1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
|
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#include "main.h"
#include <Eigen/Geometry>
#include <Eigen/LU>
#include <Eigen/SVD>
/* this test covers the following files:
Geometry/OrthoMethods.h
*/
template<typename Scalar> void orthomethods_3()
{
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Matrix<Scalar,3,3> Matrix3;
typedef Matrix<Scalar,3,1> Vector3;
typedef Matrix<Scalar,4,1> Vector4;
Vector3 v0 = Vector3::Random(),
v1 = Vector3::Random(),
v2 = Vector3::Random();
// cross product
VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(v2).dot(v1), Scalar(1));
VERIFY_IS_MUCH_SMALLER_THAN(v1.dot(v1.cross(v2)), Scalar(1));
VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(v2).dot(v2), Scalar(1));
VERIFY_IS_MUCH_SMALLER_THAN(v2.dot(v1.cross(v2)), Scalar(1));
VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(Vector3::Random()).dot(v1), Scalar(1));
Matrix3 mat3;
mat3 << v0.normalized(),
(v0.cross(v1)).normalized(),
(v0.cross(v1).cross(v0)).normalized();
VERIFY(mat3.isUnitary());
mat3.setRandom();
VERIFY_IS_APPROX(v0.cross(mat3*v1), -(mat3*v1).cross(v0));
VERIFY_IS_APPROX(v0.cross(mat3.lazyProduct(v1)), -(mat3.lazyProduct(v1)).cross(v0));
// colwise/rowwise cross product
mat3.setRandom();
Vector3 vec3 = Vector3::Random();
Matrix3 mcross;
int i = internal::random<int>(0,2);
mcross = mat3.colwise().cross(vec3);
VERIFY_IS_APPROX(mcross.col(i), mat3.col(i).cross(vec3));
VERIFY_IS_MUCH_SMALLER_THAN((mat3.adjoint() * mat3.colwise().cross(vec3)).diagonal().cwiseAbs().sum(), Scalar(1));
VERIFY_IS_MUCH_SMALLER_THAN((mat3.adjoint() * mat3.colwise().cross(Vector3::Random())).diagonal().cwiseAbs().sum(), Scalar(1));
VERIFY_IS_MUCH_SMALLER_THAN((vec3.adjoint() * mat3.colwise().cross(vec3)).cwiseAbs().sum(), Scalar(1));
VERIFY_IS_MUCH_SMALLER_THAN((vec3.adjoint() * Matrix3::Random().colwise().cross(vec3)).cwiseAbs().sum(), Scalar(1));
mcross = mat3.rowwise().cross(vec3);
VERIFY_IS_APPROX(mcross.row(i), mat3.row(i).cross(vec3));
// cross3
Vector4 v40 = Vector4::Random(),
v41 = Vector4::Random(),
v42 = Vector4::Random();
v40.w() = v41.w() = v42.w() = 0;
v42.template head<3>() = v40.template head<3>().cross(v41.template head<3>());
VERIFY_IS_APPROX(v40.cross3(v41), v42);
VERIFY_IS_MUCH_SMALLER_THAN(v40.cross3(Vector4::Random()).dot(v40), Scalar(1));
// check mixed product
typedef Matrix<RealScalar, 3, 1> RealVector3;
RealVector3 rv1 = RealVector3::Random();
VERIFY_IS_APPROX(v1.cross(rv1.template cast<Scalar>()), v1.cross(rv1));
VERIFY_IS_APPROX(rv1.template cast<Scalar>().cross(v1), rv1.cross(v1));
}
template<typename Scalar, int Size> void orthomethods(int size=Size)
{
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Matrix<Scalar,Size,1> VectorType;
typedef Matrix<Scalar,3,Size> Matrix3N;
typedef Matrix<Scalar,Size,3> MatrixN3;
typedef Matrix<Scalar,3,1> Vector3;
VectorType v0 = VectorType::Random(size);
// unitOrthogonal
VERIFY_IS_MUCH_SMALLER_THAN(v0.unitOrthogonal().dot(v0), Scalar(1));
VERIFY_IS_APPROX(v0.unitOrthogonal().norm(), RealScalar(1));
if (size>=3)
{
v0.template head<2>().setZero();
v0.tail(size-2).setRandom();
VERIFY_IS_MUCH_SMALLER_THAN(v0.unitOrthogonal().dot(v0), Scalar(1));
VERIFY_IS_APPROX(v0.unitOrthogonal().norm(), RealScalar(1));
}
// colwise/rowwise cross product
Vector3 vec3 = Vector3::Random();
int i = internal::random<int>(0,size-1);
Matrix3N mat3N(3,size), mcross3N(3,size);
mat3N.setRandom();
mcross3N = mat3N.colwise().cross(vec3);
VERIFY_IS_APPROX(mcross3N.col(i), mat3N.col(i).cross(vec3));
MatrixN3 matN3(size,3), mcrossN3(size,3);
matN3.setRandom();
mcrossN3 = matN3.rowwise().cross(vec3);
VERIFY_IS_APPROX(mcrossN3.row(i), matN3.row(i).cross(vec3));
}
EIGEN_DECLARE_TEST(geo_orthomethods)
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( orthomethods_3<float>() );
CALL_SUBTEST_2( orthomethods_3<double>() );
CALL_SUBTEST_4( orthomethods_3<std::complex<double> >() );
CALL_SUBTEST_1( (orthomethods<float,2>()) );
CALL_SUBTEST_2( (orthomethods<double,2>()) );
CALL_SUBTEST_1( (orthomethods<float,3>()) );
CALL_SUBTEST_2( (orthomethods<double,3>()) );
CALL_SUBTEST_3( (orthomethods<float,7>()) );
CALL_SUBTEST_4( (orthomethods<std::complex<double>,8>()) );
CALL_SUBTEST_5( (orthomethods<float,Dynamic>(36)) );
CALL_SUBTEST_6( (orthomethods<double,Dynamic>(35)) );
}
}
|
