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
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
|
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2009 Mathieu Gautier <mathieu.gautier@cea.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>
template<typename T> T bounded_acos(T v)
{
using std::acos;
using std::min;
using std::max;
return acos((max)(T(-1),(min)(v,T(1))));
}
template<typename QuatType> void check_slerp(const QuatType& q0, const QuatType& q1)
{
using std::abs;
typedef typename QuatType::Scalar Scalar;
typedef AngleAxis<Scalar> AA;
Scalar largeEps = test_precision<Scalar>();
Scalar theta_tot = AA(q1*q0.inverse()).angle();
if(theta_tot>Scalar(EIGEN_PI))
theta_tot = Scalar(2.)*Scalar(EIGEN_PI)-theta_tot;
for(Scalar t=0; t<=Scalar(1.001); t+=Scalar(0.1))
{
QuatType q = q0.slerp(t,q1);
Scalar theta = AA(q*q0.inverse()).angle();
VERIFY(abs(q.norm() - 1) < largeEps);
if(theta_tot==0) VERIFY(theta_tot==0);
else VERIFY(abs(theta - t * theta_tot) < largeEps);
}
}
template<typename Scalar, int Options> void quaternion(void)
{
/* this test covers the following files:
Quaternion.h
*/
using std::abs;
typedef Matrix<Scalar,3,1> Vector3;
typedef Matrix<Scalar,3,3> Matrix3;
typedef Quaternion<Scalar,Options> Quaternionx;
typedef AngleAxis<Scalar> AngleAxisx;
Scalar largeEps = test_precision<Scalar>();
if (internal::is_same<Scalar,float>::value)
largeEps = Scalar(1e-3);
Scalar eps = internal::random<Scalar>() * Scalar(1e-2);
Vector3 v0 = Vector3::Random(),
v1 = Vector3::Random(),
v2 = Vector3::Random(),
v3 = Vector3::Random();
Scalar a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI)),
b = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI));
// Quaternion: Identity(), setIdentity();
Quaternionx q1, q2;
q2.setIdentity();
VERIFY_IS_APPROX(Quaternionx(Quaternionx::Identity()).coeffs(), q2.coeffs());
q1.coeffs().setRandom();
VERIFY_IS_APPROX(q1.coeffs(), (q1*q2).coeffs());
// concatenation
q1 *= q2;
q1 = AngleAxisx(a, v0.normalized());
q2 = AngleAxisx(a, v1.normalized());
// angular distance
Scalar refangle = abs(AngleAxisx(q1.inverse()*q2).angle());
if (refangle>Scalar(EIGEN_PI))
refangle = Scalar(2)*Scalar(EIGEN_PI) - refangle;
if((q1.coeffs()-q2.coeffs()).norm() > 10*largeEps)
{
VERIFY_IS_MUCH_SMALLER_THAN(abs(q1.angularDistance(q2) - refangle), Scalar(1));
}
// rotation matrix conversion
VERIFY_IS_APPROX(q1 * v2, q1.toRotationMatrix() * v2);
VERIFY_IS_APPROX(q1 * q2 * v2,
q1.toRotationMatrix() * q2.toRotationMatrix() * v2);
VERIFY( (q2*q1).isApprox(q1*q2, largeEps)
|| !(q2 * q1 * v2).isApprox(q1.toRotationMatrix() * q2.toRotationMatrix() * v2));
q2 = q1.toRotationMatrix();
VERIFY_IS_APPROX(q1*v1,q2*v1);
Matrix3 rot1(q1);
VERIFY_IS_APPROX(q1*v1,rot1*v1);
Quaternionx q3(rot1.transpose()*rot1);
VERIFY_IS_APPROX(q3*v1,v1);
// angle-axis conversion
AngleAxisx aa = AngleAxisx(q1);
VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1);
// Do not execute the test if the rotation angle is almost zero, or
// the rotation axis and v1 are almost parallel.
