1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.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 using std::abs;
22 typedef typename HyperplaneType::Index Index;
23 const Index dim = _plane.dim();
24 enum { Options = HyperplaneType::Options };
25 typedef typename HyperplaneType::Scalar Scalar;
26 typedef typename HyperplaneType::RealScalar RealScalar;
27 typedef Matrix<Scalar, HyperplaneType::AmbientDimAtCompileTime, 1> VectorType;
28 typedef Matrix<Scalar, HyperplaneType::AmbientDimAtCompileTime,
29 HyperplaneType::AmbientDimAtCompileTime> MatrixType;
30
31 VectorType p0 = VectorType::Random(dim);
32 VectorType p1 = VectorType::Random(dim);
33
34 VectorType n0 = VectorType::Random(dim).normalized();
35 VectorType n1 = VectorType::Random(dim).normalized();
36
37 HyperplaneType pl0(n0, p0);
38 HyperplaneType pl1(n1, p1);
39 HyperplaneType pl2 = pl1;
40
41 Scalar s0 = internal::random<Scalar>();
42 Scalar s1 = internal::random<Scalar>();
43
44 VERIFY_IS_APPROX( n1.dot(n1), Scalar(1) );
45
46 VERIFY_IS_MUCH_SMALLER_THAN( pl0.absDistance(p0), Scalar(1) );
47 if(numext::abs2(s0)>RealScalar(1e-6))
48 VERIFY_IS_APPROX( pl1.signedDistance(p1 + n1 * s0), s0);
49 else
50 VERIFY_IS_MUCH_SMALLER_THAN( abs(pl1.signedDistance(p1 + n1 * s0) - s0), Scalar(1) );
51 VERIFY_IS_MUCH_SMALLER_THAN( pl1.signedDistance(pl1.projection(p0)), Scalar(1) );
52 VERIFY_IS_MUCH_SMALLER_THAN( pl1.absDistance(p1 + pl1.normal().unitOrthogonal() * s1), Scalar(1) );
53
54 // transform
55 if (!NumTraits<Scalar>::IsComplex)
56 {
57 MatrixType rot = MatrixType::Random(dim,dim).householderQr().householderQ();
58 DiagonalMatrix<Scalar,HyperplaneType::AmbientDimAtCompileTime> scaling(VectorType::Random());
59 Translation<Scalar,HyperplaneType::AmbientDimAtCompileTime> translation(VectorType::Random());
60
61 while(scaling.diagonal().cwiseAbs().minCoeff()<RealScalar(1e-4)) scaling.diagonal() = VectorType::Random();
62
63 pl2 = pl1;
64 VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot).absDistance(rot * p1), Scalar(1) );
65 pl2 = pl1;
66 VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot,Isometry).absDistance(rot * p1), Scalar(1) );
67 pl2 = pl1;
68 VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*scaling).absDistance((rot*scaling) * p1), Scalar(1) );
69 VERIFY_IS_APPROX( pl2.normal().norm(), RealScalar(1) );
70 pl2 = pl1;
71 VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*scaling*translation)
72 .absDistance((rot*scaling*translation) * p1), Scalar(1) );
73 VERIFY_IS_APPROX( pl2.normal().norm(), RealScalar(1) );
74 pl2 = pl1;
75 VERIFY_IS_MUCH_SMALLER_THAN( pl2.transform(rot*translation,Isometry)
76 .absDistance((rot*translation) * p1), Scalar(1) );
77 VERIFY_IS_APPROX( pl2.normal().norm(), RealScalar(1) );
78 }
79
80 // casting
81 const int Dim = HyperplaneType::AmbientDimAtCompileTime;
82 typedef typename GetDifferentType<Scalar>::type OtherScalar;
83 Hyperplane<OtherScalar,Dim,Options> hp1f = pl1.template cast<OtherScalar>();
84 VERIFY_IS_APPROX(hp1f.template cast<Scalar>(),pl1);
85 Hyperplane<Scalar,Dim,Options> hp1d = pl1.template cast<Scalar>();
86 VERIFY_IS_APPROX(hp1d.template cast<Scalar>(),pl1);
87 }
88
lines()89 template<typename Scalar> void lines()
90 {
91 using std::abs;
92 typedef Hyperplane<Scalar, 2> HLine;
93 typedef ParametrizedLine<Scalar, 2> PLine;
94 typedef Matrix<Scalar,2,1> Vector;
95 typedef Matrix<Scalar,3,1> CoeffsType;
96
97 for(int i = 0; i < 10; i++)
98 {
99 Vector center = Vector::Random();
100 Vector u = Vector::Random();
101 Vector v = Vector::Random();
102 Scalar a = internal::random<Scalar>();
103 while (abs(a-1) < Scalar(1e-4)) a = internal::random<Scalar>();
