1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. 3 // 4 // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud (at) inria.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 typedef typename HyperplaneType::Index Index; 22 const Index dim = _plane.dim(); 23 enum { Options = HyperplaneType::Options }; 24 typedef typename HyperplaneType::Scalar Scalar; 25 typedef typename NumTraits<Scalar>::Real RealScalar; 26 typedef Matrix<Scalar, HyperplaneType::AmbientDimAtCompileTime, 1> VectorType; 27 typedef Matrix<Scalar, HyperplaneType::AmbientDimAtCompileTime, 28 HyperplaneType::AmbientDimAtCompileTime> MatrixType; 29 30 VectorType p0 = VectorType::Random(dim); 31 VectorType p1 = VectorType::Random(dim); 32 33 VectorType n0 = VectorType::Random(dim).normalized(); 34 VectorType n1 = VectorType::Random(dim).normalized(); 35 36 HyperplaneType pl0(n0, p0); 37 HyperplaneType pl1(n1, p1); 38 HyperplaneType pl2 = pl1; 39 40 Scalar s0 = internal::random<Scalar>(); 41 Scalar s1 = internal::random<Scalar>(); 42 43 VERIFY_IS_APPROX( n1.dot(n1), Scalar(1) ); 44 45 VERIFY_IS_MUCH_SMALLER_THAN( pl0.absDistance(p0), Scalar(1) ); 46 VERIFY_IS_APPROX( pl1.signedDistance(p1 + n1 * s0), s0 ); 47 VERIFY_IS_MUCH_SMALLER_THAN( pl1.signedDistance(pl1.projection(p0)), Scalar(1) ); 48 VERIFY_IS_MUCH_SMALLER_THAN( pl1.absDistance(p1 + pl1.normal().unitOrthogonal() * s1), Scalar(1) ); 49 50 // transform 51 if (!NumTraits<Scalar>::IsComplex) 52 { 53 MatrixType rot = MatrixType::Random(dim,dim).householderQr().householderQ(); 54 DiagonalMatrix<Scalar,HyperplaneType::AmbientDimAtCompileTime> scaling(VectorType::Random()); 55 Translation<Scalar,HyperplaneType::AmbientDimAtCompileTime> translation(VectorType::Random()); 56 57 pl2 = pl1; 58 VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot).absDistance(rot * p1), Scalar(1) ); 59 pl2 = pl1; 60 VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot,Isometry).absDistance(rot * p1), Scalar(1) ); 61 pl2 = pl1; 62 VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*scaling).absDistance((rot*scaling) * p1), Scalar(1) ); 63 pl2 = pl1; 64 VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*scaling*translation) 65 .absDistance((rot*scaling*translation) * p1), Scalar(1) ); 66 pl2 = pl1; 67 VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*translation,Isometry) 68 .absDistance((rot*translation) * p1), Scalar(1) ); 69 } 70 71 // casting 72 const int Dim = HyperplaneType::AmbientDimAtCompileTime; 73 typedef typename GetDifferentType<Scalar>::type OtherScalar; 74 Hyperplane<OtherScalar,Dim,Options> hp1f = pl1.template cast<OtherScalar>(); 75 VERIFY_IS_APPROX(hp1f.template cast<Scalar>(),pl1); 76 Hyperplane<Scalar,Dim,Options> hp1d = pl1.template cast<Scalar>(); 77 VERIFY_IS_APPROX(hp1d.template cast<Scalar>(),pl1); 78 } 79 80 template<typename Scalar> void lines() 81 { 82 typedef Hyperplane<Scalar, 2> HLine; 83 typedef ParametrizedLine<Scalar, 2> PLine; 84 typedef Matrix<Scalar,2,1> Vector; 85 typedef Matrix<Scalar,3,1> CoeffsType; 86 87 for(int i = 0; i < 10; i++) 88 { 89 Vector center = Vector::Random(); 90 Vector u = Vector::Random(); 91 Vector v = Vector::Random(); 92 Scalar a = internal::random<Scalar>(); 93 while (internal::abs(a-1) < 1e-4) a = internal::random<Scalar>(); 94 while (u.norm() < 1e-4) u = Vector::Random(); 95 while (v.norm() < 1e-4) v = Vector::Random(); 96 97 HLine line_u = HLine::Through(center + u, center + a*u); 98 HLine line_v = HLine::Through(center + v, center + a*v); 99 100 // the line equations should be normalized so that a^2+b^2=1 101 VERIFY_IS_APPROX(line_u.normal().norm(), Scalar(1)); 102 VERIFY_IS_APPROX(line_v.normal().norm(), Scalar(1)); 103 104 Vector result = line_u.intersection(line_v); 105 106 // the lines should intersect at the point we called "center" 107 VERIFY_IS_APPROX(result, center); 108 109 // check conversions between two types of lines 110 PLine pl(line_u); // gcc 3.3 will commit suicide if we don't name this variable 111 CoeffsType converted_coeffs = HLine(pl).coeffs(); 112 converted_coeffs *= (line_u.coeffs()[0])/(converted_coeffs[0]); 113 VERIFY(line_u.coeffs().isApprox(converted_coeffs)); 114 } 115 } 116 117 template<typename Scalar> void hyperplane_alignment() 118 { 119 typedef Hyperplane<Scalar,3,AutoAlign> Plane3a; 120 typedef Hyperplane<Scalar,3,DontAlign> Plane3u; 121 122 EIGEN_ALIGN16 Scalar array1[4]; 123 EIGEN_ALIGN16 Scalar array2[4]; 124 EIGEN_ALIGN16 Scalar array3[4+1]; 125 Scalar* array3u = array3+1; 126 127 Plane3a *p1 = ::new(reinterpret_cast<void*>(array1)) Plane3a; 128 Plane3u *p2 = ::new(reinterpret_cast<void*>(array2)) Plane3u; 129 Plane3u *p3 = ::new(reinterpret_cast<void*>(array3u)) Plane3u; 130 131 p1->coeffs().setRandom(); 132 *p2 = *p1; 133 *p3 = *p1; 134 135 VERIFY_IS_APPROX(p1->coeffs(), p2->coeffs()); 136 VERIFY_IS_APPROX(p1->coeffs(), p3->coeffs()); 137 138 #if defined(EIGEN_VECTORIZE) && EIGEN_ALIGN_STATICALLY 139 if(internal::packet_traits<Scalar>::Vectorizable) 140 VERIFY_RAISES_ASSERT((::new(reinterpret_cast<void*>(array3u)) Plane3a)); 141 #endif 142 } 143 144 145 void test_geo_hyperplane() 146 { 147 for(int i = 0; i < g_repeat; i++) { 148 CALL_SUBTEST_1( hyperplane(Hyperplane<float,2>()) ); 149 CALL_SUBTEST_2( hyperplane(Hyperplane<float,3>()) ); 150 CALL_SUBTEST_2( hyperplane(Hyperplane<float,3,DontAlign>()) ); 151 CALL_SUBTEST_2( hyperplane_alignment<float>() ); 152 CALL_SUBTEST_3( hyperplane(Hyperplane<double,4>()) ); 153 CALL_SUBTEST_4( hyperplane(Hyperplane<std::complex<double>,5>()) ); 154 CALL_SUBTEST_1( lines<float>() ); 155 CALL_SUBTEST_3( lines<double>() ); 156 } 157 } 158
