1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra. Eigen itself is part of the KDE project.
3 //
4 // Copyright (C) 2008 Gael Guennebaud <g.gael@free.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
geometry(void)15 template<typename Scalar> void geometry(void)
16 {
17 /* this test covers the following files:
18 Cross.h Quaternion.h, Transform.cpp
19 */
20
21 typedef Matrix<Scalar,2,2> Matrix2;
22 typedef Matrix<Scalar,3,3> Matrix3;
23 typedef Matrix<Scalar,4,4> Matrix4;
24 typedef Matrix<Scalar,2,1> Vector2;
25 typedef Matrix<Scalar,3,1> Vector3;
26 typedef Matrix<Scalar,4,1> Vector4;
27 typedef Quaternion<Scalar> Quaternionx;
28 typedef AngleAxis<Scalar> AngleAxisx;
29 typedef Transform<Scalar,2> Transform2;
30 typedef Transform<Scalar,3> Transform3;
31 typedef Scaling<Scalar,2> Scaling2;
32 typedef Scaling<Scalar,3> Scaling3;
33 typedef Translation<Scalar,2> Translation2;
34 typedef Translation<Scalar,3> Translation3;
35
36 Scalar largeEps = test_precision<Scalar>();
37 if (ei_is_same_type<Scalar,float>::ret)
38 largeEps = 1e-2f;
39
40 Vector3 v0 = Vector3::Random(),
41 v1 = Vector3::Random(),
42 v2 = Vector3::Random();
43 Vector2 u0 = Vector2::Random();
44 Matrix3 matrot1;
45
46 Scalar a = ei_random<Scalar>(-Scalar(M_PI), Scalar(M_PI));
47
48 // cross product
49 VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(v2).eigen2_dot(v1), Scalar(1));
50 Matrix3 m;
51 m << v0.normalized(),
52 (v0.cross(v1)).normalized(),
53 (v0.cross(v1).cross(v0)).normalized();
54 VERIFY(m.isUnitary());
55
56 // Quaternion: Identity(), setIdentity();
57 Quaternionx q1, q2;
58 q2.setIdentity();
59 VERIFY_IS_APPROX(Quaternionx(Quaternionx::Identity()).coeffs(), q2.coeffs());
60 q1.coeffs().setRandom();
61 VERIFY_IS_APPROX(q1.coeffs(), (q1*q2).coeffs());
62
63 // unitOrthogonal
64 VERIFY_IS_MUCH_SMALLER_THAN(u0.unitOrthogonal().eigen2_dot(u0), Scalar(1));
65 VERIFY_IS_MUCH_SMALLER_THAN(v0.unitOrthogonal().eigen2_dot(v0), Scalar(1));
66 VERIFY_IS_APPROX(u0.unitOrthogonal().norm(), Scalar(1));
67 VERIFY_IS_APPROX(v0.unitOrthogonal().norm(), Scalar(1));
68
69
70 VERIFY_IS_APPROX(v0, AngleAxisx(a, v0.normalized()) * v0);
71 VERIFY_IS_APPROX(-v0, AngleAxisx(Scalar(M_PI), v0.unitOrthogonal()) * v0);
72 VERIFY_IS_APPROX(ei_cos(a)*v0.squaredNorm(), v0.eigen2_dot(AngleAxisx(a, v0.unitOrthogonal()) * v0));
73 m = AngleAxisx(a, v0.normalized()).toRotationMatrix().adjoint();
74 VERIFY_IS_APPROX(Matrix3::Identity(), m * AngleAxisx(a, v0.normalized()));
75 VERIFY_IS_APPROX(Matrix3::Identity(), AngleAxisx(a, v0.normalized()) * m);
76
77 q1 = AngleAxisx(a, v0.normalized());
78 q2 = AngleAxisx(a, v1.normalized());
79
80 // angular distance
81 Scalar refangle = ei_abs(AngleAxisx(q1.inverse()*q2).angle());
82 if (refangle>Scalar(M_PI))
83 refangle = Scalar(2)*Scalar(M_PI) - refangle;
84
85 if((q1.coeffs()-q2.coeffs()).norm() > 10*largeEps)
86 {
87 VERIFY(ei_isApprox(q1.angularDistance(q2), refangle, largeEps));
88 }
89
90 // rotation matrix conversion
91 VERIFY_IS_APPROX(q1 * v2, q1.toRotationMatrix() * v2);
92 VERIFY_IS_APPROX(q1 * q2 * v2,
93 q1.toRotationMatrix() * q2.toRotationMatrix() * v2);
