geo_hyperplane.cpp revision c981c48f5bc9aefeffc0bcb0cc3934c2fae179dd
1c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// This file is part of Eigen, a lightweight C++ template library 2c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// for linear algebra. 3c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// 4c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr> 5c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com> 6c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// 7c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// This Source Code Form is subject to the terms of the Mozilla 8c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// Public License v. 2.0. If a copy of the MPL was not distributed 9c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 10c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 11c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#include "main.h" 12c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#include <Eigen/Geometry> 13c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#include <Eigen/LU> 14c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath#include <Eigen/QR> 15c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 16c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename HyperplaneType> void hyperplane(const HyperplaneType& _plane) 17c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 18c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath /* this test covers the following files: 19c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Hyperplane.h 20c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath */ 21c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename HyperplaneType::Index Index; 22c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath const Index dim = _plane.dim(); 23c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath enum { Options = HyperplaneType::Options }; 24c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename HyperplaneType::Scalar Scalar; 25c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename NumTraits<Scalar>::Real RealScalar; 26c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar, HyperplaneType::AmbientDimAtCompileTime, 1> VectorType; 27c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar, HyperplaneType::AmbientDimAtCompileTime, 28c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath HyperplaneType::AmbientDimAtCompileTime> MatrixType; 29c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 30c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VectorType p0 = VectorType::Random(dim); 31c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VectorType p1 = VectorType::Random(dim); 32c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 33c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VectorType n0 = VectorType::Random(dim).normalized(); 34c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VectorType n1 = VectorType::Random(dim).normalized(); 35c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 36c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath HyperplaneType pl0(n0, p0); 37c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath HyperplaneType pl1(n1, p1); 38c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath HyperplaneType pl2 = pl1; 39c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 40c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scalar s0 = internal::random<Scalar>(); 41c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scalar s1 = internal::random<Scalar>(); 42c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 43c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX( n1.dot(n1), Scalar(1) ); 44c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 45c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_MUCH_SMALLER_THAN( pl0.absDistance(p0), Scalar(1) ); 46c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX( pl1.signedDistance(p1 + n1 * s0), s0 ); 47c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_MUCH_SMALLER_THAN( pl1.signedDistance(pl1.projection(p0)), Scalar(1) ); 48c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_MUCH_SMALLER_THAN( pl1.absDistance(p1 + pl1.normal().unitOrthogonal() * s1), Scalar(1) ); 49c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 50c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // transform 51c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if (!NumTraits<Scalar>::IsComplex) 52c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 53c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath MatrixType rot = MatrixType::Random(dim,dim).householderQr().householderQ(); 54c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath DiagonalMatrix<Scalar,HyperplaneType::AmbientDimAtCompileTime> scaling(VectorType::Random()); 55c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Translation<Scalar,HyperplaneType::AmbientDimAtCompileTime> translation(VectorType::Random()); 56c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 57c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath pl2 = pl1; 58c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot).absDistance(rot * p1), Scalar(1) ); 59c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath pl2 = pl1; 60c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot,Isometry).absDistance(rot * p1), Scalar(1) ); 61c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath pl2 = pl1; 62c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*scaling).absDistance((rot*scaling) * p1), Scalar(1) ); 63c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath pl2 = pl1; 64c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*scaling*translation) 65c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath .absDistance((rot*scaling*translation) * p1), Scalar(1) ); 66c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath pl2 = pl1; 67c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*translation,Isometry) 68c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath .absDistance((rot*translation) * p1), Scalar(1) ); 69c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 70c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 71c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // casting 72c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath const int Dim = HyperplaneType::AmbientDimAtCompileTime; 73c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef typename GetDifferentType<Scalar>::type OtherScalar; 74c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Hyperplane<OtherScalar,Dim,Options> hp1f = pl1.template cast<OtherScalar>(); 75c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(hp1f.template cast<Scalar>(),pl1); 76c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Hyperplane<Scalar,Dim,Options> hp1d = pl1.template cast<Scalar>(); 77c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(hp1d.template cast<Scalar>(),pl1); 