1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2008 Gael Guennebaud <[email protected]>
5 // Copyright (C) 2008 Benoit Jacob <[email protected]>
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 using std::abs;
22 const Index dim = _plane.dim();
23 enum { Options = HyperplaneType::Options };
24 typedef typename HyperplaneType::Scalar Scalar;
25 typedef typename HyperplaneType::RealScalar RealScalar;
26 typedef Matrix<Scalar, HyperplaneType::AmbientDimAtCompileTime, 1> VectorType;
27 typedef Matrix<Scalar, HyperplaneType::AmbientDimAtCompileTime,
28 HyperplaneType::AmbientDimAtCompileTime> MatrixType;
29
30 VectorType p0 = VectorType::Random(dim);
31 VectorType p1 = VectorType::Random(dim);
32
33 VectorType n0 = VectorType::Random(dim).normalized();
34 VectorType n1 = VectorType::Random(dim).normalized();
35
36 HyperplaneType pl0(n0, p0);
37 HyperplaneType pl1(n1, p1);
38 HyperplaneType pl2 = pl1;
39
40 Scalar s0 = internal::random<Scalar>();
41 Scalar s1 = internal::random<Scalar>();
42
43 VERIFY_IS_APPROX( n1.dot(n1), Scalar(1) );
44
45 VERIFY_IS_MUCH_SMALLER_THAN( pl0.absDistance(p0), Scalar(1) );
46 if(numext::abs2(s0)>RealScalar(1e-6))
47 VERIFY_IS_APPROX( pl1.signedDistance(p1 + n1 * s0), s0);
48 else
49 VERIFY_IS_MUCH_SMALLER_THAN( abs(pl1.signedDistance(p1 + n1 * s0) - s0), Scalar(1) );
50 VERIFY_IS_MUCH_SMALLER_THAN( pl1.signedDistance(pl1.projection(p0)), Scalar(1) );
51 VERIFY_IS_MUCH_SMALLER_THAN( pl1.absDistance(p1 + pl1.normal().unitOrthogonal() * s1), Scalar(1) );
52
53 // transform
54 if (!NumTraits<Scalar>::IsComplex)
55 {
56 MatrixType rot = MatrixType::Random(dim,dim).householderQr().householderQ();
57 DiagonalMatrix<Scalar,HyperplaneType::AmbientDimAtCompileTime> scaling(VectorType::Random());
58 Translation<Scalar,HyperplaneType::AmbientDimAtCompileTime> translation(VectorType::Random());
59
60 while(scaling.diagonal().cwiseAbs().minCoeff()<RealScalar(1e-4)) scaling.diagonal() = VectorType::Random();
61
62 pl2 = pl1;
63 VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot).absDistance(rot * p1), Scalar(1) );
64 pl2 = pl1;
65 VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot,Isometry).absDistance(rot * p1), Scalar(1) );
66 pl2 = pl1;
67 VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*scaling).absDistance((rot*scaling) * p1), Scalar(1) );
68 VERIFY_IS_APPROX( pl2.normal().norm(), RealScalar(1) );
69 pl2 = pl1;
70 VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*scaling*translation)
71 .absDistance((rot*scaling*translation) * p1), Scalar(1) );
72 VERIFY_IS_APPROX( pl2.normal().norm(), RealScalar(1) );
73 pl2 = pl1;
74 VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*translation,Isometry)
75 .absDistance((rot*translation) * p1), Scalar(1) );
76 VERIFY_IS_APPROX( pl2.normal().norm(), RealScalar(1) );
77 }
78
79 // casting
80 const int Dim = HyperplaneType::AmbientDimAtCompileTime;
81 typedef typename GetDifferentType<Scalar>::type OtherScalar;
82 Hyperplane<OtherScalar,Dim,Options> hp1f = pl1.template cast<OtherScalar>();
83 VERIFY_IS_APPROX(hp1f.template cast<Scalar>(),pl1);
84 Hyperplane<Scalar,Dim,Options> hp1d = pl1.template cast<Scalar>();
85 VERIFY_IS_APPROX(hp1d.template cast<Scalar>(),pl1);
86 }
87
lines()88 template<typename Scalar> void lines()
89 {
90 using std::abs;
91 typedef Hyperplane<Scalar, 2> HLine;
92 typedef ParametrizedLine<Scalar, 2> PLine;
93 typedef Matrix<Scalar,2,1> Vector;
94 typedef Matrix<Scalar,3,1> CoeffsType;
95
96 for(int i = 0; i < 10; i++)
97 {
98 Vector center = Vector::Random();
99 Vector u = Vector::Random();
100 Vector v = Vector::Random();
101 Scalar a = internal::random<Scalar>();
102 while (abs(a-1) < Scalar(1e-4)) a = internal::random<Scalar>();
103 while (u.norm() < Scalar(1e-4)) u = Vector::Random();
104 while (v.norm() < Scalar(1e-4)) v = Vector::Random();
105
106 HLine line_u = HLine::Through(center + u, center + a*u);
107 HLine line_v = HLine::Through(center + v, center + a*v);
108
109 // the line equations should be normalized so that a^2+b^2=1
110 VERIFY_IS_APPROX(line_u.normal().norm(), Scalar(1));
111 VERIFY_IS_APPROX(line_v.normal().norm(), Scalar(1));
112
113 Vector result = line_u.intersection(line_v);
114
115 // the lines should intersect at the point we called "center"
116 if(abs(a-1) > Scalar(1e-2) && abs(v.normalized().dot(u.normalized()))<Scalar(0.9))