94
95 VERIFY( (q2*q1).isApprox(q1*q2, largeEps) || !(q2 * q1 * v2).isApprox(
96 q1.toRotationMatrix() * q2.toRotationMatrix() * v2));
97
98 q2 = q1.toRotationMatrix();
99 VERIFY_IS_APPROX(q1*v1,q2*v1);
100
101 matrot1 = AngleAxisx(Scalar(0.1), Vector3::UnitX())
102 * AngleAxisx(Scalar(0.2), Vector3::UnitY())
103 * AngleAxisx(Scalar(0.3), Vector3::UnitZ());
104 VERIFY_IS_APPROX(matrot1 * v1,
105 AngleAxisx(Scalar(0.1), Vector3(1,0,0)).toRotationMatrix()
106 * (AngleAxisx(Scalar(0.2), Vector3(0,1,0)).toRotationMatrix()
107 * (AngleAxisx(Scalar(0.3), Vector3(0,0,1)).toRotationMatrix() * v1)));
108
109 // angle-axis conversion
110 AngleAxisx aa = q1;
111 VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1);
112 VERIFY_IS_NOT_APPROX(q1 * v1, Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1);
113
114 // from two vector creation
115 VERIFY_IS_APPROX(v2.normalized(),(q2.setFromTwoVectors(v1,v2)*v1).normalized());
116 VERIFY_IS_APPROX(v2.normalized(),(q2.setFromTwoVectors(v1,v2)*v1).normalized());
117
118 // inverse and conjugate
119 VERIFY_IS_APPROX(q1 * (q1.inverse() * v1), v1);
120 VERIFY_IS_APPROX(q1 * (q1.conjugate() * v1), v1);
121
122 // AngleAxis
123 VERIFY_IS_APPROX(AngleAxisx(a,v1.normalized()).toRotationMatrix(),
124 Quaternionx(AngleAxisx(a,v1.normalized())).toRotationMatrix());
125
126 AngleAxisx aa1;
127 m = q1.toRotationMatrix();
128 aa1 = m;
129 VERIFY_IS_APPROX(AngleAxisx(m).toRotationMatrix(),
130 Quaternionx(m).toRotationMatrix());
131
132 // Transform
133 // TODO complete the tests !
134 a = 0;
135 while (ei_abs(a)<Scalar(0.1))
136 a = ei_random<Scalar>(-Scalar(0.4)*Scalar(M_PI), Scalar(0.4)*Scalar(M_PI));
137 q1 = AngleAxisx(a, v0.normalized());
138 Transform3 t0, t1, t2;
139 // first test setIdentity() and Identity()
140 t0.setIdentity();
141 VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());
142 t0.matrix().setZero();
143 t0 = Transform3::Identity();
144 VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());
145
146 t0.linear() = q1.toRotationMatrix();
147 t1.setIdentity();
148 t1.linear() = q1.toRotationMatrix();
149
150 v0 << 50, 2, 1;//= ei_random_matrix<Vector3>().cwiseProduct(Vector3(10,2,0.5));
151 t0.scale(v0);
152 t1.prescale(v0);
153
154 VERIFY_IS_APPROX( (t0 * Vector3(1,0,0)).norm(), v0.x());
155 //VERIFY(!ei_isApprox((t1 * Vector3(1,0,0)).norm(), v0.x()));
156
157 t0.setIdentity();
158 t1.setIdentity();
159 v1 << 1, 2, 3;
160 t0.linear() = q1.toRotationMatrix();
161 t0.pretranslate(v0);
162 t0.scale(v1);
163 t1.linear() = q1.conjugate().toRotationMatrix();
164 t1.prescale(v1.cwise().inverse());
165 t1.translate(-v0);
166
167 VERIFY((t0.matrix() * t1.matrix()).isIdentity(test_precision<Scalar>()));
168
169 t1.fromPositionOrientationScale(v0, q1, v1);
170 VERIFY_IS_APPROX(t1.matrix(), t0.matrix());
171 VERIFY_IS_APPROX(t1*v1, t0*v1);
172
173 t0.setIdentity(); t0.scale(v0).rotate(q1.toRotationMatrix());
174 t1.setIdentity(); t1.scale(v0).rotate(q1);
175 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
176
177 t0.setIdentity(); t0.scale(v0).rotate(AngleAxisx(q1));
178 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
