source: pacpussensors/trunk/Vislab/lib3dv/eigen/test/geo_quaternion.cpp@ 136

Last change on this file since 136 was 136, checked in by ldecherf, 7 years ago

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1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra.
3//
4// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
5// Copyright (C) 2009 Mathieu Gautier <mathieu.gautier@cea.fr>
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/SVD>
15
16template<typename T> T bounded_acos(T v)
17{
18 using std::acos;
19 using std::min;
20 using std::max;
21 return acos((max)(T(-1),(min)(v,T(1))));
22}
23
24template<typename QuatType> void check_slerp(const QuatType& q0, const QuatType& q1)
25{
26 using std::abs;
27 typedef typename QuatType::Scalar Scalar;
28 typedef AngleAxis<Scalar> AA;
29
30 Scalar largeEps = test_precision<Scalar>();
31
32 Scalar theta_tot = AA(q1*q0.inverse()).angle();
33 if(theta_tot>M_PI)
34 theta_tot = Scalar(2.*M_PI)-theta_tot;
35 for(Scalar t=0; t<=Scalar(1.001); t+=Scalar(0.1))
36 {
37 QuatType q = q0.slerp(t,q1);
38 Scalar theta = AA(q*q0.inverse()).angle();
39 VERIFY(abs(q.norm() - 1) < largeEps);
40 if(theta_tot==0) VERIFY(theta_tot==0);
41 else VERIFY(abs(theta - t * theta_tot) < largeEps);
42 }
43}
44
45template<typename Scalar, int Options> void quaternion(void)
46{
47 /* this test covers the following files:
48 Quaternion.h
49 */
50 using std::abs;
51 typedef Matrix<Scalar,3,1> Vector3;
52 typedef Matrix<Scalar,4,1> Vector4;
53 typedef Quaternion<Scalar,Options> Quaternionx;
54 typedef AngleAxis<Scalar> AngleAxisx;
55
56 Scalar largeEps = test_precision<Scalar>();
57 if (internal::is_same<Scalar,float>::value)
58 largeEps = 1e-3f;
59
60 Scalar eps = internal::random<Scalar>() * Scalar(1e-2);
61
62 Vector3 v0 = Vector3::Random(),
63 v1 = Vector3::Random(),
64 v2 = Vector3::Random(),
65 v3 = Vector3::Random();
66
67 Scalar a = internal::random<Scalar>(-Scalar(M_PI), Scalar(M_PI)),
68 b = internal::random<Scalar>(-Scalar(M_PI), Scalar(M_PI));
69
70 // Quaternion: Identity(), setIdentity();
71 Quaternionx q1, q2;
72 q2.setIdentity();
73 VERIFY_IS_APPROX(Quaternionx(Quaternionx::Identity()).coeffs(), q2.coeffs());
74 q1.coeffs().setRandom();
75 VERIFY_IS_APPROX(q1.coeffs(), (q1*q2).coeffs());
76
77 // concatenation
78 q1 *= q2;
79
80 q1 = AngleAxisx(a, v0.normalized());
81 q2 = AngleAxisx(a, v1.normalized());
82
83 // angular distance
84 Scalar refangle = abs(AngleAxisx(q1.inverse()*q2).angle());
85 if (refangle>Scalar(M_PI))
86 refangle = Scalar(2)*Scalar(M_PI) - refangle;
87
88 if((q1.coeffs()-q2.coeffs()).norm() > 10*largeEps)
89 {
90 VERIFY_IS_MUCH_SMALLER_THAN(abs(q1.angularDistance(q2) - refangle), Scalar(1));
91 }
92
93 // rotation matrix conversion
94 VERIFY_IS_APPROX(q1 * v2, q1.toRotationMatrix() * v2);
95 VERIFY_IS_APPROX(q1 * q2 * v2,
96 q1.toRotationMatrix() * q2.toRotationMatrix() * v2);
97
98 VERIFY( (q2*q1).isApprox(q1*q2, largeEps)
99 || !(q2 * q1 * v2).isApprox(q1.toRotationMatrix() * q2.toRotationMatrix() * v2));
100
101 q2 = q1.toRotationMatrix();
102 VERIFY_IS_APPROX(q1*v1,q2*v1);
103
104
105 // angle-axis conversion
106 AngleAxisx aa = AngleAxisx(q1);
107 VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1);
108
109 // Do not execute the test if the rotation angle is almost zero, or
110 // the rotation axis and v1 are almost parallel.
