| 1 | // This file is part of Eigen, a lightweight C++ template library
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| 2 | // for linear algebra.
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| 3 | //
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| 4 | // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
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| 5 | // Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
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| 6 | //
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| 7 | // This Source Code Form is subject to the terms of the Mozilla
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| 8 | // Public License v. 2.0. If a copy of the MPL was not distributed
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| 9 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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| 10 |
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| 11 | #include "main.h"
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| 12 | #include <Eigen/Geometry>
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| 13 | #include <Eigen/LU>
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| 14 | #include <Eigen/QR>
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| 15 |
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| 16 | template<typename HyperplaneType> void hyperplane(const HyperplaneType& _plane)
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| 17 | {
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| 18 | /* this test covers the following files:
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| 19 | Hyperplane.h
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| 20 | */
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| 21 | typedef typename HyperplaneType::Index Index;
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| 22 | const Index dim = _plane.dim();
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| 23 | enum { Options = HyperplaneType::Options };
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| 24 | typedef typename HyperplaneType::Scalar Scalar;
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| 25 | typedef Matrix<Scalar, HyperplaneType::AmbientDimAtCompileTime, 1> VectorType;
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| 26 | typedef Matrix<Scalar, HyperplaneType::AmbientDimAtCompileTime,
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| 27 | HyperplaneType::AmbientDimAtCompileTime> MatrixType;
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| 28 |
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| 29 | VectorType p0 = VectorType::Random(dim);
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| 30 | VectorType p1 = VectorType::Random(dim);
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| 31 |
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| 32 | VectorType n0 = VectorType::Random(dim).normalized();
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| 33 | VectorType n1 = VectorType::Random(dim).normalized();
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| 34 |
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| 35 | HyperplaneType pl0(n0, p0);
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| 36 | HyperplaneType pl1(n1, p1);
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| 37 | HyperplaneType pl2 = pl1;
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| 38 |
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| 39 | Scalar s0 = internal::random<Scalar>();
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| 40 | Scalar s1 = internal::random<Scalar>();
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| 41 |
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| 42 | VERIFY_IS_APPROX( n1.dot(n1), Scalar(1) );
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| 43 |
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| 44 | VERIFY_IS_MUCH_SMALLER_THAN( pl0.absDistance(p0), Scalar(1) );
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| 45 | VERIFY_IS_APPROX( pl1.signedDistance(p1 + n1 * s0), s0 );
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| 46 | VERIFY_IS_MUCH_SMALLER_THAN( pl1.signedDistance(pl1.projection(p0)), Scalar(1) );
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| 47 | VERIFY_IS_MUCH_SMALLER_THAN( pl1.absDistance(p1 + pl1.normal().unitOrthogonal() * s1), Scalar(1) );
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| 48 |
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| 49 | // transform
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| 50 | if (!NumTraits<Scalar>::IsComplex)
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| 51 | {
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| 52 | MatrixType rot = MatrixType::Random(dim,dim).householderQr().householderQ();
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| 53 | DiagonalMatrix<Scalar,HyperplaneType::AmbientDimAtCompileTime> scaling(VectorType::Random());
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| 54 | Translation<Scalar,HyperplaneType::AmbientDimAtCompileTime> translation(VectorType::Random());
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| 55 |
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| 56 | pl2 = pl1;
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| 57 | VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot).absDistance(rot * p1), Scalar(1) );
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| 58 | pl2 = pl1;
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| 59 | VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot,Isometry).absDistance(rot * p1), Scalar(1) );
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| 60 | pl2 = pl1;
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| 61 | VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*scaling).absDistance((rot*scaling) * p1), Scalar(1) );
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| 62 | pl2 = pl1;
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| 63 | VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*scaling*translation)
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| 64 | .absDistance((rot*scaling*translation) * p1), Scalar(1) );
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| 65 | pl2 = pl1;
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| 66 | VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*translation,Isometry)
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| 67 | .absDistance((rot*translation) * p1), Scalar(1) );
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| 68 | }
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| 69 |
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| 70 | // casting
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| 71 | const int Dim = HyperplaneType::AmbientDimAtCompileTime;
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| 72 | typedef typename GetDifferentType<Scalar>::type OtherScalar;
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| 73 | Hyperplane<OtherScalar,Dim,Options> hp1f = pl1.template cast<OtherScalar>();
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| 74 | VERIFY_IS_APPROX(hp1f.template cast<Scalar>(),pl1);
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| 75 | Hyperplane<Scalar,Dim,Options> hp1d = pl1.template cast<Scalar>();
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| 76 | VERIFY_IS_APPROX(hp1d.template cast<Scalar>(),pl1);
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| 77 | }
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| 78 |
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| 79 | template<typename Scalar> void lines()
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| 80 | {
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| 81 | using std::abs;
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| 82 | typedef Hyperplane<Scalar, 2> HLine;
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| 83 | typedef ParametrizedLine<Scalar, 2> PLine;
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| 84 | typedef Matrix<Scalar,2,1> Vector;
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| 85 | typedef Matrix<Scalar,3,1> CoeffsType;
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| 86 |
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| 87 | for(int i = 0; i < 10; i++)
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| 88 | {
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| 89 | Vector center = Vector::Random();
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| 90 | Vector u = Vector::Random();
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| 91 | Vector v = Vector::Random();
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| 92 | Scalar a = internal::random<Scalar>();