if (abs(aa.angle()) > 5*test_precision<Scalar>()
&& (aa.axis() - v1.normalized()).norm() < Scalar(1.99)
&& (aa.axis() + v1.normalized()).norm() < Scalar(1.99))
{
VERIFY_IS_NOT_APPROX(q1 * v1, Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1);
}
// from two vector creation
VERIFY_IS_APPROX( v2.normalized(),(q2.setFromTwoVectors(v1, v2)*v1).normalized());
VERIFY_IS_APPROX( v1.normalized(),(q2.setFromTwoVectors(v1, v1)*v1).normalized());
VERIFY_IS_APPROX(-v1.normalized(),(q2.setFromTwoVectors(v1,-v1)*v1).normalized());
if (internal::is_same<Scalar,double>::value)
{
v3 = (v1.array()+eps).matrix();
VERIFY_IS_APPROX( v3.normalized(),(q2.setFromTwoVectors(v1, v3)*v1).normalized());
VERIFY_IS_APPROX(-v3.normalized(),(q2.setFromTwoVectors(v1,-v3)*v1).normalized());
}
// from two vector creation static function
VERIFY_IS_APPROX( v2.normalized(),(Quaternionx::FromTwoVectors(v1, v2)*v1).normalized());
VERIFY_IS_APPROX( v1.normalized(),(Quaternionx::FromTwoVectors(v1, v1)*v1).normalized());
VERIFY_IS_APPROX(-v1.normalized(),(Quaternionx::FromTwoVectors(v1,-v1)*v1).normalized());
if (internal::is_same<Scalar,double>::value)
{
v3 = (v1.array()+eps).matrix();
VERIFY_IS_APPROX( v3.normalized(),(Quaternionx::FromTwoVectors(v1, v3)*v1).normalized());
VERIFY_IS_APPROX(-v3.normalized(),(Quaternionx::FromTwoVectors(v1,-v3)*v1).normalized());
}
// inverse and conjugate
VERIFY_IS_APPROX(q1 * (q1.inverse() * v1), v1);
VERIFY_IS_APPROX(q1 * (q1.conjugate() * v1), v1);
// test casting
Quaternion<float> q1f = q1.template cast<float>();
VERIFY_IS_APPROX(q1f.template cast<Scalar>(),q1);
Quaternion<double> q1d = q1.template cast<double>();
VERIFY_IS_APPROX(q1d.template cast<Scalar>(),q1);
// test bug 369 - improper alignment.
Quaternionx *q = new Quaternionx;
delete q;
q1 = Quaternionx::UnitRandom();
q2 = Quaternionx::UnitRandom();
check_slerp(q1,q2);
q1 = AngleAxisx(b, v1.normalized());
q2 = AngleAxisx(b+Scalar(EIGEN_PI), v1.normalized());
check_slerp(q1,q2);
q1 = AngleAxisx(b, v1.normalized());
q2 = AngleAxisx(-b, -v1.normalized());
check_slerp(q1,q2);
q1 = Quaternionx::UnitRandom();
q2.coeffs() = -q1.coeffs();
check_slerp(q1,q2);
}
template<typename Scalar> void mapQuaternion(void){
typedef Map<Quaternion<Scalar>, Aligned> MQuaternionA;
typedef Map<const Quaternion<Scalar>, Aligned> MCQuaternionA;
typedef Map<Quaternion<Scalar> > MQuaternionUA;
typedef Map<const Quaternion<Scalar> > MCQuaternionUA;
typedef Quaternion<Scalar> Quaternionx;
typedef Matrix<Scalar,3,1> Vector3;
typedef AngleAxis<Scalar> AngleAxisx;
Vector3 v0 = Vector3::Random(),
v1 = Vector3::Random();
Scalar a = internal::random<Scalar>(-Scalar(EIGEN_PI), Scalar(EIGEN_PI));
EIGEN_ALIGN_MAX Scalar array1[4];
EIGEN_ALIGN_MAX Scalar array2[4];
EIGEN_ALIGN_MAX Scalar array3[4+1];
Scalar* array3unaligned = array3+1;
MQuaternionA mq1(array1);
MCQuaternionA mcq1(array1);
MQuaternionA mq2(array2);
MQuaternionUA mq3(array3unaligned);
MCQuaternionUA mcq3(array3unaligned);
// std::cerr << array1 << " " << array2 << " " << array3 << "\n";
mq1 = AngleAxisx(a, v0.normalized());
mq2 = mq1;
mq3 = mq1;
Quaternionx q1 = mq1;
Quaternionx q2 = mq2;
