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#define EIGEN2_SUPPORT_STAGE15_RESOLVE_API_CONFLICTS_WARN
11
12#include "main.h"
13#include <Eigen/Geometry>
14#include <Eigen/LU>
15#include <Eigen/SVD>
16
17template<typename Scalar> void geometry(void)
18{
19  /* this test covers the following files:
20     Cross.h Quaternion.h, Transform.cpp
21  */
22
23  typedef Matrix<Scalar,2,2> Matrix2;
24  typedef Matrix<Scalar,3,3> Matrix3;
25  typedef Matrix<Scalar,4,4> Matrix4;
26  typedef Matrix<Scalar,2,1> Vector2;
27  typedef Matrix<Scalar,3,1> Vector3;
28  typedef Matrix<Scalar,4,1> Vector4;
29  typedef eigen2_Quaternion<Scalar> Quaternionx;
30  typedef eigen2_AngleAxis<Scalar> AngleAxisx;
31  typedef eigen2_Transform<Scalar,2> Transform2;
32  typedef eigen2_Transform<Scalar,3> Transform3;
33  typedef eigen2_Scaling<Scalar,2> Scaling2;
34  typedef eigen2_Scaling<Scalar,3> Scaling3;
35  typedef eigen2_Translation<Scalar,2> Translation2;
36  typedef eigen2_Translation<Scalar,3> Translation3;
37
38  Scalar largeEps = test_precision<Scalar>();
39  if (ei_is_same_type<Scalar,float>::ret)
40    largeEps = 1e-2f;
41
42  Vector3 v0 = Vector3::Random(),
43    v1 = Vector3::Random(),
44    v2 = Vector3::Random();
45  Vector2 u0 = Vector2::Random();
46  Matrix3 matrot1;
47
48  Scalar a = ei_random<Scalar>(-Scalar(M_PI), Scalar(M_PI));
49
50  // cross product
51  VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(v2).eigen2_dot(v1), Scalar(1));
52  Matrix3 m;
53  m << v0.normalized(),
54      (v0.cross(v1)).normalized(),
55      (v0.cross(v1).cross(v0)).normalized();
56  VERIFY(m.isUnitary());
57
58  // Quaternion: Identity(), setIdentity();
59  Quaternionx q1, q2;
60  q2.setIdentity();
61  VERIFY_IS_APPROX(Quaternionx(Quaternionx::Identity()).coeffs(), q2.coeffs());
62  q1.coeffs().setRandom();
63  VERIFY_IS_APPROX(q1.coeffs(), (q1*q2).coeffs());
64
65  // unitOrthogonal
66  VERIFY_IS_MUCH_SMALLER_THAN(u0.unitOrthogonal().eigen2_dot(u0), Scalar(1));
67  VERIFY_IS_MUCH_SMALLER_THAN(v0.unitOrthogonal().eigen2_dot(v0), Scalar(1));
68  VERIFY_IS_APPROX(u0.unitOrthogonal().norm(), Scalar(1));
69  VERIFY_IS_APPROX(v0.unitOrthogonal().norm(), Scalar(1));
70
71
72  VERIFY_IS_APPROX(v0, AngleAxisx(a, v0.normalized()) * v0);
73  VERIFY_IS_APPROX(-v0, AngleAxisx(Scalar(M_PI), v0.unitOrthogonal()) * v0);
74  VERIFY_IS_APPROX(ei_cos(a)*v0.squaredNorm(), v0.eigen2_dot(AngleAxisx(a, v0.unitOrthogonal()) * v0));
75  m = AngleAxisx(a, v0.normalized()).toRotationMatrix().adjoint();
76  VERIFY_IS_APPROX(Matrix3::Identity(), m * AngleAxisx(a, v0.normalized()));
77  VERIFY_IS_APPROX(Matrix3::Identity(), AngleAxisx(a, v0.normalized()) * m);
78
79  q1 = AngleAxisx(a, v0.normalized());
80  q2 = AngleAxisx(a, v1.normalized());
81
82  // angular distance
83  Scalar refangle = ei_abs(AngleAxisx(q1.inverse()*q2).angle());
84  if (refangle>Scalar(M_PI))
85    refangle = Scalar(2)*Scalar(M_PI) - refangle;
86
87  if((q1.coeffs()-q2.coeffs()).norm() > 10*largeEps)
88  {
89    VERIFY(ei_isApprox(q1.angularDistance(q2), refangle, largeEps));
90  }
91
92  // rotation matrix conversion
93  VERIFY_IS_APPROX(q1 * v2, q1.toRotationMatrix() * v2);
94  VERIFY_IS_APPROX(q1 * q2 * v2,
95    q1.toRotationMatrix() * q2.toRotationMatrix() * v2);
