1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. Eigen itself is part of the KDE project. 3 // 4 // Copyright (C) 2008 Gael Guennebaud <g.gael (at) free.fr> 5 // Copyright (C) 2008 Benoit Jacob <jacob.benoit.1 (at) gmail.com> 6 // 7 // This Source Code Form is subject to the terms of the Mozilla 8 // Public License v. 2.0. If a copy of the MPL was not distributed 9 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 10 11 #include "main.h" 12 #include <Eigen/Geometry> 13 #include <Eigen/LU> 14 #include <Eigen/QR> 15 16 template<typename HyperplaneType> void hyperplane(const HyperplaneType& _plane) 17 { 18 /* this test covers the following files: 19 Hyperplane.h 20 */ 21 22 const int dim = _plane.dim(); 23 typedef typename HyperplaneType::Scalar Scalar; 24 typedef typename NumTraits<Scalar>::Real RealScalar; 25 typedef Matrix<Scalar, HyperplaneType::AmbientDimAtCompileTime, 1> VectorType; 26 typedef Matrix<Scalar, HyperplaneType::AmbientDimAtCompileTime, 27 HyperplaneType::AmbientDimAtCompileTime> MatrixType; 28 29 VectorType p0 = VectorType::Random(dim); 30 VectorType p1 = VectorType::Random(dim); 31 32 VectorType n0 = VectorType::Random(dim).normalized(); 33 VectorType n1 = VectorType::Random(dim).normalized(); 34 35 HyperplaneType pl0(n0, p0); 36 HyperplaneType pl1(n1, p1); 37 HyperplaneType pl2 = pl1; 38 39 Scalar s0 = ei_random<Scalar>(); 40 Scalar s1 = ei_random<Scalar>(); 41 42 VERIFY_IS_APPROX( n1.eigen2_dot(n1), Scalar(1) ); 43 44 VERIFY_IS_MUCH_SMALLER_THAN( pl0.absDistance(p0), Scalar(1) ); 45 VERIFY_IS_APPROX( pl1.signedDistance(p1 + n1 * s0), s0 ); 46 VERIFY_IS_MUCH_SMALLER_THAN( pl1.signedDistance(pl1.projection(p0)), Scalar(1) ); 47 VERIFY_IS_MUCH_SMALLER_THAN( pl1.absDistance(p1 + pl1.normal().unitOrthogonal() * s1), Scalar(1) ); 48 49 // transform 50 if (!NumTraits<Scalar>::IsComplex) 51 { 52 MatrixType rot = MatrixType::Random(dim,dim).qr().matrixQ(); 53 Scaling<Scalar,HyperplaneType::AmbientDimAtCompileTime> scaling(VectorType::Random()); 54 Translation<Scalar,HyperplaneType::AmbientDimAtCompileTime> translation(VectorType::Random()); 55 56 pl2 = pl1; 57 VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot).absDistance(rot * p1), Scalar(1) ); 58 pl2 = pl1; 59 VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot,Isometry).absDistance(rot * p1), Scalar(1) ); 60 pl2 = pl1; 61 VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*scaling).absDistance((rot*scaling) * p1), Scalar(1) ); 62 pl2 = pl1; 63 VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*scaling*translation) 64 .absDistance((rot*scaling*translation) * p1), Scalar(1) ); 65 pl2 = pl1; 66 VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*translation,Isometry) 67 .absDistance((rot*translation) * p1), Scalar(1) ); 68 } 69 70 // casting 71 const int Dim = HyperplaneType::AmbientDimAtCompileTime; 72 typedef typename GetDifferentType<Scalar>::type OtherScalar; 73 Hyperplane<OtherScalar,Dim> hp1f = pl1.template cast<OtherScalar>(); 74 VERIFY_IS_APPROX(hp1f.template cast<Scalar>(),pl1); 75 Hyperplane<Scalar,Dim> hp1d = pl1.template cast<Scalar>(); 76 VERIFY_IS_APPROX(hp1d.template cast<Scalar>(),pl1); 77 } 78 79 template<typename Scalar> void lines() 80 { 81 typedef Hyperplane<Scalar, 2> HLine; 82 typedef ParametrizedLine<Scalar, 2> PLine; 83 typedef Matrix<Scalar,2,1> Vector; 84 typedef Matrix<Scalar,3,1> CoeffsType; 85 86 for(int i = 0; i < 10; i++) 87 { 88 Vector center = Vector::Random(); 89 Vector u = Vector::Random(); 90 Vector v = Vector::Random(); 91 Scalar a = ei_random<Scalar>(); 92 while (ei_abs(a-1) < 1e-4) a = ei_random<Scalar>(); 93 while (u.norm() < 1e-4) u = Vector::Random(); 94 while (v.norm() < 1e-4) v = Vector::Random(); 95 96 HLine line_u = HLine::Through(center + u, center + a*u); 97 HLine line_v = HLine::Through(center + v, center + a*v); 98 99 // the line equations should be normalized so that a^2+b^2=1 100 VERIFY_IS_APPROX(line_u.normal().norm(), Scalar(1)); 101 VERIFY_IS_APPROX(line_v.normal().norm(), Scalar(1)); 102 103 Vector result = line_u.intersection(line_v); 104 105 // the lines should intersect at the point we called "center" 106 VERIFY_IS_APPROX(result, center); 107 108 // check conversions between two types of lines 109 PLine pl(line_u); // gcc 3.3 will commit suicide if we don't name this variable 110 CoeffsType converted_coeffs(HLine(pl).coeffs()); 111 converted_coeffs *= line_u.coeffs()(0)/converted_coeffs(0); 112 VERIFY(line_u.coeffs().isApprox(converted_coeffs)); 113 } 114 } 115 116 void test_eigen2_hyperplane() 117 { 118 for(int i = 0; i < g_repeat; i++) { 119 CALL_SUBTEST_1( hyperplane(Hyperplane<float,2>()) ); 120 CALL_SUBTEST_2( hyperplane(Hyperplane<float,3>()) ); 121 CALL_SUBTEST_3( hyperplane(Hyperplane<double,4>()) ); 122 CALL_SUBTEST_4( hyperplane(Hyperplane<std::complex<double>,5>()) ); 123 CALL_SUBTEST_5( lines<float>() ); 124 CALL_SUBTEST_6( lines<double>() ); 125 } 126 } 127
