geo_transformations.cpp revision c981c48f5bc9aefeffc0bcb0cc3934c2fae179dd
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//
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
15template<typename Scalar, int Mode, int Options> void non_projective_only()
16{
17    /* this test covers the following files:
18     Cross.h Quaternion.h, Transform.cpp
19  */
20  typedef Matrix<Scalar,2,2> Matrix2;
21  typedef Matrix<Scalar,3,3> Matrix3;
22  typedef Matrix<Scalar,4,4> Matrix4;
23  typedef Matrix<Scalar,2,1> Vector2;
24  typedef Matrix<Scalar,3,1> Vector3;
25  typedef Matrix<Scalar,4,1> Vector4;
26  typedef Quaternion<Scalar> Quaternionx;
27  typedef AngleAxis<Scalar> AngleAxisx;
28  typedef Transform<Scalar,2,Mode,Options> Transform2;
29  typedef Transform<Scalar,3,Mode,Options> Transform3;
30  typedef Transform<Scalar,2,Isometry,Options> Isometry2;
31  typedef Transform<Scalar,3,Isometry,Options> Isometry3;
32  typedef typename Transform3::MatrixType MatrixType;
33  typedef DiagonalMatrix<Scalar,2> AlignedScaling2;
34  typedef DiagonalMatrix<Scalar,3> AlignedScaling3;
35  typedef Translation<Scalar,2> Translation2;
36  typedef Translation<Scalar,3> Translation3;
37
38  Vector3 v0 = Vector3::Random(),
39          v1 = Vector3::Random();
40
41  Transform3 t0, t1, t2;
42
43  Scalar a = internal::random<Scalar>(-Scalar(M_PI), Scalar(M_PI));
44
45  Quaternionx q1, q2;
46
47  q1 = AngleAxisx(a, v0.normalized());
48
49  t0 = Transform3::Identity();
50  VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());
51
52  t0.linear() = q1.toRotationMatrix();
53
54  v0 << 50, 2, 1;
55  t0.scale(v0);
56
57  VERIFY_IS_APPROX( (t0 * Vector3(1,0,0)).template head<3>().norm(), v0.x());
58
59  t0.setIdentity();
60  t1.setIdentity();
61  v1 << 1, 2, 3;
62  t0.linear() = q1.toRotationMatrix();
63  t0.pretranslate(v0);
64  t0.scale(v1);
65  t1.linear() = q1.conjugate().toRotationMatrix();
66  t1.prescale(v1.cwiseInverse());
67  t1.translate(-v0);
68
69  VERIFY((t0 * t1).matrix().isIdentity(test_precision<Scalar>()));
70
71  t1.fromPositionOrientationScale(v0, q1, v1);
72  VERIFY_IS_APPROX(t1.matrix(), t0.matrix());
73  VERIFY_IS_APPROX(t1*v1, t0*v1);
74
75  // translation * vector
76  t0.setIdentity();
77  t0.translate(v0);
78  VERIFY_IS_APPROX((t0 * v1).template head<3>(), Translation3(v0) * v1);
79
80  // AlignedScaling * vector
81  t0.setIdentity();
82  t0.scale(v0);
83  VERIFY_IS_APPROX((t0 * v1).template head<3>(), AlignedScaling3(v0) * v1);
84}
85
86template<typename Scalar, int Mode, int Options> void transformations()
87{
88  /* this test covers the following files:
89     Cross.h Quaternion.h, Transform.cpp
90  */
91  typedef Matrix<Scalar,2,2> Matrix2;
92  typedef Matrix<Scalar,3,3> Matrix3;
93  typedef Matrix<Scalar,4,4> Matrix4;
94  typedef Matrix<Scalar,2,1> Vector2;
95  typedef Matrix<Scalar,3,1> Vector3;
96  typedef Matrix<Scalar,4,1> Vector4;
97  typedef Quaternion<Scalar> Quaternionx;
98  typedef AngleAxis<Scalar> AngleAxisx;
99  typedef Transform<Scalar,2,Mode,Options> Transform2;
100  typedef Transform<Scalar,3,Mode,Options> Transform3;
101  typedef Transform<Scalar,2,Isometry,Options> Isometry2;
102  typedef Transform<Scalar,3,Isometry,Options> Isometry3;
103  typedef typename Transform3::MatrixType MatrixType;
104  typedef DiagonalMatrix<Scalar,2> AlignedScaling2;
105  typedef DiagonalMatrix<Scalar,3> AlignedScaling3;