96
97  VERIFY( (q2*q1).isApprox(q1*q2, largeEps) || !(q2 * q1 * v2).isApprox(
98    q1.toRotationMatrix() * q2.toRotationMatrix() * v2));
99
100  q2 = q1.toRotationMatrix();
101  VERIFY_IS_APPROX(q1*v1,q2*v1);
102
103  matrot1 = AngleAxisx(Scalar(0.1), Vector3::UnitX())
104          * AngleAxisx(Scalar(0.2), Vector3::UnitY())
105          * AngleAxisx(Scalar(0.3), Vector3::UnitZ());
106  VERIFY_IS_APPROX(matrot1 * v1,
107       AngleAxisx(Scalar(0.1), Vector3(1,0,0)).toRotationMatrix()
108    * (AngleAxisx(Scalar(0.2), Vector3(0,1,0)).toRotationMatrix()
109    * (AngleAxisx(Scalar(0.3), Vector3(0,0,1)).toRotationMatrix() * v1)));
110
111  // angle-axis conversion
112  AngleAxisx aa = q1;
113  VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1);
114  VERIFY_IS_NOT_APPROX(q1 * v1, Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1);
115
116  // from two vector creation
117  VERIFY_IS_APPROX(v2.normalized(),(q2.setFromTwoVectors(v1,v2)*v1).normalized());
118  VERIFY_IS_APPROX(v2.normalized(),(q2.setFromTwoVectors(v1,v2)*v1).normalized());
119
120  // inverse and conjugate
121  VERIFY_IS_APPROX(q1 * (q1.inverse() * v1), v1);
122  VERIFY_IS_APPROX(q1 * (q1.conjugate() * v1), v1);
123
124  // AngleAxis
125  VERIFY_IS_APPROX(AngleAxisx(a,v1.normalized()).toRotationMatrix(),
126    Quaternionx(AngleAxisx(a,v1.normalized())).toRotationMatrix());
127
128  AngleAxisx aa1;
129  m = q1.toRotationMatrix();
130  aa1 = m;
131  VERIFY_IS_APPROX(AngleAxisx(m).toRotationMatrix(),
132    Quaternionx(m).toRotationMatrix());
133
134  // Transform
135  // TODO complete the tests !
136  a = 0;
137  while (ei_abs(a)<Scalar(0.1))
138    a = ei_random<Scalar>(-Scalar(0.4)*Scalar(M_PI), Scalar(0.4)*Scalar(M_PI));
139  q1 = AngleAxisx(a, v0.normalized());
140  Transform3 t0, t1, t2;
141  // first test setIdentity() and Identity()
142  t0.setIdentity();
143  VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());
144  t0.matrix().setZero();
145  t0 = Transform3::Identity();
146  VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());
147
148  t0.linear() = q1.toRotationMatrix();
149  t1.setIdentity();
150  t1.linear() = q1.toRotationMatrix();
151
152  v0 << 50, 2, 1;//= ei_random_matrix<Vector3>().cwiseProduct(Vector3(10,2,0.5));
153  t0.scale(v0);
154  t1.prescale(v0);
155
156  VERIFY_IS_APPROX( (t0 * Vector3(1,0,0)).norm(), v0.x());
157  //VERIFY(!ei_isApprox((t1 * Vector3(1,0,0)).norm(), v0.x()));
158
159  t0.setIdentity();
160  t1.setIdentity();
161  v1 << 1, 2, 3;
162  t0.linear() = q1.toRotationMatrix();
163  t0.pretranslate(v0);
164  t0.scale(v1);
165  t1.linear() = q1.conjugate().toRotationMatrix();
166  t1.prescale(v1.cwise().inverse());
167  t1.translate(-v0);
168
169  VERIFY((t0.matrix() * t1.matrix()).isIdentity(test_precision<Scalar>()));
170
171  t1.fromPositionOrientationScale(v0, q1, v1);
172  VERIFY_IS_APPROX(t1.matrix(), t0.matrix());
173  VERIFY_IS_APPROX(t1*v1, t0*v1);
174
175  t0.setIdentity(); t0.scale(v0).rotate(q1.toRotationMatrix());
176  t1.setIdentity(); t1.scale(v0).rotate(q1);
177  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
178
179  t0.setIdentity(); t0.scale(v0).rotate(AngleAxisx(q1));
180  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
181
