geo_hyperplane.cpp revision 615d816d068b4d0f5e8df601930b5f160bf7eda1
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 16template<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 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 = internal::random<Scalar>(); 40 Scalar s1 = internal::random<Scalar>(); 41 42 VERIFY_IS_APPROX( n1.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).householderQr().householderQ(); 53 DiagonalMatrix<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,Options> hp1f = pl1.template cast<OtherScalar>(); 74 VERIFY_IS_APPROX(hp1f.template cast<Scalar>(),pl1); 75 Hyperplane<Scalar,Dim,Options> hp1d = pl1.template cast<Scalar>(); 76 VERIFY_IS_APPROX(hp1d.template cast<Scalar>(),pl1); 77} 78 79template<typename Scalar> void lines() 80{ 81 using std::abs; 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 (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 117template<typename Scalar> void planes() 118{ 119 using std::abs; 120 typedef Hyperplane<Scalar, 3> Plane; 121 typedef Matrix<Scalar,3,1> Vector; 122 123 for(int i = 0; i < 10; i++) 124 { 125 Vector v0 = Vector::Random(); 126 Vector v1(v0), v2(v0); 127 if(internal::random<double>(0,1)>0.25) 128 v1 += Vector::Random(); 129 if(internal::random<double>(0,1)>0.25) 130 v2 += v1 * std::pow(internal::random<Scalar>(0,1),internal::random<int>(1,16)); 131 if(internal::random<double>(0,1)>0.25) 132 v2 += Vector::Random() * std::pow(internal::random<Scalar>(0,1),internal::random<int>(1,16)); 133 134 Plane p0 = Plane::Through(v0, v1, v2); 135 136 VERIFY_IS_APPROX(p0.normal().norm(), Scalar(1)); 137 VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v0), Scalar(1)); 138 VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v1), Scalar(1)); 139 VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v2), Scalar(1)); 140 } 141} 142 143template<typename Scalar> void hyperplane_alignment() 144{ 145 typedef Hyperplane<Scalar,3,AutoAlign> Plane3a; 146 typedef Hyperplane<Scalar,3,DontAlign> Plane3u; 147 148 EIGEN_ALIGN16 Scalar array1[4]; 149 EIGEN_ALIGN16 Scalar array2[4]; 150 EIGEN_ALIGN16 Scalar array3[4+1]; 151 Scalar* array3u = array3+1; 152 153 Plane3a *p1 = ::new(reinterpret_cast<void*>(array1)) Plane3a; 154 Plane3u *p2 = ::new(reinterpret_cast<void*>(array2)) Plane3u; 155 Plane3u *p3 = ::new(reinterpret_cast<void*>(array3u)) Plane3u; 156 157 p1->coeffs().setRandom(); 158 *p2 = *p1; 159 *p3 = *p1; 160 161 VERIFY_IS_APPROX(p1->coeffs(), p2->coeffs()); 162 VERIFY_IS_APPROX(p1->coeffs(), p3->coeffs()); 163 164 #if defined(EIGEN_VECTORIZE) && EIGEN_ALIGN_STATICALLY 165 if(internal::packet_traits<Scalar>::Vectorizable) 166 VERIFY_RAISES_ASSERT((::new(reinterpret_cast<void*>(array3u)) Plane3a)); 167 #endif 168} 169 170 171void test_geo_hyperplane() 172{ 173 for(int i = 0; i < g_repeat; i++) { 174 CALL_SUBTEST_1( hyperplane(Hyperplane<float,2>()) ); 175 CALL_SUBTEST_2( hyperplane(Hyperplane<float,3>()) ); 176 CALL_SUBTEST_2( hyperplane(Hyperplane<float,3,DontAlign>()) ); 177 CALL_SUBTEST_2( hyperplane_alignment<float>() ); 178 CALL_SUBTEST_3( hyperplane(Hyperplane<double,4>()) ); 179 CALL_SUBTEST_4( hyperplane(Hyperplane<std::complex<double>,5>()) ); 180 CALL_SUBTEST_1( lines<float>() ); 181 CALL_SUBTEST_3( lines<double>() ); 182 CALL_SUBTEST_2( planes<float>() ); 183 CALL_SUBTEST_5( planes<double>() ); 184 } 185} 186