185 lines
7.1 KiB
C++
185 lines
7.1 KiB
C++
// 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 Gael Guennebaud <gael.guennebaud@inria.fr>
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// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
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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/QR>
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template <typename HyperplaneType>
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void hyperplane(const HyperplaneType &_plane) {
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/* this test covers the following files:
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Hyperplane.h
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*/
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using std::abs;
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const Index dim = _plane.dim();
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enum { Options = HyperplaneType::Options };
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typedef typename HyperplaneType::Scalar Scalar;
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typedef typename HyperplaneType::RealScalar RealScalar;
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typedef Matrix<Scalar, HyperplaneType::AmbientDimAtCompileTime, 1> VectorType;
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typedef Matrix<Scalar, HyperplaneType::AmbientDimAtCompileTime, HyperplaneType::AmbientDimAtCompileTime> MatrixType;
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VectorType p0 = VectorType::Random(dim);
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VectorType p1 = VectorType::Random(dim);
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VectorType n0 = VectorType::Random(dim).normalized();
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VectorType n1 = VectorType::Random(dim).normalized();
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HyperplaneType pl0(n0, p0);
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HyperplaneType pl1(n1, p1);
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HyperplaneType pl2 = pl1;
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Scalar s0 = internal::random<Scalar>();
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Scalar s1 = internal::random<Scalar>();
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VERIFY_IS_APPROX(n1.dot(n1), Scalar(1));
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VERIFY_IS_MUCH_SMALLER_THAN(pl0.absDistance(p0), Scalar(1));
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if (numext::abs2(s0) > RealScalar(1e-6))
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VERIFY_IS_APPROX(pl1.signedDistance(p1 + n1 * s0), s0);
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else
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VERIFY_IS_MUCH_SMALLER_THAN(abs(pl1.signedDistance(p1 + n1 * s0) - s0), Scalar(1));
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VERIFY_IS_MUCH_SMALLER_THAN(pl1.signedDistance(pl1.projection(p0)), Scalar(1));
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VERIFY_IS_MUCH_SMALLER_THAN(pl1.absDistance(p1 + pl1.normal().unitOrthogonal() * s1), Scalar(1));
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// transform
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if (!NumTraits<Scalar>::IsComplex) {
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MatrixType rot = MatrixType::Random(dim, dim).householderQr().householderQ();
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DiagonalMatrix<Scalar, HyperplaneType::AmbientDimAtCompileTime> scaling(VectorType::Random());
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Translation<Scalar, HyperplaneType::AmbientDimAtCompileTime> translation(VectorType::Random());
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while (scaling.diagonal().cwiseAbs().minCoeff() < RealScalar(1e-4)) scaling.diagonal() = VectorType::Random();
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pl2 = pl1;
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VERIFY_IS_MUCH_SMALLER_THAN(pl2.transform(rot).absDistance(rot * p1), Scalar(1));
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pl2 = pl1;
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VERIFY_IS_MUCH_SMALLER_THAN(pl2.transform(rot, Isometry).absDistance(rot * p1), Scalar(1));
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pl2 = pl1;
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VERIFY_IS_MUCH_SMALLER_THAN(pl2.transform(rot * scaling).absDistance((rot * scaling) * p1), Scalar(1));
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VERIFY_IS_APPROX(pl2.normal().norm(), RealScalar(1));
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pl2 = pl1;
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VERIFY_IS_MUCH_SMALLER_THAN(
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pl2.transform(rot * scaling * translation).absDistance((rot * scaling * translation) * p1), Scalar(1));
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VERIFY_IS_APPROX(pl2.normal().norm(), RealScalar(1));
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pl2 = pl1;
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VERIFY_IS_MUCH_SMALLER_THAN(pl2.transform(rot * translation, Isometry).absDistance((rot * translation) * p1),
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Scalar(1));
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VERIFY_IS_APPROX(pl2.normal().norm(), RealScalar(1));
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}
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// casting
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const int Dim = HyperplaneType::AmbientDimAtCompileTime;
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typedef typename GetDifferentType<Scalar>::type OtherScalar;
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Hyperplane<OtherScalar, Dim, Options> hp1f = pl1.template cast<OtherScalar>();
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VERIFY_IS_APPROX(hp1f.template cast<Scalar>(), pl1);
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Hyperplane<Scalar, Dim, Options> hp1d = pl1.template cast<Scalar>();
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VERIFY_IS_APPROX(hp1d.template cast<Scalar>(), pl1);
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}
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template <typename Scalar>
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void lines() {
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using std::abs;
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typedef Hyperplane<Scalar, 2> HLine;
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typedef ParametrizedLine<Scalar, 2> PLine;
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typedef Matrix<Scalar, 2, 1> Vector;
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typedef Matrix<Scalar, 3, 1> CoeffsType;
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for (int i = 0; i < 10; i++) {
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Vector center = Vector::Random();
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Vector u = Vector::Random();
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Vector v = Vector::Random();
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Scalar a = internal::random<Scalar>();
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while (abs(a - 1) < Scalar(1e-4)) a = internal::random<Scalar>();
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while (u.norm() < Scalar(1e-4)) u = Vector::Random();
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while (v.norm() < Scalar(1e-4)) v = Vector::Random();
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HLine line_u = HLine::Through(center + u, center + a * u);
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HLine line_v = HLine::Through(center + v, center + a * v);
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// the line equations should be normalized so that a^2+b^2=1
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VERIFY_IS_APPROX(line_u.normal().norm(), Scalar(1));
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VERIFY_IS_APPROX(line_v.normal().norm(), Scalar(1));
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Vector result = line_u.intersection(line_v);
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// the lines should intersect at the point we called "center"
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if (abs(a - 1) > Scalar(1e-2) && abs(v.normalized().dot(u.normalized())) < Scalar(0.9))
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VERIFY_IS_APPROX(result, center);
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// check conversions between two types of lines
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PLine pl(line_u); // gcc 3.3 will crash if we don't name this variable.
