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
hyperplane(const HyperplaneType & _plane)16 template<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
lines()79 template<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
test_eigen2_hyperplane()116 void 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