106  typedef Translation<Scalar,2> Translation2;
107  typedef Translation<Scalar,3> Translation3;
108
109  Vector3 v0 = Vector3::Random(),
110          v1 = Vector3::Random();
111  Matrix3 matrot1, m;
112
113  Scalar a = internal::random<Scalar>(-Scalar(M_PI), Scalar(M_PI));
114  Scalar s0 = internal::random<Scalar>();
115
116  VERIFY_IS_APPROX(v0, AngleAxisx(a, v0.normalized()) * v0);
117  VERIFY_IS_APPROX(-v0, AngleAxisx(Scalar(M_PI), v0.unitOrthogonal()) * v0);
118  VERIFY_IS_APPROX(internal::cos(a)*v0.squaredNorm(), v0.dot(AngleAxisx(a, v0.unitOrthogonal()) * v0));
119  m = AngleAxisx(a, v0.normalized()).toRotationMatrix().adjoint();
120  VERIFY_IS_APPROX(Matrix3::Identity(), m * AngleAxisx(a, v0.normalized()));
121  VERIFY_IS_APPROX(Matrix3::Identity(), AngleAxisx(a, v0.normalized()) * m);
122
123  Quaternionx q1, q2;
124  q1 = AngleAxisx(a, v0.normalized());
125  q2 = AngleAxisx(a, v1.normalized());
126
127  // rotation matrix conversion
128  matrot1 = AngleAxisx(Scalar(0.1), Vector3::UnitX())
129          * AngleAxisx(Scalar(0.2), Vector3::UnitY())
130          * AngleAxisx(Scalar(0.3), Vector3::UnitZ());
131  VERIFY_IS_APPROX(matrot1 * v1,
132       AngleAxisx(Scalar(0.1), Vector3(1,0,0)).toRotationMatrix()
133    * (AngleAxisx(Scalar(0.2), Vector3(0,1,0)).toRotationMatrix()
134    * (AngleAxisx(Scalar(0.3), Vector3(0,0,1)).toRotationMatrix() * v1)));
135
136  // angle-axis conversion
137  AngleAxisx aa = AngleAxisx(q1);
138  VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1);
139  VERIFY_IS_NOT_APPROX(q1 * v1, Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1);
140
141  aa.fromRotationMatrix(aa.toRotationMatrix());
142  VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1);
143  VERIFY_IS_NOT_APPROX(q1 * v1, Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1);
144
145  // AngleAxis
146  VERIFY_IS_APPROX(AngleAxisx(a,v1.normalized()).toRotationMatrix(),
147    Quaternionx(AngleAxisx(a,v1.normalized())).toRotationMatrix());
148
149  AngleAxisx aa1;
150  m = q1.toRotationMatrix();
151  aa1 = m;
152  VERIFY_IS_APPROX(AngleAxisx(m).toRotationMatrix(),
153    Quaternionx(m).toRotationMatrix());
154
155  // Transform
156  // TODO complete the tests !
157  a = 0;
158  while (internal::abs(a)<Scalar(0.1))
159    a = internal::random<Scalar>(-Scalar(0.4)*Scalar(M_PI), Scalar(0.4)*Scalar(M_PI));
160  q1 = AngleAxisx(a, v0.normalized());
161  Transform3 t0, t1, t2;
162
163  // first test setIdentity() and Identity()
164  t0.setIdentity();
165  VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());
166  t0.matrix().setZero();
167  t0 = Transform3::Identity();
168  VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());
169
170  t0.setIdentity();
171  t1.setIdentity();
172  v1 << 1, 2, 3;
173  t0.linear() = q1.toRotationMatrix();
174  t0.pretranslate(v0);
175  t0.scale(v1);
176  t1.linear() = q1.conjugate().toRotationMatrix();
177  t1.prescale(v1.cwiseInverse());
178  t1.translate(-v0);
179
180  VERIFY((t0 * t1).matrix().isIdentity(test_precision<Scalar>()));
181
182  t1.fromPositionOrientationScale(v0, q1, v1);
183  VERIFY_IS_APPROX(t1.matrix(), t0.matrix());
184
185  t0.setIdentity(); t0.scale(v0).rotate(q1.toRotationMatrix());
186  t1.setIdentity(); t1.scale(v0).rotate(q1);
187  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
188
