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typedef DiagonalMatrix<Scalar,2> AlignedScaling2;
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typedef DiagonalMatrix<Scalar,3> AlignedScaling3;
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typedef Translation<Scalar,2> Translation2;
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typedef Translation<Scalar,3> Translation3;
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Vector3 v0 = Vector3::Random(),
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v1 = Vector3::Random();
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Transform3 t0, t1, t2;
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Scalar a = internal::random<Scalar>(-Scalar(M_PI), Scalar(M_PI));
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Quaternionx q1, q2;
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q1 = AngleAxisx(a, v0.normalized());
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t0 = Transform3::Identity();
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VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());
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t0.linear() = q1.toRotationMatrix();
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v0 << 50, 2, 1;
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t0.scale(v0);
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VERIFY_IS_APPROX( (t0 * Vector3(1,0,0)).template head<3>().norm(), v0.x());
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t0.setIdentity();
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t1.setIdentity();
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v1 << 1, 2, 3;
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t0.linear() = q1.toRotationMatrix();
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t0.pretranslate(v0);
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t0.scale(v1);
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t1.linear() = q1.conjugate().toRotationMatrix();
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t1.prescale(v1.cwiseInverse());
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t1.translate(-v0);
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VERIFY((t0 * t1).matrix().isIdentity(test_precision<Scalar>()));
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t1.fromPositionOrientationScale(v0, q1, v1);
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VERIFY_IS_APPROX(t1.matrix(), t0.matrix());
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VERIFY_IS_APPROX(t1*v1, t0*v1);
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// translation * vector
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t0.setIdentity();
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t0.translate(v0);
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VERIFY_IS_APPROX((t0 * v1).template head<3>(), Translation3(v0) * v1);
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// AlignedScaling * vector
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t0.setIdentity();
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t0.scale(v0);
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VERIFY_IS_APPROX((t0 * v1).template head<3>(), AlignedScaling3(v0) * v1);
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}
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template<typename Scalar, int Mode, int Options> void transformations()
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{
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/* this test covers the following files:
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Cross.h Quaternion.h, Transform.cpp
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*/
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typedef Matrix<Scalar,2,2> Matrix2;
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typedef Matrix<Scalar,3,3> Matrix3;
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typedef Matrix<Scalar,4,4> Matrix4;
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typedef Matrix<Scalar,2,1> Vector2;
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typedef Matrix<Scalar,3,1> Vector3;
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typedef Matrix<Scalar,4,1> Vector4;
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typedef Quaternion<Scalar> Quaternionx;
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typedef AngleAxis<Scalar> AngleAxisx;
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typedef Transform<Scalar,2,Mode,Options> Transform2;
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typedef Transform<Scalar,3,Mode,Options> Transform3;
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typedef Transform<Scalar,2,Isometry,Options> Isometry2;
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typedef Transform<Scalar,3,Isometry,Options> Isometry3;
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typedef typename Transform3::MatrixType MatrixType;
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typedef DiagonalMatrix<Scalar,2> AlignedScaling2;
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typedef DiagonalMatrix<Scalar,3> AlignedScaling3;
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typedef Translation<Scalar,2> Translation2;
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typedef Translation<Scalar,3> Translation3;
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Vector3 v0 = Vector3::Random(),
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v1 = Vector3::Random();
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Matrix3 matrot1, m;
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Scalar a = internal::random<Scalar>(-Scalar(M_PI), Scalar(M_PI));
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Scalar s0 = internal::random<Scalar>();
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VERIFY_IS_APPROX(v0, AngleAxisx(a, v0.normalized()) * v0);
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VERIFY_IS_APPROX(-v0, AngleAxisx(Scalar(M_PI), v0.unitOrthogonal()) * v0);
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VERIFY_IS_APPROX(internal::cos(a)*v0.squaredNorm(), v0.dot(AngleAxisx(a, v0.unitOrthogonal()) * v0));
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m = AngleAxisx(a, v0.normalized()).toRotationMatrix().adjoint();
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VERIFY_IS_APPROX(Matrix3::Identity(), m * AngleAxisx(a, v0.normalized()));
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VERIFY_IS_APPROX(Matrix3::Identity(), AngleAxisx(a, v0.normalized()) * m);
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Quaternionx q1, q2;
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q1 = AngleAxisx(a, v0.normalized());
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q2 = AngleAxisx(a, v1.normalized());