111 if (abs(aa.angle()) > 5*test_precision<Scalar>()
112 && (aa.axis() - v1.normalized()).norm() < 1.99
113 && (aa.axis() + v1.normalized()).norm() < 1.99)
114 {
115 VERIFY_IS_NOT_APPROX(q1 * v1, Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1);
116 }
117
118 // from two vector creation
119 VERIFY_IS_APPROX( v2.normalized(),(q2.setFromTwoVectors(v1, v2)*v1).normalized());
120 VERIFY_IS_APPROX( v1.normalized(),(q2.setFromTwoVectors(v1, v1)*v1).normalized());
121 VERIFY_IS_APPROX(-v1.normalized(),(q2.setFromTwoVectors(v1,-v1)*v1).normalized());
122 if (internal::is_same<Scalar,double>::value)
123 {
124 v3 = (v1.array()+eps).matrix();
125 VERIFY_IS_APPROX( v3.normalized(),(q2.setFromTwoVectors(v1, v3)*v1).normalized());
126 VERIFY_IS_APPROX(-v3.normalized(),(q2.setFromTwoVectors(v1,-v3)*v1).normalized());
127 }
128
129 // from two vector creation static function
130 VERIFY_IS_APPROX( v2.normalized(),(Quaternionx::FromTwoVectors(v1, v2)*v1).normalized());
131 VERIFY_IS_APPROX( v1.normalized(),(Quaternionx::FromTwoVectors(v1, v1)*v1).normalized());
132 VERIFY_IS_APPROX(-v1.normalized(),(Quaternionx::FromTwoVectors(v1,-v1)*v1).normalized());
133 if (internal::is_same<Scalar,double>::value)
134 {
135 v3 = (v1.array()+eps).matrix();
136 VERIFY_IS_APPROX( v3.normalized(),(Quaternionx::FromTwoVectors(v1, v3)*v1).normalized());
137 VERIFY_IS_APPROX(-v3.normalized(),(Quaternionx::FromTwoVectors(v1,-v3)*v1).normalized());
138 }
139
140 // inverse and conjugate
141 VERIFY_IS_APPROX(q1 * (q1.inverse() * v1), v1);
142 VERIFY_IS_APPROX(q1 * (q1.conjugate() * v1), v1);
143
144 // test casting
145 Quaternion<float> q1f = q1.template cast<float>();
146 VERIFY_IS_APPROX(q1f.template cast<Scalar>(),q1);
147 Quaternion<double> q1d = q1.template cast<double>();
148 VERIFY_IS_APPROX(q1d.template cast<Scalar>(),q1);
149
150 // test bug 369 - improper alignment.
151 Quaternionx *q = new Quaternionx;
152 delete q;
153
154 q1 = AngleAxisx(a, v0.normalized());
155 q2 = AngleAxisx(b, v1.normalized());
156 check_slerp(q1,q2);
157
158 q1 = AngleAxisx(b, v1.normalized());
159 q2 = AngleAxisx(b+Scalar(M_PI), v1.normalized());
160 check_slerp(q1,q2);
161
162 q1 = AngleAxisx(b, v1.normalized());
163 q2 = AngleAxisx(-b, -v1.normalized());
164 check_slerp(q1,q2);
165
166 q1.coeffs() = Vector4::Random().normalized();
167 q2.coeffs() = -q1.coeffs();
168 check_slerp(q1,q2);
169}
170
171template<typename Scalar> void mapQuaternion(void){
172 typedef Map<Quaternion<Scalar>, Aligned> MQuaternionA;
173 typedef Map<const Quaternion<Scalar>, Aligned> MCQuaternionA;
174 typedef Map<Quaternion<Scalar> > MQuaternionUA;
175 typedef Map<const Quaternion<Scalar> > MCQuaternionUA;
176 typedef Quaternion<Scalar> Quaternionx;
177 typedef Matrix<Scalar,3,1> Vector3;
178 typedef AngleAxis<Scalar> AngleAxisx;
179
180 Vector3 v0 = Vector3::Random(),
181 v1 = Vector3::Random();
182 Scalar a = internal::random<Scalar>(-Scalar(M_PI), Scalar(M_PI));
183
184 EIGEN_ALIGN16 Scalar array1[4];
185 EIGEN_ALIGN16 Scalar array2[4];
186 EIGEN_ALIGN16 Scalar array3[4+1];
187 Scalar* array3unaligned = array3+1;
188
189 MQuaternionA mq1(array1);
190 MCQuaternionA mcq1(array1);
191 MQuaternionA mq2(array2);
192 MQuaternionUA mq3(array3unaligned);
193 MCQuaternionUA mcq3(array3unaligned);
194
195// std::cerr << array1 << " " << array2 << " " << array3 << "\n";
196 mq1 = AngleAxisx(a, v0.normalized());
197 mq2 = mq1;
198 mq3 = mq1;
199
200 Quaternionx q1 = mq1;