78c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 79c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 80c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename Scalar> void lines() 81c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 82c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Hyperplane<Scalar, 2> HLine; 83c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef ParametrizedLine<Scalar, 2> PLine; 84c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar,2,1> Vector; 85c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Matrix<Scalar,3,1> CoeffsType; 86c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 87c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath for(int i = 0; i < 10; i++) 88c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath { 89c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Vector center = Vector::Random(); 90c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Vector u = Vector::Random(); 91c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Vector v = Vector::Random(); 92c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scalar a = internal::random<Scalar>(); 93c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath while (internal::abs(a-1) < 1e-4) a = internal::random<Scalar>(); 94c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath while (u.norm() < 1e-4) u = Vector::Random(); 95c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath while (v.norm() < 1e-4) v = Vector::Random(); 96c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 97c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath HLine line_u = HLine::Through(center + u, center + a*u); 98c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath HLine line_v = HLine::Through(center + v, center + a*v); 99c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 100c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // the line equations should be normalized so that a^2+b^2=1 101c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(line_u.normal().norm(), Scalar(1)); 102c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(line_v.normal().norm(), Scalar(1)); 103c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 104c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Vector result = line_u.intersection(line_v); 105c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 106c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // the lines should intersect at the point we called "center" 107c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(result, center); 108c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 109c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath // check conversions between two types of lines 110c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath PLine pl(line_u); // gcc 3.3 will commit suicide if we don't name this variable 111c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CoeffsType converted_coeffs = HLine(pl).coeffs(); 112c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath converted_coeffs *= (line_u.coeffs()[0])/(converted_coeffs[0]); 113c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY(line_u.coeffs().isApprox(converted_coeffs)); 114c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 115c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 116c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 117c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathtemplate<typename Scalar> void hyperplane_alignment() 118c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 119c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Hyperplane<Scalar,3,AutoAlign> Plane3a; 120c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath typedef Hyperplane<Scalar,3,DontAlign> Plane3u; 121c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 122c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath EIGEN_ALIGN16 Scalar array1[4]; 123c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath EIGEN_ALIGN16 Scalar array2[4]; 124c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath EIGEN_ALIGN16 Scalar array3[4+1]; 125c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Scalar* array3u = array3+1; 126c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 127c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Plane3a *p1 = ::new(reinterpret_cast<void*>(array1)) Plane3a; 128c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Plane3u *p2 = ::new(reinterpret_cast<void*>(array2)) Plane3u; 129c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath Plane3u *p3 = ::new(reinterpret_cast<void*>(array3u)) Plane3u; 130c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 131c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath p1->coeffs().setRandom(); 132c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath *p2 = *p1; 133c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath *p3 = *p1; 134c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 135c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(p1->coeffs(), p2->coeffs()); 136c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_IS_APPROX(p1->coeffs(), p3->coeffs()); 137c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 138c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath #if defined(EIGEN_VECTORIZE) && EIGEN_ALIGN_STATICALLY 139c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath if(internal::packet_traits<Scalar>::Vectorizable) 140c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath VERIFY_RAISES_ASSERT((::new(reinterpret_cast<void*>(array3u)) Plane3a)); 141c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath #endif 142c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 143c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 144c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath 145c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamathvoid test_geo_hyperplane() 146c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath{ 147c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath for(int i = 0; i < g_repeat; i++) { 148c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_1( hyperplane(Hyperplane<float,2>()) ); 149c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_2( hyperplane(Hyperplane<float,3>()) ); 150c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_2( hyperplane(Hyperplane<float,3,DontAlign>()) ); 151c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_2( hyperplane_alignment<float>() ); 152c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_3( hyperplane(Hyperplane<double,4>()) ); 153c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_4( hyperplane(Hyperplane<std::complex<double>,5>()) ); 154c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_1( lines<float>() ); 155c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath CALL_SUBTEST_3( lines<double>() ); 156c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath } 157c981c48f5bc9aefeffc0bcb0cc3934c2fae179ddNarayan Kamath} 158