182  VERIFY_IS_APPROX(t0.scale(a).matrix(), t1.scale(Vector3::Constant(a)).matrix());
183  VERIFY_IS_APPROX(t0.prescale(a).matrix(), t1.prescale(Vector3::Constant(a)).matrix());
184
185  // More transform constructors, operator=, operator*=
186
187  Matrix3 mat3 = Matrix3::Random();
188  Matrix4 mat4;
189  mat4 << mat3 , Vector3::Zero() , Vector4::Zero().transpose();
190  Transform3 tmat3(mat3), tmat4(mat4);
191  tmat4.matrix()(3,3) = Scalar(1);
192  VERIFY_IS_APPROX(tmat3.matrix(), tmat4.matrix());
193
194  Scalar a3 = ei_random<Scalar>(-Scalar(M_PI), Scalar(M_PI));
195  Vector3 v3 = Vector3::Random().normalized();
196  AngleAxisx aa3(a3, v3);
197  Transform3 t3(aa3);
198  Transform3 t4;
199  t4 = aa3;
200  VERIFY_IS_APPROX(t3.matrix(), t4.matrix());
201  t4.rotate(AngleAxisx(-a3,v3));
202  VERIFY_IS_APPROX(t4.matrix(), Matrix4::Identity());
203  t4 *= aa3;
204  VERIFY_IS_APPROX(t3.matrix(), t4.matrix());
205
206  v3 = Vector3::Random();
207  Translation3 tv3(v3);
208  Transform3 t5(tv3);
209  t4 = tv3;
210  VERIFY_IS_APPROX(t5.matrix(), t4.matrix());
211  t4.translate(-v3);
212  VERIFY_IS_APPROX(t4.matrix(), Matrix4::Identity());
213  t4 *= tv3;
214  VERIFY_IS_APPROX(t5.matrix(), t4.matrix());
215
216  Scaling3 sv3(v3);
217  Transform3 t6(sv3);
218  t4 = sv3;
219  VERIFY_IS_APPROX(t6.matrix(), t4.matrix());
220  t4.scale(v3.cwise().inverse());
221  VERIFY_IS_APPROX(t4.matrix(), Matrix4::Identity());
222  t4 *= sv3;
223  VERIFY_IS_APPROX(t6.matrix(), t4.matrix());
224
225  // matrix * transform
226  VERIFY_IS_APPROX(Transform3(t3.matrix()*t4).matrix(), Transform3(t3*t4).matrix());
227
228  // chained Transform product
229  VERIFY_IS_APPROX(((t3*t4)*t5).matrix(), (t3*(t4*t5)).matrix());
230
231  // check that Transform product doesn't have aliasing problems
232  t5 = t4;
233  t5 = t5*t5;
234  VERIFY_IS_APPROX(t5, t4*t4);
235
236  // 2D transformation
237  Transform2 t20, t21;
238  Vector2 v20 = Vector2::Random();
239  Vector2 v21 = Vector2::Random();
240  for (int k=0; k<2; ++k)
241    if (ei_abs(v21[k])<Scalar(1e-3)) v21[k] = Scalar(1e-3);
242  t21.setIdentity();
243  t21.linear() = Rotation2D<Scalar>(a).toRotationMatrix();
244  VERIFY_IS_APPROX(t20.fromPositionOrientationScale(v20,a,v21).matrix(),
245    t21.pretranslate(v20).scale(v21).matrix());
246
247  t21.setIdentity();
248  t21.linear() = Rotation2D<Scalar>(-a).toRotationMatrix();
249  VERIFY( (t20.fromPositionOrientationScale(v20,a,v21)
250        * (t21.prescale(v21.cwise().inverse()).translate(-v20))).matrix().isIdentity(test_precision<Scalar>()) );
251
252  // Transform - new API
253  // 3D
254  t0.setIdentity();
255  t0.rotate(q1).scale(v0).translate(v0);
256  // mat * scaling and mat * translation
257  t1 = (Matrix3(q1) * Scaling3(v0)) * Translation3(v0);
258  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
259  // mat * transformation and scaling * translation
260  t1 = Matrix3(q1) * (Scaling3(v0) * Translation3(v0));
261  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
262
263  t0.setIdentity();
264  t0.prerotate(q1).prescale(v0).pretranslate(v0);
265  // translation * scaling and transformation * mat
266  t1 = (Translation3(v0) * Scaling3(v0)) * Matrix3(q1);
267  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