104 while (u.norm() < Scalar(1e-4)) u = Vector::Random();
105 while (v.norm() < Scalar(1e-4)) v = Vector::Random();
106
107 HLine line_u = HLine::Through(center + u, center + a*u);
108 HLine line_v = HLine::Through(center + v, center + a*v);
109
110 // the line equations should be normalized so that a^2+b^2=1
111 VERIFY_IS_APPROX(line_u.normal().norm(), Scalar(1));
112 VERIFY_IS_APPROX(line_v.normal().norm(), Scalar(1));
113
114 Vector result = line_u.intersection(line_v);
115
116 // the lines should intersect at the point we called "center"
117 if(abs(a-1) > Scalar(1e-2) && abs(v.normalized().dot(u.normalized()))<Scalar(0.9))
118 VERIFY_IS_APPROX(result, center);
119
120 // check conversions between two types of lines
121 PLine pl(line_u); // gcc 3.3 will commit suicide if we don't name this variable
122 HLine line_u2(pl);
123 CoeffsType converted_coeffs = line_u2.coeffs();
124 if(line_u2.normal().dot(line_u.normal())<Scalar(0))
125 converted_coeffs = -line_u2.coeffs();
126 VERIFY(line_u.coeffs().isApprox(converted_coeffs));
127 }
128 }
129
planes()130 template<typename Scalar> void planes()
131 {
132 using std::abs;
133 typedef Hyperplane<Scalar, 3> Plane;
134 typedef Matrix<Scalar,3,1> Vector;
135
136 for(int i = 0; i < 10; i++)
137 {
138 Vector v0 = Vector::Random();
139 Vector v1(v0), v2(v0);
140 if(internal::random<double>(0,1)>0.25)
141 v1 += Vector::Random();
142 if(internal::random<double>(0,1)>0.25)
143 v2 += v1 * std::pow(internal::random<Scalar>(0,1),internal::random<int>(1,16));
144 if(internal::random<double>(0,1)>0.25)
145 v2 += Vector::Random() * std::pow(internal::random<Scalar>(0,1),internal::random<int>(1,16));
146
147 Plane p0 = Plane::Through(v0, v1, v2);
148
149 VERIFY_IS_APPROX(p0.normal().norm(), Scalar(1));
150 VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v0), Scalar(1));
151 VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v1), Scalar(1));
152 VERIFY_IS_MUCH_SMALLER_THAN(p0.absDistance(v2), Scalar(1));
153 }
154 }
155
hyperplane_alignment()156 template<typename Scalar> void hyperplane_alignment()
157 {
158 typedef Hyperplane<Scalar,3,AutoAlign> Plane3a;
159 typedef Hyperplane<Scalar,3,DontAlign> Plane3u;
160
161 EIGEN_ALIGN_MAX Scalar array1[4];
162 EIGEN_ALIGN_MAX Scalar array2[4];
163 EIGEN_ALIGN_MAX Scalar array3[4+1];
164 Scalar* array3u = array3+1;
165
166 Plane3a *p1 = ::new(reinterpret_cast<void*>(array1)) Plane3a;
167 Plane3u *p2 = ::new(reinterpret_cast<void*>(array2)) Plane3u;
168 Plane3u *p3 = ::new(reinterpret_cast<void*>(array3u)) Plane3u;
169
170 p1->coeffs().setRandom();
171 *p2 = *p1;
172 *p3 = *p1;
173
174 VERIFY_IS_APPROX(p1->coeffs(), p2->coeffs());
175 VERIFY_IS_APPROX(p1->coeffs(), p3->coeffs());
176
177 #if defined(EIGEN_VECTORIZE) && EIGEN_MAX_STATIC_ALIGN_BYTES > 0
178 if(internal::packet_traits<Scalar>::Vectorizable && internal::packet_traits<Scalar>::size<=4)
179 VERIFY_RAISES_ASSERT((::new(reinterpret_cast<void*>(array3u)) Plane3a));
180 #endif
181 }
182
183
test_geo_hyperplane()184 void test_geo_hyperplane()
185 {
186 for(int i = 0; i < g_repeat; i++) {
187 CALL_SUBTEST_1( hyperplane(Hyperplane<float,2>()) );
188 CALL_SUBTEST_2( hyperplane(Hyperplane<float,3>()) );
189 CALL_SUBTEST_2( hyperplane(Hyperplane<float,3,DontAlign>()) );
190 CALL_SUBTEST_2( hyperplane_alignment<float>() );
191 CALL_SUBTEST_3( hyperplane(Hyperplane<double,4>()) );
192 CALL_SUBTEST_4( hyperplane(Hyperplane<std::complex<double>,5>()) );
193 CALL_SUBTEST_1( lines<float>() );
194 CALL_SUBTEST_3( lines<double>() );
195 CALL_SUBTEST_2( planes<float>() );
196 CALL_SUBTEST_5( planes<double>() );
197 }
198 }
199