179
180 VERIFY_IS_APPROX(t0.scale(a).matrix(), t1.scale(Vector3::Constant(a)).matrix());
181 VERIFY_IS_APPROX(t0.prescale(a).matrix(), t1.prescale(Vector3::Constant(a)).matrix());
182
183 // More transform constructors, operator=, operator*=
184
185 Matrix3 mat3 = Matrix3::Random();
186 Matrix4 mat4;
187 mat4 << mat3 , Vector3::Zero() , Vector4::Zero().transpose();
188 Transform3 tmat3(mat3), tmat4(mat4);
189 tmat4.matrix()(3,3) = Scalar(1);
190 VERIFY_IS_APPROX(tmat3.matrix(), tmat4.matrix());
191
192 Scalar a3 = ei_random<Scalar>(-Scalar(M_PI), Scalar(M_PI));
193 Vector3 v3 = Vector3::Random().normalized();
194 AngleAxisx aa3(a3, v3);
195 Transform3 t3(aa3);
196 Transform3 t4;
197 t4 = aa3;
198 VERIFY_IS_APPROX(t3.matrix(), t4.matrix());
199 t4.rotate(AngleAxisx(-a3,v3));
200 VERIFY_IS_APPROX(t4.matrix(), Matrix4::Identity());
201 t4 *= aa3;
202 VERIFY_IS_APPROX(t3.matrix(), t4.matrix());
203
204 v3 = Vector3::Random();
205 Translation3 tv3(v3);
206 Transform3 t5(tv3);
207 t4 = tv3;
208 VERIFY_IS_APPROX(t5.matrix(), t4.matrix());
209 t4.translate(-v3);
210 VERIFY_IS_APPROX(t4.matrix(), Matrix4::Identity());
211 t4 *= tv3;
212 VERIFY_IS_APPROX(t5.matrix(), t4.matrix());
213
214 Scaling3 sv3(v3);
215 Transform3 t6(sv3);
216 t4 = sv3;
217 VERIFY_IS_APPROX(t6.matrix(), t4.matrix());
218 t4.scale(v3.cwise().inverse());
219 VERIFY_IS_APPROX(t4.matrix(), Matrix4::Identity());
220 t4 *= sv3;
221 VERIFY_IS_APPROX(t6.matrix(), t4.matrix());
222
223 // matrix * transform
224 VERIFY_IS_APPROX(Transform3(t3.matrix()*t4).matrix(), Transform3(t3*t4).matrix());
225
226 // chained Transform product
227 VERIFY_IS_APPROX(((t3*t4)*t5).matrix(), (t3*(t4*t5)).matrix());
228
229 // check that Transform product doesn't have aliasing problems
230 t5 = t4;
231 t5 = t5*t5;
232 VERIFY_IS_APPROX(t5, t4*t4);
233
234 // 2D transformation
235 Transform2 t20, t21;
236 Vector2 v20 = Vector2::Random();
237 Vector2 v21 = Vector2::Random();
238 for (int k=0; k<2; ++k)
239 if (ei_abs(v21[k])<Scalar(1e-3)) v21[k] = Scalar(1e-3);
240 t21.setIdentity();
241 t21.linear() = Rotation2D<Scalar>(a).toRotationMatrix();
242 VERIFY_IS_APPROX(t20.fromPositionOrientationScale(v20,a,v21).matrix(),
243 t21.pretranslate(v20).scale(v21).matrix());
244
245 t21.setIdentity();
246 t21.linear() = Rotation2D<Scalar>(-a).toRotationMatrix();
247 VERIFY( (t20.fromPositionOrientationScale(v20,a,v21)
248 * (t21.prescale(v21.cwise().inverse()).translate(-v20))).matrix().isIdentity(test_precision<Scalar>()) );
249
250 // Transform - new API
251 // 3D
252 t0.setIdentity();
253 t0.rotate(q1).scale(v0).translate(v0);
254 // mat * scaling and mat * translation
255 t1 = (Matrix3(q1) * Scaling3(v0)) * Translation3(v0);
256 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
257 // mat * transformation and scaling * translation
258 t1 = Matrix3(q1) * (Scaling3(v0) * Translation3(v0));
259 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
260
261 t0.setIdentity();
262 t0.prerotate(q1).prescale(v0).pretranslate(v0);
263 // translation * scaling and transformation * mat
264 t1 = (Translation3(v0) * Scaling3(v0)) * Matrix3(q1);
