1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
5 //
6 // This Source Code Form is subject to the terms of the Mozilla
7 // Public License v. 2.0. If a copy of the MPL was not distributed
8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9
10 #include "main.h"
11 #include <Eigen/Geometry>
12 #include <Eigen/LU>
13 #include <Eigen/SVD>
14
15 /* this test covers the following files:
16 Geometry/OrthoMethods.h
17 */
18
orthomethods_3()19 template<typename Scalar> void orthomethods_3()
20 {
21 typedef typename NumTraits<Scalar>::Real RealScalar;
22 typedef Matrix<Scalar,3,3> Matrix3;
23 typedef Matrix<Scalar,3,1> Vector3;
24
25 typedef Matrix<Scalar,4,1> Vector4;
26
27 Vector3 v0 = Vector3::Random(),
28 v1 = Vector3::Random(),
29 v2 = Vector3::Random();
30
31 // cross product
32 VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(v2).dot(v1), Scalar(1));
33 VERIFY_IS_MUCH_SMALLER_THAN(v1.dot(v1.cross(v2)), Scalar(1));
34 VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(v2).dot(v2), Scalar(1));
35 VERIFY_IS_MUCH_SMALLER_THAN(v2.dot(v1.cross(v2)), Scalar(1));
36 Matrix3 mat3;
37 mat3 << v0.normalized(),
38 (v0.cross(v1)).normalized(),
39 (v0.cross(v1).cross(v0)).normalized();
40 VERIFY(mat3.isUnitary());
41
42
43 // colwise/rowwise cross product
44 mat3.setRandom();
45 Vector3 vec3 = Vector3::Random();
46 Matrix3 mcross;
47 int i = internal::random<int>(0,2);
48 mcross = mat3.colwise().cross(vec3);
49 VERIFY_IS_APPROX(mcross.col(i), mat3.col(i).cross(vec3));
50 mcross = mat3.rowwise().cross(vec3);
51 VERIFY_IS_APPROX(mcross.row(i), mat3.row(i).cross(vec3));
52
53 // cross3
54 Vector4 v40 = Vector4::Random(),
55 v41 = Vector4::Random(),
56 v42 = Vector4::Random();
57 v40.w() = v41.w() = v42.w() = 0;
58 v42.template head<3>() = v40.template head<3>().cross(v41.template head<3>());
59 VERIFY_IS_APPROX(v40.cross3(v41), v42);
60
61 // check mixed product
62 typedef Matrix<RealScalar, 3, 1> RealVector3;
63 RealVector3 rv1 = RealVector3::Random();
64 VERIFY_IS_APPROX(v1.cross(rv1.template cast<Scalar>()), v1.cross(rv1));
65 VERIFY_IS_APPROX(rv1.template cast<Scalar>().cross(v1), rv1.cross(v1));
66 }
67
orthomethods(int size=Size)68 template<typename Scalar, int Size> void orthomethods(int size=Size)
69 {
70 typedef typename NumTraits<Scalar>::Real RealScalar;
71 typedef Matrix<Scalar,Size,1> VectorType;
72 typedef Matrix<Scalar,3,Size> Matrix3N;
73 typedef Matrix<Scalar,Size,3> MatrixN3;
74 typedef Matrix<Scalar,3,1> Vector3;
75
76 VectorType v0 = VectorType::Random(size);
77
78 // unitOrthogonal
79 VERIFY_IS_MUCH_SMALLER_THAN(v0.unitOrthogonal().dot(v0), Scalar(1));
80 VERIFY_IS_APPROX(v0.unitOrthogonal().norm(), RealScalar(1));
81
82 if (size>=3)
83 {
84 v0.template head<2>().setZero();
85 v0.tail(size-2).setRandom();
86
87 VERIFY_IS_MUCH_SMALLER_THAN(v0.unitOrthogonal().dot(v0), Scalar(1));
88 VERIFY_IS_APPROX(v0.unitOrthogonal().norm(), RealScalar(1));
89 }
90
91 // colwise/rowwise cross product
92 Vector3 vec3 = Vector3::Random();
93 int i = internal::random<int>(0,size-1);
94
95 Matrix3N mat3N(3,size), mcross3N(3,size);
96 mat3N.setRandom();
97 mcross3N = mat3N.colwise().cross(vec3);
98 VERIFY_IS_APPROX(mcross3N.col(i), mat3N.col(i).cross(vec3));
99
100 MatrixN3 matN3(size,3), mcrossN3(size,3);
101 matN3.setRandom();
102 mcrossN3 = matN3.rowwise().cross(vec3);
103 VERIFY_IS_APPROX(mcrossN3.row(i), matN3.row(i).cross(vec3));
104 }
105
test_geo_orthomethods()106 void test_geo_orthomethods()
107 {
108 for(int i = 0; i < g_repeat; i++) {
109 CALL_SUBTEST_1( orthomethods_3<float>() );
110 CALL_SUBTEST_2( orthomethods_3<double>() );
111 CALL_SUBTEST_4( orthomethods_3<std::complex<double> >() );
112 CALL_SUBTEST_1( (orthomethods<float,2>()) );
113 CALL_SUBTEST_2( (orthomethods<double,2>()) );
114 CALL_SUBTEST_1( (orthomethods<float,3>()) );
115 CALL_SUBTEST_2( (orthomethods<double,3>()) );
116 CALL_SUBTEST_3( (orthomethods<float,7>()) );
117 CALL_SUBTEST_4( (orthomethods<std::complex<double>,8>()) );
118 CALL_SUBTEST_5( (orthomethods<float,Dynamic>(36)) );
119 CALL_SUBTEST_6( (orthomethods<double,Dynamic>(35)) );
120 }
121 }
122