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// rotation matrix conversion
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matrot1 = AngleAxisx(Scalar(0.1), Vector3::UnitX())
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* AngleAxisx(Scalar(0.2), Vector3::UnitY())
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* AngleAxisx(Scalar(0.3), Vector3::UnitZ());
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VERIFY_IS_APPROX(matrot1 * v1,
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AngleAxisx(Scalar(0.1), Vector3(1,0,0)).toRotationMatrix()
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* (AngleAxisx(Scalar(0.2), Vector3(0,1,0)).toRotationMatrix()
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* (AngleAxisx(Scalar(0.3), Vector3(0,0,1)).toRotationMatrix() * v1)));
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// angle-axis conversion
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AngleAxisx aa = AngleAxisx(q1);
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VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1);
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VERIFY_IS_NOT_APPROX(q1 * v1, Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1);
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aa.fromRotationMatrix(aa.toRotationMatrix());
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VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1);
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VERIFY_IS_NOT_APPROX(q1 * v1, Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1);
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// AngleAxis
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VERIFY_IS_APPROX(AngleAxisx(a,v1.normalized()).toRotationMatrix(),
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Quaternionx(AngleAxisx(a,v1.normalized())).toRotationMatrix());
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AngleAxisx aa1;
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m = q1.toRotationMatrix();
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aa1 = m;
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VERIFY_IS_APPROX(AngleAxisx(m).toRotationMatrix(),
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Quaternionx(m).toRotationMatrix());
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// Transform
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// TODO complete the tests !
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a = 0;
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while (internal::abs(a)<Scalar(0.1))
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a = internal::random<Scalar>(-Scalar(0.4)*Scalar(M_PI), Scalar(0.4)*Scalar(M_PI));
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q1 = AngleAxisx(a, v0.normalized());
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Transform3 t0, t1, t2;
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// first test setIdentity() and Identity()
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t0.setIdentity();
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VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());
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t0.matrix().setZero();
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t0 = Transform3::Identity();
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VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());
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t0.setIdentity();
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t1.setIdentity();
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v1 << 1, 2, 3;
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t0.linear() = q1.toRotationMatrix();
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t0.pretranslate(v0);
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t0.scale(v1);
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t1.linear() = q1.conjugate().toRotationMatrix();
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t1.prescale(v1.cwiseInverse());
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t1.translate(-v0);
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VERIFY((t0 * t1).matrix().isIdentity(test_precision<Scalar>()));
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t1.fromPositionOrientationScale(v0, q1, v1);
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VERIFY_IS_APPROX(t1.matrix(), t0.matrix());
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t0.setIdentity(); t0.scale(v0).rotate(q1.toRotationMatrix());
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t1.setIdentity(); t1.scale(v0).rotate(q1);
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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t0.setIdentity(); t0.scale(v0).rotate(AngleAxisx(q1));
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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VERIFY_IS_APPROX(t0.scale(a).matrix(), t1.scale(Vector3::Constant(a)).matrix());
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VERIFY_IS_APPROX(t0.prescale(a).matrix(), t1.prescale(Vector3::Constant(a)).matrix());
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// More transform constructors, operator=, operator*=
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Matrix3 mat3 = Matrix3::Random();
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Matrix4 mat4;
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mat4 << mat3 , Vector3::Zero() , Vector4::Zero().transpose();
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Transform3 tmat3(mat3), tmat4(mat4);
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if(Mode!=int(AffineCompact))
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tmat4.matrix()(3,3) = Scalar(1);
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VERIFY_IS_APPROX(tmat3.matrix(), tmat4.matrix());
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Scalar a3 = internal::random<Scalar>(-Scalar(M_PI), Scalar(M_PI));
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Vector3 v3 = Vector3::Random().normalized();
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AngleAxisx aa3(a3, v3);
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Transform3 t3(aa3);
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Transform3 t4;
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t4 = aa3;
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VERIFY_IS_APPROX(t3.matrix(), t4.matrix());
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t4.rotate(AngleAxisx(-a3,v3));
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VERIFY_IS_APPROX(t4.matrix(), MatrixType::Identity());
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t4 *= aa3;
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VERIFY_IS_APPROX(t3.matrix(), t4.matrix());
