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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