117 VERIFY_IS_APPROX(result, center);
118
119 // check conversions between two types of lines
120 PLine pl(line_u); // gcc 3.3 will crash if we don't name this variable.
121 HLine line_u2(pl);
122 CoeffsType converted_coeffs = line_u2.coeffs();
123 if(line_u2.normal().dot(line_u.normal())<Scalar(0))
124 converted_coeffs = -line_u2.coeffs();
125 VERIFY(line_u.coeffs().isApprox(converted_coeffs));
126 }
127 }
128
planes()129 template<typename Scalar> void planes()
130 {
131 using std::abs;
132 typedef Hyperplane<Scalar, 3> Plane;
133 typedef Matrix<Scalar,3,1> Vector;
134
135 for(int i = 0; i < 10; i++)
136 {
137 Vector v0 = Vector::Random();
138 Vector v1(v0), v2(v0);
139 if(internal::random<double>(0,1)>0.25)
140 v1 += Vector::Random();
141 if(internal::random<double>(0,1)>0.25)
142 v2 += v1 * std::pow(internal::random<Scalar>(0,1),internal::random<int>(1,16));
143 if(internal::random<double>(0,1)>0.25)
144 v2 += Vector::Random() * std::pow(internal::random<Scalar>(0,1),internal::random<int>(1,16));
145
146 Plane p0 = Plane::Through(v0, v1, v2);
147
148 VERIFY_IS_APPROX(p0.normal().norm(), Scalar(1));
149 VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v0), Scalar(1));
150 VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v1), Scalar(1));
151 VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v2), Scalar(1));
152 }
153 }
154
hyperplane_alignment()155 template<typename Scalar> void hyperplane_alignment()
156 {
157 typedef Hyperplane<Scalar,3,AutoAlign> Plane3a;
158 typedef Hyperplane<Scalar,3,DontAlign> Plane3u;
159
160 EIGEN_ALIGN_MAX Scalar array1[4];
161 EIGEN_ALIGN_MAX Scalar array2[4];
162 EIGEN_ALIGN_MAX Scalar array3[4+1];
163 Scalar* array3u = array3+1;
164
165 Plane3a *p1 = ::new(reinterpret_cast<void*>(array1)) Plane3a;
166 Plane3u *p2 = ::new(reinterpret_cast<void*>(array2)) Plane3u;
167 Plane3u *p3 = ::new(reinterpret_cast<void*>(array3u)) Plane3u;
168
169 p1->coeffs().setRandom();
170 *p2 = *p1;
171 *p3 = *p1;
172
173 VERIFY_IS_APPROX(p1->coeffs(), p2->coeffs());
174 VERIFY_IS_APPROX(p1->coeffs(), p3->coeffs());
175 }
176
177
EIGEN_DECLARE_TEST(geo_hyperplane)178 EIGEN_DECLARE_TEST(geo_hyperplane)
179 {
180 for(int i = 0; i < g_repeat; i++) {
181 CALL_SUBTEST_1( hyperplane(Hyperplane<float,2>()) );
182 CALL_SUBTEST_2( hyperplane(Hyperplane<float,3>()) );
183 CALL_SUBTEST_2( hyperplane(Hyperplane<float,3,DontAlign>()) );
184 CALL_SUBTEST_2( hyperplane_alignment<float>() );
185 CALL_SUBTEST_3( hyperplane(Hyperplane<double,4>()) );
186 CALL_SUBTEST_4( hyperplane(Hyperplane<std::complex<double>,5>()) );
187 CALL_SUBTEST_1( lines<float>() );
188 CALL_SUBTEST_3( lines<double>() );
189 CALL_SUBTEST_2( planes<float>() );
190 CALL_SUBTEST_5( planes<double>() );
191 }
192 }
193