1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2008-2012 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
16 template<typename Scalar>
verify_euler(const Matrix<Scalar,3,1> & ea,int i,int j,int k)17 void verify_euler(const Matrix<Scalar,3,1>& ea, int i, int j, int k)
18 {
19 typedef Matrix<Scalar,3,3> Matrix3;
20 typedef Matrix<Scalar,3,1> Vector3;
21 typedef AngleAxis<Scalar> AngleAxisx;
22 using std::abs;
23 Matrix3 m(AngleAxisx(ea[0], Vector3::Unit(i)) * AngleAxisx(ea[1], Vector3::Unit(j)) * AngleAxisx(ea[2], Vector3::Unit(k)));
24 Vector3 eabis = m.eulerAngles(i, j, k);
25 Matrix3 mbis(AngleAxisx(eabis[0], Vector3::Unit(i)) * AngleAxisx(eabis[1], Vector3::Unit(j)) * AngleAxisx(eabis[2], Vector3::Unit(k)));
26 VERIFY_IS_APPROX(m, mbis);
27 /* If I==K, and ea[1]==0, then there no unique solution. */
28 /* The remark apply in the case where I!=K, and |ea[1]| is close to pi/2. */
29 if( (i!=k || ea[1]!=0) && (i==k || !internal::isApprox(abs(ea[1]),Scalar(EIGEN_PI/2),test_precision<Scalar>())) )
30 VERIFY((ea-eabis).norm() <= test_precision<Scalar>());
31
32 // approx_or_less_than does not work for 0
33 VERIFY(0 < eabis[0] || test_isMuchSmallerThan(eabis[0], Scalar(1)));
34 VERIFY_IS_APPROX_OR_LESS_THAN(eabis[0], Scalar(EIGEN_PI));
35 VERIFY_IS_APPROX_OR_LESS_THAN(-Scalar(EIGEN_PI), eabis[1]);
36 VERIFY_IS_APPROX_OR_LESS_THAN(eabis[1], Scalar(EIGEN_PI));
37 VERIFY_IS_APPROX_OR_LESS_THAN(-Scalar(EIGEN_PI), eabis[2]);
38 VERIFY_IS_APPROX_OR_LESS_THAN(eabis[2], Scalar(EIGEN_PI));
39 }
40
check_all_var(const Matrix<Scalar,3,1> & ea)41 template<typename Scalar> void check_all_var(const Matrix<Scalar,3,1>& ea)
42 {
43 verify_euler(ea, 0,1,2);
44 verify_euler(ea, 0,1,0);
45 verify_euler(ea, 0,2,1);
46 verify_euler(ea, 0,2,0);
47
48 verify_euler(ea, 1,2,0);
49 verify_euler(ea, 1,2,1);
50 verify_euler(ea, 1,0,2);
51 verify_euler(ea, 1,0,1);
52
53 verify_euler(ea, 2,0,1);
54 verify_euler(ea, 2,0,2);
55 verify_euler(ea, 2,1,0);
56 verify_euler(ea, 2,1,2);
57 }
58
eulerangles()59 template<typename Scalar> void eulerangles()
60 {
61 typedef Matrix<Scalar,3,3> Matrix3;
62 typedef Matrix<Scalar,3,1> Vector3;
63 typedef Array<Scalar,3,1> Array3;
64 typedef Quaternion<Scalar> Quaternionx;
65 typedef AngleAxis<Scalar> AngleAxisx;
66
67 Scalar a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI));
68 Quaternionx q1;
69 q1 = AngleAxisx(a, Vector3::Random().normalized());
70 Matrix3 m;
71 m = q1;
72
73 Vector3 ea = m.eulerAngles(0,1,2);
74 check_all_var(ea);
75 ea = m.eulerAngles(0,1,0);
76 check_all_var(ea);
77
78 // Check with purely random Quaternion:
79 q1.coeffs() = Quaternionx::Coefficients::Random().normalized();
80 m = q1;
81 ea = m.eulerAngles(0,1,2);
82 check_all_var(ea);
83 ea = m.eulerAngles(0,1,0);
84 check_all_var(ea);
85
86 // Check with random angles in range [0:pi]x[-pi:pi]x[-pi:pi].
87 ea = (Array3::Random() + Array3(1,0,0))*Scalar(EIGEN_PI)*Array3(0.5,1,1);
88 check_all_var(ea);
89
90 ea[2] = ea[0] = internal::random<Scalar>(0,Scalar(EIGEN_PI));
91 check_all_var(ea);
92
93 ea[0] = ea[1] = internal::random<Scalar>(0,Scalar(EIGEN_PI));
94 check_all_var(ea);
95
96 ea[1] = 0;
97 check_all_var(ea);
98
99 ea.head(2).setZero();
100 check_all_var(ea);
101
102 ea.setZero();
103 check_all_var(ea);
104 }
105
test_geo_eulerangles()106 void test_geo_eulerangles()
107 {
108 for(int i = 0; i < g_repeat; i++) {
109 CALL_SUBTEST_1( eulerangles<float>() );
110 CALL_SUBTEST_2( eulerangles<double>() );
111 }
112 }
113