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v3 = Vector3::Random();
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Translation3 tv3(v3);
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Transform3 t5(tv3);
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t4 = tv3;
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VERIFY_IS_APPROX(t5.matrix(), t4.matrix());
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t4.translate(-v3);
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VERIFY_IS_APPROX(t4.matrix(), MatrixType::Identity());
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t4 *= tv3;
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VERIFY_IS_APPROX(t5.matrix(), t4.matrix());
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AlignedScaling3 sv3(v3);
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Transform3 t6(sv3);
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t4 = sv3;
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VERIFY_IS_APPROX(t6.matrix(), t4.matrix());
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t4.scale(v3.cwiseInverse());
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VERIFY_IS_APPROX(t4.matrix(), MatrixType::Identity());
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t4 *= sv3;
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VERIFY_IS_APPROX(t6.matrix(), t4.matrix());
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// matrix * transform
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VERIFY_IS_APPROX((t3.matrix()*t4).matrix(), (t3*t4).matrix());
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// chained Transform product
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VERIFY_IS_APPROX(((t3*t4)*t5).matrix(), (t3*(t4*t5)).matrix());
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// check that Transform product doesn't have aliasing problems
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t5 = t4;
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t5 = t5*t5;
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VERIFY_IS_APPROX(t5, t4*t4);
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// 2D transformation
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Transform2 t20, t21;
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Vector2 v20 = Vector2::Random();
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Vector2 v21 = Vector2::Random();
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for (int k=0; k<2; ++k)
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if (internal::abs(v21[k])<Scalar(1e-3)) v21[k] = Scalar(1e-3);
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t21.setIdentity();
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t21.linear() = Rotation2D<Scalar>(a).toRotationMatrix();
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VERIFY_IS_APPROX(t20.fromPositionOrientationScale(v20,a,v21).matrix(),
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t21.pretranslate(v20).scale(v21).matrix());
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t21.setIdentity();
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t21.linear() = Rotation2D<Scalar>(-a).toRotationMatrix();
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VERIFY( (t20.fromPositionOrientationScale(v20,a,v21)
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* (t21.prescale(v21.cwiseInverse()).translate(-v20))).matrix().isIdentity(test_precision<Scalar>()) );
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// Transform - new API
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// 3D
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t0.setIdentity();
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t0.rotate(q1).scale(v0).translate(v0);
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// mat * aligned scaling and mat * translation
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t1 = (Matrix3(q1) * AlignedScaling3(v0)) * Translation3(v0);
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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t1 = (Matrix3(q1) * Eigen::Scaling(v0)) * Translation3(v0);
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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t1 = (q1 * Eigen::Scaling(v0)) * Translation3(v0);
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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// mat * transformation and aligned scaling * translation
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t1 = Matrix3(q1) * (AlignedScaling3(v0) * Translation3(v0));
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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t0.setIdentity();
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t0.scale(s0).translate(v0);
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t1 = Eigen::Scaling(s0) * Translation3(v0);
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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t0.prescale(s0);
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t1 = Eigen::Scaling(s0) * t1;
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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t0 = t3;
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t0.scale(s0);
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t1 = t3 * Eigen::Scaling(s0,s0,s0);
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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t0.prescale(s0);
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t1 = Eigen::Scaling(s0,s0,s0) * t1;
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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t0.setIdentity();
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t0.prerotate(q1).prescale(v0).pretranslate(v0);
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// translation * aligned scaling and transformation * mat
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t1 = (Translation3(v0) * AlignedScaling3(v0)) * Transform3(q1);
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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// scaling * mat and translation * mat
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t1 = Translation3(v0) * (AlignedScaling3(v0) * Transform3(q1));
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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t0.setIdentity();
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t0.scale(v0).translate(v0).rotate(q1);
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// translation * mat and aligned scaling * transformation
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t1 = AlignedScaling3(v0) * (Translation3(v0) * Transform3(q1));