Quaternionx q3 = mq3;
Quaternionx q4 = MCQuaternionUA(array3unaligned);
VERIFY_IS_APPROX(q1.coeffs(), q2.coeffs());
VERIFY_IS_APPROX(q1.coeffs(), q3.coeffs());
VERIFY_IS_APPROX(q4.coeffs(), q3.coeffs());
#ifdef EIGEN_VECTORIZE
if(internal::packet_traits<Scalar>::Vectorizable)
VERIFY_RAISES_ASSERT((MQuaternionA(array3unaligned)));
#endif
VERIFY_IS_APPROX(mq1 * (mq1.inverse() * v1), v1);
VERIFY_IS_APPROX(mq1 * (mq1.conjugate() * v1), v1);
VERIFY_IS_APPROX(mcq1 * (mcq1.inverse() * v1), v1);
VERIFY_IS_APPROX(mcq1 * (mcq1.conjugate() * v1), v1);
VERIFY_IS_APPROX(mq3 * (mq3.inverse() * v1), v1);
VERIFY_IS_APPROX(mq3 * (mq3.conjugate() * v1), v1);
VERIFY_IS_APPROX(mcq3 * (mcq3.inverse() * v1), v1);
VERIFY_IS_APPROX(mcq3 * (mcq3.conjugate() * v1), v1);
VERIFY_IS_APPROX(mq1*mq2, q1*q2);
VERIFY_IS_APPROX(mq3*mq2, q3*q2);
VERIFY_IS_APPROX(mcq1*mq2, q1*q2);
VERIFY_IS_APPROX(mcq3*mq2, q3*q2);
}
template<typename Scalar> void quaternionAlignment(void){
typedef Quaternion<Scalar,AutoAlign> QuaternionA;
typedef Quaternion<Scalar,DontAlign> QuaternionUA;
EIGEN_ALIGN_MAX Scalar array1[4];
EIGEN_ALIGN_MAX Scalar array2[4];
EIGEN_ALIGN_MAX Scalar array3[4+1];
Scalar* arrayunaligned = array3+1;
QuaternionA *q1 = ::new(reinterpret_cast<void*>(array1)) QuaternionA;
QuaternionUA *q2 = ::new(reinterpret_cast<void*>(array2)) QuaternionUA;
QuaternionUA *q3 = ::new(reinterpret_cast<void*>(arrayunaligned)) QuaternionUA;
q1->coeffs().setRandom();
*q2 = *q1;
*q3 = *q1;
VERIFY_IS_APPROX(q1->coeffs(), q2->coeffs());
VERIFY_IS_APPROX(q1->coeffs(), q3->coeffs());
#if defined(EIGEN_VECTORIZE) && EIGEN_MAX_STATIC_ALIGN_BYTES>0
if(internal::packet_traits<Scalar>::Vectorizable && internal::packet_traits<Scalar>::size<=4)
VERIFY_RAISES_ASSERT((::new(reinterpret_cast<void*>(arrayunaligned)) QuaternionA));
#endif
}
template<typename PlainObjectType> void check_const_correctness(const PlainObjectType&)
{
// there's a lot that we can't test here while still having this test compile!
// the only possible approach would be to run a script trying to compile stuff and checking that it fails.
// CMake can help with that.
// verify that map-to-const don't have LvalueBit
typedef typename internal::add_const<PlainObjectType>::type ConstPlainObjectType;
VERIFY( !(internal::traits<Map<ConstPlainObjectType> >::Flags & LvalueBit) );
VERIFY( !(internal::traits<Map<ConstPlainObjectType, Aligned> >::Flags & LvalueBit) );
VERIFY( !(Map<ConstPlainObjectType>::Flags & LvalueBit) );
VERIFY( !(Map<ConstPlainObjectType, Aligned>::Flags & LvalueBit) );
}
void test_geo_quaternion()
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1(( quaternion<float,AutoAlign>() ));
CALL_SUBTEST_1( check_const_correctness(Quaternionf()) );
CALL_SUBTEST_2(( quaternion<double,AutoAlign>() ));
CALL_SUBTEST_2( check_const_correctness(Quaterniond()) );
CALL_SUBTEST_3(( quaternion<float,DontAlign>() ));
CALL_SUBTEST_4(( quaternion<double,DontAlign>() ));
CALL_SUBTEST_5(( quaternionAlignment<float>() ));
CALL_SUBTEST_6(( quaternionAlignment<double>() ));
CALL_SUBTEST_1( mapQuaternion<float>() );
CALL_SUBTEST_2( mapQuaternion<double>() );
}
}
|
