geo_hyperplane.cpp (7304B)
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@inria.fr> 5 // Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@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 const Index dim = _plane.dim(); 23 enum { Options = HyperplaneType::Options }; 24 typedef typename HyperplaneType::Scalar Scalar; 25 typedef typename HyperplaneType::RealScalar 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 if(numext::abs2(s0)>RealScalar(1e-6)) 47 VERIFY_IS_APPROX( pl1.signedDistance(p1 + n1 * s0), s0); 48 else 49 VERIFY_IS_MUCH_SMALLER_THAN( abs(pl1.signedDistance(p1 + n1 * s0) - s0), Scalar(1) ); 50 VERIFY_IS_MUCH_SMALLER_THAN( pl1.signedDistance(pl1.projection(p0)), Scalar(1) ); 51 VERIFY_IS_MUCH_SMALLER_THAN( pl1.absDistance(p1 + pl1.normal().unitOrthogonal() * s1), Scalar(1) ); 52 53 // transform 54 if (!NumTraits<Scalar>::IsComplex) 55 { 56 MatrixType rot = MatrixType::Random(dim,dim).householderQr().householderQ(); 57 DiagonalMatrix<Scalar,HyperplaneType::AmbientDimAtCompileTime> scaling(VectorType::Random()); 58 Translation<Scalar,HyperplaneType::AmbientDimAtCompileTime> translation(VectorType::Random()); 59 60 while(scaling.diagonal().cwiseAbs().minCoeff()<RealScalar(1e-4)) scaling.diagonal() = VectorType::Random(); 61 62 pl2 = pl1; 63 VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot).absDistance(rot * p1), Scalar(1) ); 64 pl2 = pl1; 65 VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot,Isometry).absDistance(rot * p1), Scalar(1) ); 66 pl2 = pl1; 67 VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*scaling).absDistance((rot*scaling) * p1), Scalar(1) ); 68 VERIFY_IS_APPROX( pl2.normal().norm(), RealScalar(1) ); 69 pl2 = pl1; 70 VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*scaling*translation) 71 .absDistance((rot*scaling*translation) * p1), Scalar(1) ); 72 VERIFY_IS_APPROX( pl2.normal().norm(), RealScalar(1) ); 73 pl2 = pl1; 74 VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*translation,Isometry) 75 .absDistance((rot*translation) * p1), Scalar(1) ); 76 VERIFY_IS_APPROX( pl2.normal().norm(), RealScalar(1) ); 77 } 78 79 // casting 80 const int Dim = HyperplaneType::AmbientDimAtCompileTime; 81 typedef typename GetDifferentType<Scalar>::type OtherScalar; 82 Hyperplane<OtherScalar,Dim,Options> hp1f = pl1.template cast<OtherScalar>(); 83 VERIFY_IS_APPROX(hp1f.template cast<Scalar>(),pl1); 84 Hyperplane<Scalar,Dim,Options> hp1d = pl1.template cast<Scalar>(); 85 VERIFY_IS_APPROX(hp1d.template cast<Scalar>(),pl1); 86 } 87 88 template<typename Scalar> void lines() 89 { 90 using std::abs; 91 typedef Hyperplane<Scalar, 2> HLine; 92 typedef ParametrizedLine<Scalar, 2> PLine; 93 typedef Matrix<Scalar,2,1> Vector; 94 typedef Matrix<Scalar,3,1> CoeffsType; 95 96 for(int i = 0; i < 10; i++) 97 { 98 Vector center = Vector::Random(); 99 Vector u = Vector::Random(); 100 Vector v = Vector::Random(); 101 Scalar a = internal::random<Scalar>(); 102 while (abs(a-1) < Scalar(1e-4)) a = internal::random<Scalar>(); 103 while (u.norm() < Scalar(1e-4)) u = Vector::Random(); 104 while (v.norm() < Scalar(1e-4)) v = Vector::Random(); 105 106 HLine line_u = HLine::Through(center + u, center + a*u); 107 HLine line_v = HLine::Through(center + v, center + a*v); 108 109 // the line equations should be normalized so that a^2+b^2=1 110 VERIFY_IS_APPROX(line_u.normal().norm(), Scalar(1)); 111 VERIFY_IS_APPROX(line_v.normal().norm(), Scalar(1)); 112 113 Vector result = line_u.intersection(line_v); 114 115 // the lines should intersect at the point we called "center" 116 if(abs(a-1) > Scalar(1e-2) && abs(v.normalized().dot(u.normalized()))<Scalar(0.9)) 117 VERIFY_IS_APPROX(result, center); 118 119 // check conversions between two types of lines 120 PLine pl(line_u); // gcc 3.3 will crash if we don't name this variable. 121 HLine line_u2(pl); 122 CoeffsType converted_coeffs = line_u2.coeffs(); 123 if(line_u2.normal().dot(line_u.normal())<Scalar(0)) 124 converted_coeffs = -line_u2.coeffs(); 125 VERIFY(line_u.coeffs().isApprox(converted_coeffs)); 126 } 127 } 128 129 template<typename Scalar> void planes() 130 { 131 using std::abs; 132 typedef Hyperplane<Scalar, 3> Plane; 133 typedef Matrix<Scalar,3,1> Vector; 134 135 for(int i = 0; i < 10; i++) 136 { 137 Vector v0 = Vector::Random(); 138 Vector v1(v0), v2(v0); 139 if(internal::random<double>(0,1)>0.25) 140 v1 += Vector::Random(); 141 if(internal::random<double>(0,1)>0.25) 142 v2 += v1 * std::pow(internal::random<Scalar>(0,1),internal::random<int>(1,16)); 143 if(internal::random<double>(0,1)>0.25) 144 v2 += Vector::Random() * std::pow(internal::random<Scalar>(0,1),internal::random<int>(1,16)); 145 146 Plane p0 = Plane::Through(v0, v1, v2); 147 148 VERIFY_IS_APPROX(p0.normal().norm(), Scalar(1)); 149 VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v0), Scalar(1)); 150 VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v1), Scalar(1)); 151 VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v2), Scalar(1)); 152 } 153 } 154 155 template<typename Scalar> void hyperplane_alignment() 156 { 157 typedef Hyperplane<Scalar,3,AutoAlign> Plane3a; 158 typedef Hyperplane<Scalar,3,DontAlign> Plane3u; 159 160 EIGEN_ALIGN_MAX Scalar array1[4]; 161 EIGEN_ALIGN_MAX Scalar array2[4]; 162 EIGEN_ALIGN_MAX Scalar array3[4+1]; 163 Scalar* array3u = array3+1; 164 165 Plane3a *p1 = ::new(reinterpret_cast<void*>(array1)) Plane3a; 166 Plane3u *p2 = ::new(reinterpret_cast<void*>(array2)) Plane3u; 167 Plane3u *p3 = ::new(reinterpret_cast<void*>(array3u)) Plane3u; 168 169 p1->coeffs().setRandom(); 170 *p2 = *p1; 171 *p3 = *p1; 172 173 VERIFY_IS_APPROX(p1->coeffs(), p2->coeffs()); 174 VERIFY_IS_APPROX(p1->coeffs(), p3->coeffs()); 175 } 176 177 178 EIGEN_DECLARE_TEST(geo_hyperplane) 179 { 180 for(int i = 0; i < g_repeat; i++) { 181 CALL_SUBTEST_1( hyperplane(Hyperplane<float,2>()) ); 182 CALL_SUBTEST_2( hyperplane(Hyperplane<float,3>()) ); 183 CALL_SUBTEST_2( hyperplane(Hyperplane<float,3,DontAlign>()) ); 184 CALL_SUBTEST_2( hyperplane_alignment<float>() ); 185 CALL_SUBTEST_3( hyperplane(Hyperplane<double,4>()) ); 186 CALL_SUBTEST_4( hyperplane(Hyperplane<std::complex<double>,5>()) ); 187 CALL_SUBTEST_1( lines<float>() ); 188 CALL_SUBTEST_3( lines<double>() ); 189 CALL_SUBTEST_2( planes<float>() ); 190 CALL_SUBTEST_5( planes<double>() ); 191 } 192 }