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HLine line_u2(pl);
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CoeffsType converted_coeffs = line_u2.coeffs();
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if (line_u2.normal().dot(line_u.normal()) < Scalar(0)) converted_coeffs = -line_u2.coeffs();
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VERIFY(line_u.coeffs().isApprox(converted_coeffs));
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}
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}
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template <typename Scalar>
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void planes() {
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using std::abs;
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typedef Hyperplane<Scalar, 3> Plane;
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typedef Matrix<Scalar, 3, 1> Vector;
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for (int i = 0; i < 10; i++) {
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Vector v0 = Vector::Random();
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Vector v1(v0), v2(v0);
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if (internal::random<double>(0, 1) > 0.25) v1 += Vector::Random();
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if (internal::random<double>(0, 1) > 0.25)
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v2 += v1 * std::pow(internal::random<Scalar>(0, 1), internal::random<int>(1, 16));
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if (internal::random<double>(0, 1) > 0.25)
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v2 += Vector::Random() * std::pow(internal::random<Scalar>(0, 1), internal::random<int>(1, 16));
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Plane p0 = Plane::Through(v0, v1, v2);
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VERIFY_IS_APPROX(p0.normal().norm(), Scalar(1));
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VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v0), Scalar(1));
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VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v1), Scalar(1));
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VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v2), Scalar(1));
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}
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}
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template <typename Scalar>
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void hyperplane_alignment() {
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typedef Hyperplane<Scalar, 3, AutoAlign> Plane3a;
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typedef Hyperplane<Scalar, 3, DontAlign> Plane3u;
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EIGEN_ALIGN_MAX Scalar array1[4];
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EIGEN_ALIGN_MAX Scalar array2[4];
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EIGEN_ALIGN_MAX Scalar array3[4 + 1];
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Scalar *array3u = array3 + 1;
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Plane3a *p1 = ::new (reinterpret_cast<void *>(array1)) Plane3a;
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Plane3u *p2 = ::new (reinterpret_cast<void *>(array2)) Plane3u;
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Plane3u *p3 = ::new (reinterpret_cast<void *>(array3u)) Plane3u;
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p1->coeffs().setRandom();
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*p2 = *p1;
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*p3 = *p1;
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VERIFY_IS_APPROX(p1->coeffs(), p2->coeffs());
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VERIFY_IS_APPROX(p1->coeffs(), p3->coeffs());
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}
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EIGEN_DECLARE_TEST(geo_hyperplane) {
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for (int i = 0; i < g_repeat; i++) {
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CALL_SUBTEST_1(hyperplane(Hyperplane<float, 2>()));
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CALL_SUBTEST_2(hyperplane(Hyperplane<float, 3>()));
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CALL_SUBTEST_2(hyperplane(Hyperplane<float, 3, DontAlign>()));
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CALL_SUBTEST_2(hyperplane_alignment<float>());
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CALL_SUBTEST_3(hyperplane(Hyperplane<double, 4>()));
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CALL_SUBTEST_4(hyperplane(Hyperplane<std::complex<double>, 5>()));
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CALL_SUBTEST_1(lines<float>());
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CALL_SUBTEST_3(lines<double>());
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CALL_SUBTEST_2(planes<float>());
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CALL_SUBTEST_5(planes<double>());
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}
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}
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