265 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
266 // scaling * mat and translation * mat
267 t1 = Translation3(v0) * (Scaling3(v0) * Matrix3(q1));
268 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
269
270 t0.setIdentity();
271 t0.scale(v0).translate(v0).rotate(q1);
272 // translation * mat and scaling * transformation
273 t1 = Scaling3(v0) * (Translation3(v0) * Matrix3(q1));
274 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
275 // transformation * scaling
276 t0.scale(v0);
277 t1 = t1 * Scaling3(v0);
278 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
279 // transformation * translation
280 t0.translate(v0);
281 t1 = t1 * Translation3(v0);
282 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
283 // translation * transformation
284 t0.pretranslate(v0);
285 t1 = Translation3(v0) * t1;
286 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
287
288 // transform * quaternion
289 t0.rotate(q1);
290 t1 = t1 * q1;
291 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
292
293 // translation * quaternion
294 t0.translate(v1).rotate(q1);
295 t1 = t1 * (Translation3(v1) * q1);
296 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
297
298 // scaling * quaternion
299 t0.scale(v1).rotate(q1);
300 t1 = t1 * (Scaling3(v1) * q1);
301 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
302
303 // quaternion * transform
304 t0.prerotate(q1);
305 t1 = q1 * t1;
306 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
307
308 // quaternion * translation
309 t0.rotate(q1).translate(v1);
310 t1 = t1 * (q1 * Translation3(v1));
311 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
312
313 // quaternion * scaling
314 t0.rotate(q1).scale(v1);
315 t1 = t1 * (q1 * Scaling3(v1));
316 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
317
318 // translation * vector
319 t0.setIdentity();
320 t0.translate(v0);
321 VERIFY_IS_APPROX(t0 * v1, Translation3(v0) * v1);
322
323 // scaling * vector
324 t0.setIdentity();
325 t0.scale(v0);
326 VERIFY_IS_APPROX(t0 * v1, Scaling3(v0) * v1);
327
328 // test transform inversion
329 t0.setIdentity();
330 t0.translate(v0);
331 t0.linear().setRandom();
332 VERIFY_IS_APPROX(t0.inverse(Affine), t0.matrix().inverse());
333 t0.setIdentity();
334 t0.translate(v0).rotate(q1);
335 VERIFY_IS_APPROX(t0.inverse(Isometry), t0.matrix().inverse());
336
337 // test extract rotation and scaling
338 t0.setIdentity();
339 t0.translate(v0).rotate(q1).scale(v1);
340 VERIFY_IS_APPROX(t0.rotation() * v1, Matrix3(q1) * v1);
341
342 Matrix3 mat_rotation, mat_scaling;
343 t0.setIdentity();
344 t0.translate(v0).rotate(q1).scale(v1);
345 t0.computeRotationScaling(&mat_rotation, &mat_scaling);
346 VERIFY_IS_APPROX(t0.linear(), mat_rotation * mat_scaling);
347 VERIFY_IS_APPROX(mat_rotation*mat_rotation.adjoint(), Matrix3::Identity());
348 VERIFY_IS_APPROX(mat_rotation.determinant(), Scalar(1));
349 t0.computeScalingRotation(&mat_scaling, &mat_rotation);
350 VERIFY_IS_APPROX(t0.linear(), mat_scaling * mat_rotation);
351 VERIFY_IS_APPROX(mat_rotation*mat_rotation.adjoint(), Matrix3::Identity());