201 Quaternionx q2 = mq2;
202 Quaternionx q3 = mq3;
203 Quaternionx q4 = MCQuaternionUA(array3unaligned);
204
205 VERIFY_IS_APPROX(q1.coeffs(), q2.coeffs());
206 VERIFY_IS_APPROX(q1.coeffs(), q3.coeffs());
207 VERIFY_IS_APPROX(q4.coeffs(), q3.coeffs());
208 #ifdef EIGEN_VECTORIZE
209 if(internal::packet_traits<Scalar>::Vectorizable)
210 VERIFY_RAISES_ASSERT((MQuaternionA(array3unaligned)));
211 #endif
212
213 VERIFY_IS_APPROX(mq1 * (mq1.inverse() * v1), v1);
214 VERIFY_IS_APPROX(mq1 * (mq1.conjugate() * v1), v1);
215
216 VERIFY_IS_APPROX(mcq1 * (mcq1.inverse() * v1), v1);
217 VERIFY_IS_APPROX(mcq1 * (mcq1.conjugate() * v1), v1);
218
219 VERIFY_IS_APPROX(mq3 * (mq3.inverse() * v1), v1);
220 VERIFY_IS_APPROX(mq3 * (mq3.conjugate() * v1), v1);
221
222 VERIFY_IS_APPROX(mcq3 * (mcq3.inverse() * v1), v1);
223 VERIFY_IS_APPROX(mcq3 * (mcq3.conjugate() * v1), v1);
224
225 VERIFY_IS_APPROX(mq1*mq2, q1*q2);
226 VERIFY_IS_APPROX(mq3*mq2, q3*q2);
227 VERIFY_IS_APPROX(mcq1*mq2, q1*q2);
228 VERIFY_IS_APPROX(mcq3*mq2, q3*q2);
229}
230
231template<typename Scalar> void quaternionAlignment(void){
232 typedef Quaternion<Scalar,AutoAlign> QuaternionA;
233 typedef Quaternion<Scalar,DontAlign> QuaternionUA;
234
235 EIGEN_ALIGN16 Scalar array1[4];
236 EIGEN_ALIGN16 Scalar array2[4];
237 EIGEN_ALIGN16 Scalar array3[4+1];
238 Scalar* arrayunaligned = array3+1;
239
240 QuaternionA *q1 = ::new(reinterpret_cast<void*>(array1)) QuaternionA;
241 QuaternionUA *q2 = ::new(reinterpret_cast<void*>(array2)) QuaternionUA;
242 QuaternionUA *q3 = ::new(reinterpret_cast<void*>(arrayunaligned)) QuaternionUA;
243
244 q1->coeffs().setRandom();
245 *q2 = *q1;
246 *q3 = *q1;
247
248 VERIFY_IS_APPROX(q1->coeffs(), q2->coeffs());
249 VERIFY_IS_APPROX(q1->coeffs(), q3->coeffs());
250 #if defined(EIGEN_VECTORIZE) && EIGEN_ALIGN_STATICALLY
251 if(internal::packet_traits<Scalar>::Vectorizable)
252 VERIFY_RAISES_ASSERT((::new(reinterpret_cast<void*>(arrayunaligned)) QuaternionA));
253 #endif
254}
255
256template<typename PlainObjectType> void check_const_correctness(const PlainObjectType&)
257{
258 // there's a lot that we can't test here while still having this test compile!
259 // the only possible approach would be to run a script trying to compile stuff and checking that it fails.
260 // CMake can help with that.
261
262 // verify that map-to-const don't have LvalueBit
263 typedef typename internal::add_const<PlainObjectType>::type ConstPlainObjectType;
264 VERIFY( !(internal::traits<Map<ConstPlainObjectType> >::Flags & LvalueBit) );
265 VERIFY( !(internal::traits<Map<ConstPlainObjectType, Aligned> >::Flags & LvalueBit) );
266 VERIFY( !(Map<ConstPlainObjectType>::Flags & LvalueBit) );
267 VERIFY( !(Map<ConstPlainObjectType, Aligned>::Flags & LvalueBit) );
268}
269
270void test_geo_quaternion()
271{
272 for(int i = 0; i < g_repeat; i++) {
273 CALL_SUBTEST_1(( quaternion<float,AutoAlign>() ));
274 CALL_SUBTEST_1( check_const_correctness(Quaternionf()) );
275 CALL_SUBTEST_2(( quaternion<double,AutoAlign>() ));
276 CALL_SUBTEST_2( check_const_correctness(Quaterniond()) );
277 CALL_SUBTEST_3(( quaternion<float,DontAlign>() ));
278 CALL_SUBTEST_4(( quaternion<double,DontAlign>() ));
279 CALL_SUBTEST_5(( quaternionAlignment<float>() ));
280 CALL_SUBTEST_6(( quaternionAlignment<double>() ));
281 CALL_SUBTEST_1( mapQuaternion<float>() );
282 CALL_SUBTEST_2( mapQuaternion<double>() );
283 }
284}
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