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 using std::abs; 22 typedef typename HyperplaneType::Index Index; 23 const Index dim = _plane.dim(); 24 enum { Options = HyperplaneType::Options }; 25 typedef typename HyperplaneType::Scalar Scalar; 26 typedef typename HyperplaneType::RealScalar RealScalar; 27 typedef Matrix<Scalar, HyperplaneType::AmbientDimAtCompileTime, 1> VectorType; 28 typedef Matrix<Scalar, HyperplaneType::AmbientDimAtCompileTime, 29 HyperplaneType::AmbientDimAtCompileTime> MatrixType; 30 31 VectorType p0 = VectorType::Random(dim); 32 VectorType p1 = VectorType::Random(dim); 33 34 VectorType n0 = VectorType::Random(dim).normalized(); 35 VectorType n1 = VectorType::Random(dim).normalized(); 36 37 HyperplaneType pl0(n0, p0); 38 HyperplaneType pl1(n1, p1); 39 HyperplaneType pl2 = pl1; 40 41 Scalar s0 = internal::random<Scalar>(); 42 Scalar s1 = internal::random<Scalar>(); 43 44 VERIFY_IS_APPROX( n1.dot(n1), Scalar(1) ); 45 46 VERIFY_IS_MUCH_SMALLER_THAN( pl0.absDistance(p0), Scalar(1) ); 47 if(numext::abs2(s0)>RealScalar(1e-6)) 48 VERIFY_IS_APPROX( pl1.signedDistance(p1 + n1 * s0), s0); 49 else 50 VERIFY_IS_MUCH_SMALLER_THAN( abs(pl1.signedDistance(p1 + n1 * s0) - s0), Scalar(1) ); 51 VERIFY_IS_MUCH_SMALLER_THAN( pl1.signedDistance(pl1.projection(p0)), Scalar(1) ); 52 VERIFY_IS_MUCH_SMALLER_THAN( pl1.absDistance(p1 + pl1.normal().unitOrthogonal() * s1), Scalar(1) ); 53 54 // transform 55 if (!NumTraits<Scalar>::IsComplex) 56 { 57 MatrixType rot = MatrixType::Random(dim,dim).householderQr().householderQ(); 58 DiagonalMatrix<Scalar,HyperplaneType::AmbientDimAtCompileTime> scaling(VectorType::Random()); 59 Translation<Scalar,HyperplaneType::AmbientDimAtCompileTime> translation(VectorType::Random()); 60 61 while(scaling.diagonal().cwiseAbs().minCoeff()<RealScalar(1e-4)) scaling.diagonal() = VectorType::Random(); 62 63 pl2 = pl1; 64 VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot).absDistance(rot * p1), Scalar(1) ); 65 pl2 = pl1; 66 VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot,Isometry).absDistance(rot * p1), Scalar(1) ); 67 pl2 = pl1; 68 VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*scaling).absDistance((rot*scaling) * p1), Scalar(1) ); 69 VERIFY_IS_APPROX( pl2.normal().norm(), RealScalar(1) ); 70 pl2 = pl1; 71 VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*scaling*translation) 72 .absDistance((rot*scaling*translation) * p1), Scalar(1) ); 73 VERIFY_IS_APPROX( pl2.normal().norm(), RealScalar(1) ); 74 pl2 = pl1; 75 VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*translation,Isometry) 76 .absDistance((rot*translation) * p1), Scalar(1) ); 77 VERIFY_IS_APPROX( pl2.normal().norm(), RealScalar(1) ); 78 } 79 80 // casting 81 const int Dim = HyperplaneType::AmbientDimAtCompileTime; 82 typedef typename GetDifferentType<Scalar>::type OtherScalar; 83 Hyperplane<OtherScalar,Dim,Options> hp1f = pl1.template cast<OtherScalar>(); 84 VERIFY_IS_APPROX(hp1f.template cast<Scalar>(),pl1); 85 Hyperplane<Scalar,Dim,Options> hp1d = pl1.template cast<Scalar>(); 86 VERIFY_IS_APPROX(hp1d.template cast<Scalar>(),pl1); 87 } 88 89 template<typename Scalar> void lines() 90 { 91 using std::abs; 92 typedef Hyperplane<Scalar, 2> HLine; 93 typedef ParametrizedLine<Scalar, 2> PLine; 94 typedef Matrix<Scalar,2,1> Vector; 95 typedef Matrix<Scalar,3,1> CoeffsType; 96 97 for(int i = 0; i < 10; i++) 98 { 99 Vector center = Vector::Random(); 100 Vector u = Vector::Random(); 101 Vector v = Vector::Random(); 102 Scalar a = internal::random<Scalar>(); 103 while (abs(a-1) < Scalar(1e-4)) a = internal::random<Scalar>(); 104 while (u.norm() < Scalar(1e-4)) u = Vector::Random(); 105 while (v.norm() < Scalar(1e-4)) v = Vector::Random(); 106 107 HLine line_u = HLine::Through(center + u, center + a*u); 108 HLine line_v = HLine::Through(center + v, center + a*v); 109 110 // the line equations should be normalized so that a^2+b^2=1 111 VERIFY_IS_APPROX(line_u.normal().norm(), Scalar(1)); 112 VERIFY_IS_APPROX(line_v.normal().norm(), Scalar(1)); 113 114 Vector result = line_u.intersection(line_v); 115 116 // the lines should intersect at the point we called "center" 117 if(abs(a-1) > Scalar(1e-2) && abs(v.normalized().dot(u.normalized()))<Scalar(0.9)) 118 VERIFY_IS_APPROX(result, center); 119 120 // check conversions between two types of lines 121 PLine pl(line_u); // gcc 3.3 will commit suicide if we don't name this variable 122 HLine line_u2(pl); 123 CoeffsType converted_coeffs = line_u2.coeffs(); 124 if(line_u2.normal().dot(line_u.normal())<Scalar(0)) 125 converted_coeffs = -line_u2.coeffs(); 126 VERIFY(line_u.coeffs().isApprox(converted_coeffs)); 127 } 128 } 129 130 template<typename Scalar> void planes() 131 { 132 using std::abs; 133 typedef Hyperplane<Scalar, 3> Plane; 134 typedef Matrix<Scalar,3,1> Vector; 135 136 for(int i = 0; i < 10; i++) 137 { 138 Vector v0 = Vector::Random(); 139 Vector v1(v0), v2(v0); 140 if(internal::random<double>(0,1)>0.25) 141 v1 += Vector::Random(); 142 if(internal::random<double>(0,1)>0.25) 143 v2 += v1 * std::pow(internal::random<Scalar>(0,1),internal::random<int>(1,16)); 144 if(internal::random<double>(0,1)>0.25) 145 v2 += Vector::Random() * std::pow(internal::random<Scalar>(0,1),internal::random<int>(1,16)); 146 147 Plane p0 = Plane::Through(v0, v1, v2); 148 149 VERIFY_IS_APPROX(p0.normal().norm(), Scalar(1)); 150 VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v0), Scalar(1)); 151 VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v1), Scalar(1)); 152 VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v2), Scalar(1)); 153 } 154 } 155 156 template<typename Scalar> void hyperplane_alignment() 157 { 158 typedef Hyperplane<Scalar,3,AutoAlign> Plane3a; 159 typedef Hyperplane<Scalar,3,DontAlign> Plane3u; 160 161 EIGEN_ALIGN_MAX Scalar array1[4]; 162 EIGEN_ALIGN_MAX Scalar array2[4]; 163 EIGEN_ALIGN_MAX Scalar array3[4+1]; 164 Scalar* array3u = array3+1; 165 166 Plane3a *p1 = ::new(reinterpret_cast<void*>(array1)) Plane3a; 167 Plane3u *p2 = ::new(reinterpret_cast<void*>(array2)) Plane3u; 168 Plane3u *p3 = ::new(reinterpret_cast<void*>(array3u)) Plane3u; 169 170 p1->coeffs().setRandom(); 171 *p2 = *p1; 172 *p3 = *p1; 173 174 VERIFY_IS_APPROX(p1->coeffs(), p2->coeffs()); 175 VERIFY_IS_APPROX(p1->coeffs(), p3->coeffs()); 176 177 #if defined(EIGEN_VECTORIZE) && EIGEN_MAX_STATIC_ALIGN_BYTES > 0 178 if(internal::packet_traits<Scalar>::Vectorizable && internal::packet_traits<Scalar>::size<=4) 179 VERIFY_RAISES_ASSERT((::new(reinterpret_cast<void*>(array3u)) Plane3a)); 180 #endif 181 } 182 183 184 void test_geo_hyperplane() 185 { 186 for(int i = 0; i < g_repeat; i++) { 187 CALL_SUBTEST_1( hyperplane(Hyperplane<float,2>()) ); 188 CALL_SUBTEST_2( hyperplane(Hyperplane<float,3>()) ); 189 CALL_SUBTEST_2( hyperplane(Hyperplane<float,3,DontAlign>()) ); 190 CALL_SUBTEST_2( hyperplane_alignment<float>() ); 191 CALL_SUBTEST_3( hyperplane(Hyperplane<double,4>()) ); 192 CALL_SUBTEST_4( hyperplane(Hyperplane<std::complex<double>,5>()) ); 193 CALL_SUBTEST_1( lines<float>() ); 194 CALL_SUBTEST_3( lines<double>() ); 195 CALL_SUBTEST_2( planes<float>() ); 196 CALL_SUBTEST_5( planes<double>() ); 197 } 198 } 199