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| 93 | while (abs(a-1) < 1e-4) a = internal::random<Scalar>();
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| 94 | while (u.norm() < 1e-4) u = Vector::Random();
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| 95 | while (v.norm() < 1e-4) v = Vector::Random();
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| 96 |
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| 97 | HLine line_u = HLine::Through(center + u, center + a*u);
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| 98 | HLine line_v = HLine::Through(center + v, center + a*v);
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| 99 |
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| 100 | // the line equations should be normalized so that a^2+b^2=1
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| 101 | VERIFY_IS_APPROX(line_u.normal().norm(), Scalar(1));
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| 102 | VERIFY_IS_APPROX(line_v.normal().norm(), Scalar(1));
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| 103 |
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| 104 | Vector result = line_u.intersection(line_v);
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| 105 |
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| 106 | // the lines should intersect at the point we called "center"
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| 107 | VERIFY_IS_APPROX(result, center);
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| 108 |
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| 109 | // check conversions between two types of lines
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| 110 | PLine pl(line_u); // gcc 3.3 will commit suicide if we don't name this variable
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| 111 | CoeffsType converted_coeffs = HLine(pl).coeffs();
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| 112 | converted_coeffs *= (line_u.coeffs()[0])/(converted_coeffs[0]);
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| 113 | VERIFY(line_u.coeffs().isApprox(converted_coeffs));
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| 114 | }
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| 115 | }
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| 116 |
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| 117 | template<typename Scalar> void planes()
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| 118 | {
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| 119 | using std::abs;
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| 120 | typedef Hyperplane<Scalar, 3> Plane;
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| 121 | typedef Matrix<Scalar,3,1> Vector;
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| 122 |
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| 123 | for(int i = 0; i < 10; i++)
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| 124 | {
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| 125 | Vector v0 = Vector::Random();
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| 126 | Vector v1(v0), v2(v0);
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| 127 | if(internal::random<double>(0,1)>0.25)
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| 128 | v1 += Vector::Random();
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| 129 | if(internal::random<double>(0,1)>0.25)
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| 130 | v2 += v1 * std::pow(internal::random<Scalar>(0,1),internal::random<int>(1,16));
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| 131 | if(internal::random<double>(0,1)>0.25)
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| 132 | v2 += Vector::Random() * std::pow(internal::random<Scalar>(0,1),internal::random<int>(1,16));
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| 133 |
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| 134 | Plane p0 = Plane::Through(v0, v1, v2);
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| 135 |
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| 136 | VERIFY_IS_APPROX(p0.normal().norm(), Scalar(1));
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| 137 | VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v0), Scalar(1));
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| 138 | VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v1), Scalar(1));
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| 139 | VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v2), Scalar(1));
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| 140 | }
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| 141 | }
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| 142 |
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| 143 | template<typename Scalar> void hyperplane_alignment()
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| 144 | {
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| 145 | typedef Hyperplane<Scalar,3,AutoAlign> Plane3a;
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| 146 | typedef Hyperplane<Scalar,3,DontAlign> Plane3u;
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| 147 |
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| 148 | EIGEN_ALIGN16 Scalar array1[4];
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| 149 | EIGEN_ALIGN16 Scalar array2[4];
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| 150 | EIGEN_ALIGN16 Scalar array3[4+1];
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| 151 | Scalar* array3u = array3+1;
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| 152 |
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| 153 | Plane3a *p1 = ::new(reinterpret_cast<void*>(array1)) Plane3a;
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| 154 | Plane3u *p2 = ::new(reinterpret_cast<void*>(array2)) Plane3u;
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| 155 | Plane3u *p3 = ::new(reinterpret_cast<void*>(array3u)) Plane3u;
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| 156 |
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| 157 | p1->coeffs().setRandom();
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| 158 | *p2 = *p1;
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| 159 | *p3 = *p1;
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| 160 |
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| 161 | VERIFY_IS_APPROX(p1->coeffs(), p2->coeffs());
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| 162 | VERIFY_IS_APPROX(p1->coeffs(), p3->coeffs());
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| 163 |
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| 164 | #if defined(EIGEN_VECTORIZE) && EIGEN_ALIGN_STATICALLY
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| 165 | if(internal::packet_traits<Scalar>::Vectorizable)
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| 166 | VERIFY_RAISES_ASSERT((::new(reinterpret_cast<void*>(array3u)) Plane3a));
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| 167 | #endif
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| 168 | }
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| 169 |
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| 170 |
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| 171 | void test_geo_hyperplane()
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| 172 | {
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| 173 | for(int i = 0; i < g_repeat; i++) {
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| 174 | CALL_SUBTEST_1( hyperplane(Hyperplane<float,2>()) );
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| 175 | CALL_SUBTEST_2( hyperplane(Hyperplane<float,3>()) );
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| 176 | CALL_SUBTEST_2( hyperplane(Hyperplane<float,3,DontAlign>()) );
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| 177 | CALL_SUBTEST_2( hyperplane_alignment<float>() );
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| 178 | CALL_SUBTEST_3( hyperplane(Hyperplane<double,4>()) );
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| 179 | CALL_SUBTEST_4( hyperplane(Hyperplane<std::complex<double>,5>()) );
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| 180 | CALL_SUBTEST_1( lines<float>() );
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| 181 | CALL_SUBTEST_3( lines<double>() );
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| 182 | CALL_SUBTEST_2( planes<float>() );
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| 183 | CALL_SUBTEST_5( planes<double>() );
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| 184 | }
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| 185 | }
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