352 VERIFY_IS_APPROX(mat_rotation.determinant(), Scalar(1));
353
354 // test casting
355 Transform<float,3> t1f = t1.template cast<float>();
356 VERIFY_IS_APPROX(t1f.template cast<Scalar>(),t1);
357 Transform<double,3> t1d = t1.template cast<double>();
358 VERIFY_IS_APPROX(t1d.template cast<Scalar>(),t1);
359
360 Translation3 tr1(v0);
361 Translation<float,3> tr1f = tr1.template cast<float>();
362 VERIFY_IS_APPROX(tr1f.template cast<Scalar>(),tr1);
363 Translation<double,3> tr1d = tr1.template cast<double>();
364 VERIFY_IS_APPROX(tr1d.template cast<Scalar>(),tr1);
365
366 Scaling3 sc1(v0);
367 Scaling<float,3> sc1f = sc1.template cast<float>();
368 VERIFY_IS_APPROX(sc1f.template cast<Scalar>(),sc1);
369 Scaling<double,3> sc1d = sc1.template cast<double>();
370 VERIFY_IS_APPROX(sc1d.template cast<Scalar>(),sc1);
371
372 Quaternion<float> q1f = q1.template cast<float>();
373 VERIFY_IS_APPROX(q1f.template cast<Scalar>(),q1);
374 Quaternion<double> q1d = q1.template cast<double>();
375 VERIFY_IS_APPROX(q1d.template cast<Scalar>(),q1);
376
377 AngleAxis<float> aa1f = aa1.template cast<float>();
378 VERIFY_IS_APPROX(aa1f.template cast<Scalar>(),aa1);
379 AngleAxis<double> aa1d = aa1.template cast<double>();
380 VERIFY_IS_APPROX(aa1d.template cast<Scalar>(),aa1);
381
382 Rotation2D<Scalar> r2d1(ei_random<Scalar>());
383 Rotation2D<float> r2d1f = r2d1.template cast<float>();
384 VERIFY_IS_APPROX(r2d1f.template cast<Scalar>(),r2d1);
385 Rotation2D<double> r2d1d = r2d1.template cast<double>();
386 VERIFY_IS_APPROX(r2d1d.template cast<Scalar>(),r2d1);
387
388 m = q1;
389 // m.col(1) = Vector3(0,ei_random<Scalar>(),ei_random<Scalar>()).normalized();
390 // m.col(0) = Vector3(-1,0,0).normalized();
391 // m.col(2) = m.col(0).cross(m.col(1));
392 #define VERIFY_EULER(I,J,K, X,Y,Z) { \
393 Vector3 ea = m.eulerAngles(I,J,K); \
394 Matrix3 m1 = Matrix3(AngleAxisx(ea[0], Vector3::Unit##X()) * AngleAxisx(ea[1], Vector3::Unit##Y()) * AngleAxisx(ea[2], Vector3::Unit##Z())); \
395 VERIFY_IS_APPROX(m, Matrix3(AngleAxisx(ea[0], Vector3::Unit##X()) * AngleAxisx(ea[1], Vector3::Unit##Y()) * AngleAxisx(ea[2], Vector3::Unit##Z()))); \
396 }
397 VERIFY_EULER(0,1,2, X,Y,Z);
398 VERIFY_EULER(0,1,0, X,Y,X);
399 VERIFY_EULER(0,2,1, X,Z,Y);
400 VERIFY_EULER(0,2,0, X,Z,X);
401
402 VERIFY_EULER(1,2,0, Y,Z,X);
403 VERIFY_EULER(1,2,1, Y,Z,Y);
404 VERIFY_EULER(1,0,2, Y,X,Z);
405 VERIFY_EULER(1,0,1, Y,X,Y);
406
407 VERIFY_EULER(2,0,1, Z,X,Y);
408 VERIFY_EULER(2,0,2, Z,X,Z);
409 VERIFY_EULER(2,1,0, Z,Y,X);
410 VERIFY_EULER(2,1,2, Z,Y,Z);
411
412 // colwise/rowwise cross product
413 mat3.setRandom();
414 Vector3 vec3 = Vector3::Random();
415 Matrix3 mcross;
416 int i = ei_random<int>(0,2);
417 mcross = mat3.colwise().cross(vec3);
418 VERIFY_IS_APPROX(mcross.col(i), mat3.col(i).cross(vec3));
419 mcross = mat3.rowwise().cross(vec3);
420 VERIFY_IS_APPROX(mcross.row(i), mat3.row(i).cross(vec3));
421
422
423 }
424
test_eigen2_geometry()425 void test_eigen2_geometry()
426 {
427 for(int i = 0; i < g_repeat; i++) {
428 CALL_SUBTEST_1( geometry<float>() );
429 CALL_SUBTEST_2( geometry<double>() );
430 }
431 }
432