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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// transformation * aligned scaling
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t0.scale(v0);
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t1 *= AlignedScaling3(v0);
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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// transformation * translation
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t0.translate(v0);
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t1 = t1 * Translation3(v0);
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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// translation * transformation
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t0.pretranslate(v0);
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t1 = Translation3(v0) * t1;
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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// transform * quaternion
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t0.rotate(q1);
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t1 = t1 * q1;
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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// translation * quaternion
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t0.translate(v1).rotate(q1);
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t1 = t1 * (Translation3(v1) * q1);
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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// aligned scaling * quaternion
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t0.scale(v1).rotate(q1);
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t1 = t1 * (AlignedScaling3(v1) * q1);
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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// quaternion * transform
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t0.prerotate(q1);
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t1 = q1 * t1;
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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// quaternion * translation
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t0.rotate(q1).translate(v1);
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t1 = t1 * (q1 * Translation3(v1));
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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// quaternion * aligned scaling
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t0.rotate(q1).scale(v1);
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t1 = t1 * (q1 * AlignedScaling3(v1));
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VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
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// test transform inversion
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t0.setIdentity();
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t0.translate(v0);
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t0.linear().setRandom();
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Matrix4 t044 = Matrix4::Zero();
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t044(3,3) = 1;
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t044.block(0,0,t0.matrix().rows(),4) = t0.matrix();
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VERIFY_IS_APPROX(t0.inverse(Affine).matrix(), t044.inverse().block(0,0,t0.matrix().rows(),4));
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t0.setIdentity();
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t0.translate(v0).rotate(q1);
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t044 = Matrix4::Zero();
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t044(3,3) = 1;
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t044.block(0,0,t0.matrix().rows(),4) = t0.matrix();
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VERIFY_IS_APPROX(t0.inverse(Isometry).matrix(), t044.inverse().block(0,0,t0.matrix().rows(),4));
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Matrix3 mat_rotation, mat_scaling;
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t0.setIdentity();
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t0.translate(v0).rotate(q1).scale(v1);
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t0.computeRotationScaling(&mat_rotation, &mat_scaling);
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VERIFY_IS_APPROX(t0.linear(), mat_rotation * mat_scaling);
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VERIFY_IS_APPROX(mat_rotation*mat_rotation.adjoint(), Matrix3::Identity());
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VERIFY_IS_APPROX(mat_rotation.determinant(), Scalar(1));
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t0.computeScalingRotation(&mat_scaling, &mat_rotation);
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VERIFY_IS_APPROX(t0.linear(), mat_scaling * mat_rotation);
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VERIFY_IS_APPROX(mat_rotation*mat_rotation.adjoint(), Matrix3::Identity());
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VERIFY_IS_APPROX(mat_rotation.determinant(), Scalar(1));
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// test casting
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Transform<float,3,Mode> t1f = t1.template cast<float>();
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VERIFY_IS_APPROX(t1f.template cast<Scalar>(),t1);
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Transform<double,3,Mode> t1d = t1.template cast<double>();
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VERIFY_IS_APPROX(t1d.template cast<Scalar>(),t1);
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Translation3 tr1(v0);
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Translation<float,3> tr1f = tr1.template cast<float>();
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VERIFY_IS_APPROX(tr1f.template cast<Scalar>(),tr1);
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Translation<double,3> tr1d = tr1.template cast<double>();
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VERIFY_IS_APPROX(tr1d.template cast<Scalar>(),tr1);
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AngleAxis<float> aa1f = aa1.template cast<float>();
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VERIFY_IS_APPROX(aa1f.template cast<Scalar>(),aa1);
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AngleAxis<double> aa1d = aa1.template cast<double>();
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VERIFY_IS_APPROX(aa1d.template cast<Scalar>(),aa1);
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Rotation2D<Scalar> r2d1(internal::random<Scalar>());
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Rotation2D<float> r2d1f = r2d1.template cast<float>();
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VERIFY_IS_APPROX(r2d1f.template cast<Scalar>(),r2d1);
