eigen2_hyperplane.cpp revision c981c48f5bc9aefeffc0bcb0cc3934c2fae179dd 
1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra. Eigen itself is part of the KDE project.
3//
4// Copyright (C) 2008 Gael Guennebaud <g.gael@free.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
22  const int dim = _plane.dim();
23  typedef typename HyperplaneType::Scalar Scalar;
24  typedef typename NumTraits<Scalar>::Real RealScalar;
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 = ei_random<Scalar>();
40  Scalar s1 = ei_random<Scalar>();
41
42  VERIFY_IS_APPROX( n1.eigen2_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).qr().matrixQ();
53    Scaling<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> hp1f = pl1.template cast<OtherScalar>();
74  VERIFY_IS_APPROX(hp1f.template cast<Scalar>(),pl1);
75  Hyperplane<Scalar,Dim> hp1d = pl1.template cast<Scalar>();
76  VERIFY_IS_APPROX(hp1d.template cast<Scalar>(),pl1);
77}
78
79template<typename Scalar> void lines()
80{
81  typedef Hyperplane<Scalar, 2> HLine;
82  typedef ParametrizedLine<Scalar, 2> PLine;
83  typedef Matrix<Scalar,2,1> Vector;
84  typedef Matrix<Scalar,3,1> CoeffsType;
85
86  for(int i = 0; i < 10; i++)
87  {
88    Vector center = Vector::Random();
89    Vector u = Vector::Random();
90    Vector v = Vector::Random();
91    Scalar a = ei_random<Scalar>();
92    while (ei_abs(a-1) < 1e-4) a = ei_random<Scalar>();
93    while (u.norm() < 1e-4) u = Vector::Random();
94    while (v.norm() < 1e-4) v = Vector::Random();
95
96    HLine line_u = HLine::Through(center + u, center + a*u);
97    HLine line_v = HLine::Through(center + v, center + a*v);
98
99    // the line equations should be normalized so that a^2+b^2=1
100    VERIFY_IS_APPROX(line_u.normal().norm(), Scalar(1));
101    VERIFY_IS_APPROX(line_v.normal().norm(), Scalar(1));
102
103    Vector result = line_u.intersection(line_v);
104
105    // the lines should intersect at the point we called "center"
106    VERIFY_IS_APPROX(result, center);
107
108    // check conversions between two types of lines
109    PLine pl(line_u); // gcc 3.3 will commit suicide if we don't name this variable
110    CoeffsType converted_coeffs(HLine(pl).coeffs());
111    converted_coeffs *= line_u.coeffs()(0)/converted_coeffs(0);
112    VERIFY(line_u.coeffs().isApprox(converted_coeffs));
113  }
114}
115
116void test_eigen2_hyperplane()
117{
118  for(int i = 0; i < g_repeat; i++) {
119    CALL_SUBTEST_1( hyperplane(Hyperplane<float,2>()) );
120    CALL_SUBTEST_2( hyperplane(Hyperplane<float,3>()) );
121    CALL_SUBTEST_3( hyperplane(Hyperplane<double,4>()) );
122    CALL_SUBTEST_4( hyperplane(Hyperplane<std::complex<double>,5>()) );
123    CALL_SUBTEST_5( lines<float>() );
124    CALL_SUBTEST_6( lines<double>() );
125  }
126}
127