initial commit
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huangweifeng
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// 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 T>
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Matrix<T, 2, 1> angleToVec(T a) {
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return Matrix<T, 2, 1>(std::cos(a), std::sin(a));
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}
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// This permits to workaround a bug in clang/llvm code generation.
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template <typename T>
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EIGEN_DONT_INLINE void dont_over_optimize(T& x) {
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volatile typename T::Scalar tmp = x(0);
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x(0) = tmp;
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}
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template <typename Scalar, int Mode, int Options>
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void non_projective_only() {
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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, 3, 1> Vector3;
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typedef Quaternion<Scalar> Quaternionx;
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typedef AngleAxis<Scalar> AngleAxisx;
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typedef Transform<Scalar, 3, Mode, Options> Transform3;
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typedef DiagonalMatrix<Scalar, 3> AlignedScaling3;
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typedef Translation<Scalar, 3> Translation3;
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Vector3 v0 = Vector3::Random(), v1 = Vector3::Random();
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Transform3 t0, t1, t2;
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Scalar a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_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>
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void transformations() {
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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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using std::abs;
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using std::cos;
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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 typename Transform3::MatrixType MatrixType;
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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(), v1 = Vector3::Random();
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Matrix3 matrot1, m;
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Scalar a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI));
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Scalar s0 = internal::random<Scalar>(), s1 = internal::random<Scalar>();
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while (v0.norm() < test_precision<Scalar>()) v0 = Vector3::Random();
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while (v1.norm() < test_precision<Scalar>()) v1 = Vector3::Random();
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VERIFY_IS_APPROX(v0, AngleAxisx(a, v0.normalized()) * v0);
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VERIFY_IS_APPROX(-v0, AngleAxisx(Scalar(EIGEN_PI), v0.unitOrthogonal()) * v0);
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if (abs(cos(a)) > test_precision<Scalar>()) {
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VERIFY_IS_APPROX(cos(a) * v0.squaredNorm(), v0.dot(AngleAxisx(a, v0.unitOrthogonal()) * v0));
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}
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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()) * 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, 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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// The following test is stable only if 2*angle != angle and v1 is not colinear with axis
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if ((abs(aa.angle()) > test_precision<Scalar>()) &&
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(abs(aa.axis().dot(v1.normalized())) < (Scalar(1) - Scalar(4) * test_precision<Scalar>()))) {
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VERIFY(!(q1 * v1).isApprox(Quaternionx(AngleAxisx(aa.angle() * 2, aa.axis())) * v1));
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}
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aa.fromRotationMatrix(aa.toRotationMatrix());
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VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1);
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// The following test is stable only if 2*angle != angle and v1 is not colinear with axis
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if ((abs(aa.angle()) > test_precision<Scalar>()) &&
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(abs(aa.axis().dot(v1.normalized())) < (Scalar(1) - Scalar(4) * test_precision<Scalar>()))) {
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VERIFY(!(q1 * v1).isApprox(Quaternionx(AngleAxisx(aa.angle() * 2, aa.axis())) * v1));
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}
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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(), 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 (abs(a) < Scalar(0.1))
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a = internal::random<Scalar>(-Scalar(0.4) * Scalar(EIGEN_PI), Scalar(0.4) * Scalar(EIGEN_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();
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t0.scale(v0).rotate(q1.toRotationMatrix());
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t1.setIdentity();
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t1.scale(v0).rotate(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).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)) 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(EIGEN_PI), Scalar(EIGEN_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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do {
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v3 = Vector3::Random();
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dont_over_optimize(v3);
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} while (v3.cwiseAbs().minCoeff() < NumTraits<Scalar>::epsilon());
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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).eval());
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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 (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(), 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) * (t21.prescale(v21.cwiseInverse()).translate(-v20)))
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.matrix()
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.isIdentity(test_precision<Scalar>()));
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t20.setIdentity();
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t20.shear(Scalar(2), Scalar(3));
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Transform2 t23 = t20 * t21;
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t21.preshear(Scalar(2), Scalar(3));
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VERIFY_IS_APPROX(t21, t23);
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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 = t3;
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t0.scale(s0);
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t1 = t3 * Eigen::Scaling(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) * 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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t1 = AlignedScaling3(v0) * (Translation3(v0) * Transform3(q1));
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t1 = t1 * v0.asDiagonal();
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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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do {
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t0.linear().setRandom();
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} while (t0.linear().jacobiSvd().singularValues()(2) < test_precision<Scalar>());
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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;
|
||||
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));
|
||||
}
|
||||
|
||||
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));
|
||||
|
||||
VERIFY_IS_APPROX(t3.rotation(), t3.linear());
|
||||
if (Mode == Isometry) VERIFY(t3.rotation().data() == t3.linear().data());
|
||||
}
|
||||
|
||||
template <typename Scalar, int Mode, int Options>
|
||||
void transformations_computed_scaling_continuity() {
|
||||
typedef Matrix<Scalar, 3, 1> Vector3;
|
||||
typedef Transform<Scalar, 3, Mode, Options> Transform3;
|
||||
typedef Matrix<Scalar, 3, 3> Matrix3;
|
||||
|
||||
// Given: two transforms that differ by '2*eps'.
|
||||
Scalar eps(1e-3);
|
||||
Vector3 v0 = Vector3::Random().normalized(), v1 = Vector3::Random().normalized(), v3 = Vector3::Random().normalized();
|
||||
Transform3 t0, t1;
|
||||
// The interesting case is when their determinants have different signs.
|
||||
Matrix3 rank2 = 50 * v0 * v0.adjoint() + 20 * v1 * v1.adjoint();
|
||||
t0.linear() = rank2 + eps * v3 * v3.adjoint();
|
||||
t1.linear() = rank2 - eps * v3 * v3.adjoint();
|
||||
|
||||
// When: computing the rotation-scaling parts
|
||||
Matrix3 r0, s0, r1, s1;
|
||||
t0.computeRotationScaling(&r0, &s0);
|
||||
t1.computeRotationScaling(&r1, &s1);
|
||||
|
||||
// Then: the scaling parts should differ by no more than '2*eps'.
|
||||
const Scalar c(2.1); // 2 + room for rounding errors
|
||||
VERIFY((s0 - s1).norm() < c * eps);
|
||||
}
|
||||
|
||||
EIGEN_DECLARE_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_1((transformations_computed_scaling_continuity<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>()));
|
||||
}
|
||||
}
|
||||
Reference in New Issue
Block a user