268  // scaling * mat and translation * mat
269  t1 = Translation3(v0) * (Scaling3(v0) * Matrix3(q1));
270  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
271
272  t0.setIdentity();
273  t0.scale(v0).translate(v0).rotate(q1);
274  // translation * mat and scaling * transformation
275  t1 = Scaling3(v0) * (Translation3(v0) * Matrix3(q1));
276  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
277  // transformation * scaling
278  t0.scale(v0);
279  t1 = t1 * Scaling3(v0);
280  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
281  // transformation * translation
282  t0.translate(v0);
283  t1 = t1 * Translation3(v0);
284  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
285  // translation * transformation
286  t0.pretranslate(v0);
287  t1 = Translation3(v0) * t1;
288  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
289
290  // transform * quaternion
291  t0.rotate(q1);
292  t1 = t1 * q1;
293  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
294
295  // translation * quaternion
296  t0.translate(v1).rotate(q1);
297  t1 = t1 * (Translation3(v1) * q1);
298  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
299
300  // scaling * quaternion
301  t0.scale(v1).rotate(q1);
302  t1 = t1 * (Scaling3(v1) * q1);
303  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
304
305  // quaternion * transform
306  t0.prerotate(q1);
307  t1 = q1 * t1;
308  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
309
310  // quaternion * translation
311  t0.rotate(q1).translate(v1);
312  t1 = t1 * (q1 * Translation3(v1));
313  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
314
315  // quaternion * scaling
316  t0.rotate(q1).scale(v1);
317  t1 = t1 * (q1 * Scaling3(v1));
318  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
319
320  // translation * vector
321  t0.setIdentity();
322  t0.translate(v0);
323  VERIFY_IS_APPROX(t0 * v1, Translation3(v0) * v1);
324
325  // scaling * vector
326  t0.setIdentity();
327  t0.scale(v0);
328  VERIFY_IS_APPROX(t0 * v1, Scaling3(v0) * v1);
329
330  // test transform inversion
331  t0.setIdentity();
332  t0.translate(v0);
333  t0.linear().setRandom();
334  VERIFY_IS_APPROX(t0.inverse(Affine), t0.matrix().inverse());
335  t0.setIdentity();
336  t0.translate(v0).rotate(q1);
337  VERIFY_IS_APPROX(t0.inverse(Isometry), t0.matrix().inverse());
338
339  // test extract rotation and scaling
340  t0.setIdentity();
341  t0.translate(v0).rotate(q1).scale(v1);
342  VERIFY_IS_APPROX(t0.rotation() * v1, Matrix3(q1) * v1);
343
344  Matrix3 mat_rotation, mat_scaling;
345  t0.setIdentity();
346  t0.translate(v0).rotate(q1).scale(v1);
347  t0.computeRotationScaling(&mat_rotation, &mat_scaling);
348  VERIFY_IS_APPROX(t0.linear(), mat_rotation * mat_scaling);
349  VERIFY_IS_APPROX(mat_rotation*mat_rotation.adjoint(), Matrix3::Identity());
350  VERIFY_IS_APPROX(mat_rotation.determinant(), Scalar(1));
351  t0.computeScalingRotation(&mat_scaling, &mat_rotation);
352  VERIFY_IS_APPROX(t0.linear(), mat_scaling * mat_rotation);
353  VERIFY_IS_APPROX(mat_rotation*mat_rotation.adjoint(), Matrix3::Identity());
354  VERIFY_IS_APPROX(mat_rotation.determinant(), Scalar(1));
355
356  // test casting
357  eigen2_Transform<float,3> t1f = t1.template cast<float>();