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Rotation2D<double> r2d1d = r2d1.template cast<double>();
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VERIFY_IS_APPROX(r2d1d.template cast<Scalar>(),r2d1);
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t20 = Translation2(v20) * (Rotation2D<Scalar>(s0) * Scaling(s0));
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t21 = Translation2(v20) * Rotation2D<Scalar>(s0) * Scaling(s0);
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VERIFY_IS_APPROX(t20,t21);
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}
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template<typename Scalar> void transform_alignment()
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{
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typedef Transform<Scalar,3,Projective,AutoAlign> Projective3a;
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typedef Transform<Scalar,3,Projective,DontAlign> Projective3u;
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EIGEN_ALIGN16 Scalar array1[16];
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EIGEN_ALIGN16 Scalar array2[16];
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EIGEN_ALIGN16 Scalar array3[16+1];
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Scalar* array3u = array3+1;
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Projective3a *p1 = ::new(reinterpret_cast<void*>(array1)) Projective3a;
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Projective3u *p2 = ::new(reinterpret_cast<void*>(array2)) Projective3u;
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Projective3u *p3 = ::new(reinterpret_cast<void*>(array3u)) Projective3u;
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p1->matrix().setRandom();
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*p2 = *p1;
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*p3 = *p1;
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VERIFY_IS_APPROX(p1->matrix(), p2->matrix());
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VERIFY_IS_APPROX(p1->matrix(), p3->matrix());
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VERIFY_IS_APPROX( (*p1) * (*p1), (*p2)*(*p3));
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#if defined(EIGEN_VECTORIZE) && EIGEN_ALIGN_STATICALLY
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if(internal::packet_traits<Scalar>::Vectorizable)
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VERIFY_RAISES_ASSERT((::new(reinterpret_cast<void*>(array3u)) Projective3a));
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#endif
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}
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template<typename Scalar, int Dim, int Options> void transform_products()
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{
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typedef Matrix<Scalar,Dim+1,Dim+1> Mat;
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typedef Transform<Scalar,Dim,Projective,Options> Proj;
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typedef Transform<Scalar,Dim,Affine,Options> Aff;
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typedef Transform<Scalar,Dim,AffineCompact,Options> AffC;
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Proj p; p.matrix().setRandom();
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Aff a; a.linear().setRandom(); a.translation().setRandom();
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AffC ac = a;
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Mat p_m(p.matrix()), a_m(a.matrix());
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VERIFY_IS_APPROX((p*p).matrix(), p_m*p_m);
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VERIFY_IS_APPROX((a*a).matrix(), a_m*a_m);
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VERIFY_IS_APPROX((p*a).matrix(), p_m*a_m);
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VERIFY_IS_APPROX((a*p).matrix(), a_m*p_m);
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VERIFY_IS_APPROX((ac*a).matrix(), a_m*a_m);
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VERIFY_IS_APPROX((a*ac).matrix(), a_m*a_m);
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VERIFY_IS_APPROX((p*ac).matrix(), p_m*a_m);
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VERIFY_IS_APPROX((ac*p).matrix(), a_m*p_m);
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}
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void test_geo_transformations()
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{
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for(int i = 0; i < g_repeat; i++) {
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CALL_SUBTEST_1(( transformations<double,Affine,AutoAlign>() ));
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CALL_SUBTEST_1(( non_projective_only<double,Affine,AutoAlign>() ));
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CALL_SUBTEST_2(( transformations<float,AffineCompact,AutoAlign>() ));
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CALL_SUBTEST_2(( non_projective_only<float,AffineCompact,AutoAlign>() ));
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CALL_SUBTEST_2(( transform_alignment<float>() ));
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CALL_SUBTEST_3(( transformations<double,Projective,AutoAlign>() ));
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CALL_SUBTEST_3(( transformations<double,Projective,DontAlign>() ));
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CALL_SUBTEST_3(( transform_alignment<double>() ));
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CALL_SUBTEST_4(( transformations<float,Affine,RowMajor|AutoAlign>() ));
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CALL_SUBTEST_4(( non_projective_only<float,Affine,RowMajor>() ));
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CALL_SUBTEST_5(( transformations<double,AffineCompact,RowMajor|AutoAlign>() ));
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CALL_SUBTEST_5(( non_projective_only<double,AffineCompact,RowMajor>() ));
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CALL_SUBTEST_6(( transformations<double,Projective,RowMajor|AutoAlign>() ));
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CALL_SUBTEST_6(( transformations<double,Projective,RowMajor|DontAlign>() ));
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CALL_SUBTEST_7(( transform_products<double,3,RowMajor|AutoAlign>() ));
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CALL_SUBTEST_7(( transform_products<float,2,AutoAlign>() ));
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}
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}
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