358  VERIFY_IS_APPROX(t1f.template cast<Scalar>(),t1);
359  eigen2_Transform<double,3> t1d = t1.template cast<double>();
360  VERIFY_IS_APPROX(t1d.template cast<Scalar>(),t1);
361
362  Translation3 tr1(v0);
363  eigen2_Translation<float,3> tr1f = tr1.template cast<float>();
364  VERIFY_IS_APPROX(tr1f.template cast<Scalar>(),tr1);
365  eigen2_Translation<double,3> tr1d = tr1.template cast<double>();
366  VERIFY_IS_APPROX(tr1d.template cast<Scalar>(),tr1);
367
368  Scaling3 sc1(v0);
369  eigen2_Scaling<float,3> sc1f = sc1.template cast<float>();
370  VERIFY_IS_APPROX(sc1f.template cast<Scalar>(),sc1);
371  eigen2_Scaling<double,3> sc1d = sc1.template cast<double>();
372  VERIFY_IS_APPROX(sc1d.template cast<Scalar>(),sc1);
373
374  eigen2_Quaternion<float> q1f = q1.template cast<float>();
375  VERIFY_IS_APPROX(q1f.template cast<Scalar>(),q1);
376  eigen2_Quaternion<double> q1d = q1.template cast<double>();
377  VERIFY_IS_APPROX(q1d.template cast<Scalar>(),q1);
378
379  eigen2_AngleAxis<float> aa1f = aa1.template cast<float>();
380  VERIFY_IS_APPROX(aa1f.template cast<Scalar>(),aa1);
381  eigen2_AngleAxis<double> aa1d = aa1.template cast<double>();
382  VERIFY_IS_APPROX(aa1d.template cast<Scalar>(),aa1);
383
384  eigen2_Rotation2D<Scalar> r2d1(ei_random<Scalar>());
385  eigen2_Rotation2D<float> r2d1f = r2d1.template cast<float>();
386  VERIFY_IS_APPROX(r2d1f.template cast<Scalar>(),r2d1);
387  eigen2_Rotation2D<double> r2d1d = r2d1.template cast<double>();
388  VERIFY_IS_APPROX(r2d1d.template cast<Scalar>(),r2d1);
389
390  m = q1;
391//   m.col(1) = Vector3(0,ei_random<Scalar>(),ei_random<Scalar>()).normalized();
392//   m.col(0) = Vector3(-1,0,0).normalized();
393//   m.col(2) = m.col(0).cross(m.col(1));
394  #define VERIFY_EULER(I,J,K, X,Y,Z) { \
395    Vector3 ea = m.eulerAngles(I,J,K); \
396    Matrix3 m1 = Matrix3(AngleAxisx(ea[0], Vector3::Unit##X()) * AngleAxisx(ea[1], Vector3::Unit##Y()) * AngleAxisx(ea[2], Vector3::Unit##Z())); \
397    VERIFY_IS_APPROX(m, m1); \
398    VERIFY_IS_APPROX(m,  Matrix3(AngleAxisx(ea[0], Vector3::Unit##X()) * AngleAxisx(ea[1], Vector3::Unit##Y()) * AngleAxisx(ea[2], Vector3::Unit##Z()))); \
399  }
400  VERIFY_EULER(0,1,2, X,Y,Z);
401  VERIFY_EULER(0,1,0, X,Y,X);
402  VERIFY_EULER(0,2,1, X,Z,Y);
403  VERIFY_EULER(0,2,0, X,Z,X);
404
405  VERIFY_EULER(1,2,0, Y,Z,X);
406  VERIFY_EULER(1,2,1, Y,Z,Y);
407  VERIFY_EULER(1,0,2, Y,X,Z);
408  VERIFY_EULER(1,0,1, Y,X,Y);
409
410  VERIFY_EULER(2,0,1, Z,X,Y);
411  VERIFY_EULER(2,0,2, Z,X,Z);
412  VERIFY_EULER(2,1,0, Z,Y,X);
413  VERIFY_EULER(2,1,2, Z,Y,Z);
414
415  // colwise/rowwise cross product
416  mat3.setRandom();
417  Vector3 vec3 = Vector3::Random();
418  Matrix3 mcross;
419  int i = ei_random<int>(0,2);
420  mcross = mat3.colwise().cross(vec3);
421  VERIFY_IS_APPROX(mcross.col(i), mat3.col(i).cross(vec3));
422  mcross = mat3.rowwise().cross(vec3);
423  VERIFY_IS_APPROX(mcross.row(i), mat3.row(i).cross(vec3));
424
425
426}
427
428void test_eigen2_geometry_with_eigen2_prefix()
429{
430  std::cout << "eigen2 support: " << EIGEN2_SUPPORT_STAGE << std::endl;
431  for(int i = 0; i < g_repeat; i++) {
432    CALL_SUBTEST_1( geometry<float>() );
433    CALL_SUBTEST_2( geometry<double>() );
434  }
435}
436