189  t0.setIdentity(); t0.scale(v0).rotate(AngleAxisx(q1));
190  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
191
192  VERIFY_IS_APPROX(t0.scale(a).matrix(), t1.scale(Vector3::Constant(a)).matrix());
193  VERIFY_IS_APPROX(t0.prescale(a).matrix(), t1.prescale(Vector3::Constant(a)).matrix());
194
195  // More transform constructors, operator=, operator*=
196
197  Matrix3 mat3 = Matrix3::Random();
198  Matrix4 mat4;
199  mat4 << mat3 , Vector3::Zero() , Vector4::Zero().transpose();
200  Transform3 tmat3(mat3), tmat4(mat4);
201  if(Mode!=int(AffineCompact))
202    tmat4.matrix()(3,3) = Scalar(1);
203  VERIFY_IS_APPROX(tmat3.matrix(), tmat4.matrix());
204
205  Scalar a3 = internal::random<Scalar>(-Scalar(M_PI), Scalar(M_PI));
206  Vector3 v3 = Vector3::Random().normalized();
207  AngleAxisx aa3(a3, v3);
208  Transform3 t3(aa3);
209  Transform3 t4;
210  t4 = aa3;
211  VERIFY_IS_APPROX(t3.matrix(), t4.matrix());
212  t4.rotate(AngleAxisx(-a3,v3));
213  VERIFY_IS_APPROX(t4.matrix(), MatrixType::Identity());
214  t4 *= aa3;
215  VERIFY_IS_APPROX(t3.matrix(), t4.matrix());
216
217  v3 = Vector3::Random();
218  Translation3 tv3(v3);
219  Transform3 t5(tv3);
220  t4 = tv3;
221  VERIFY_IS_APPROX(t5.matrix(), t4.matrix());
222  t4.translate(-v3);
223  VERIFY_IS_APPROX(t4.matrix(), MatrixType::Identity());
224  t4 *= tv3;
225  VERIFY_IS_APPROX(t5.matrix(), t4.matrix());
226
227  AlignedScaling3 sv3(v3);
228  Transform3 t6(sv3);
229  t4 = sv3;
230  VERIFY_IS_APPROX(t6.matrix(), t4.matrix());
231  t4.scale(v3.cwiseInverse());
232  VERIFY_IS_APPROX(t4.matrix(), MatrixType::Identity());
233  t4 *= sv3;
234  VERIFY_IS_APPROX(t6.matrix(), t4.matrix());
235
236  // matrix * transform
237  VERIFY_IS_APPROX((t3.matrix()*t4).matrix(), (t3*t4).matrix());
238
239  // chained Transform product
240  VERIFY_IS_APPROX(((t3*t4)*t5).matrix(), (t3*(t4*t5)).matrix());
241
242  // check that Transform product doesn't have aliasing problems
243  t5 = t4;
244  t5 = t5*t5;
245  VERIFY_IS_APPROX(t5, t4*t4);
246
247  // 2D transformation
248  Transform2 t20, t21;
249  Vector2 v20 = Vector2::Random();
250  Vector2 v21 = Vector2::Random();
251  for (int k=0; k<2; ++k)
252    if (internal::abs(v21[k])<Scalar(1e-3)) v21[k] = Scalar(1e-3);
253  t21.setIdentity();
254  t21.linear() = Rotation2D<Scalar>(a).toRotationMatrix();
255  VERIFY_IS_APPROX(t20.fromPositionOrientationScale(v20,a,v21).matrix(),
256    t21.pretranslate(v20).scale(v21).matrix());
257
258  t21.setIdentity();
259  t21.linear() = Rotation2D<Scalar>(-a).toRotationMatrix();
260  VERIFY( (t20.fromPositionOrientationScale(v20,a,v21)
261        * (t21.prescale(v21.cwiseInverse()).translate(-v20))).matrix().isIdentity(test_precision<Scalar>()) );
262
263  // Transform - new API
264  // 3D
265  t0.setIdentity();
266  t0.rotate(q1).scale(v0).translate(v0);
267  // mat * aligned scaling and mat * translation
268  t1 = (Matrix3(q1) * AlignedScaling3(v0)) * Translation3(v0);
269  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
270  t1 = (Matrix3(q1) * Eigen::Scaling(v0)) * Translation3(v0);
271  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
272  t1 = (q1 * Eigen::Scaling(v0)) * Translation3(v0);
273  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
274  // mat * transformation and aligned scaling * translation
275  t1 = Matrix3(q1) * (AlignedScaling3(v0) * Translation3(v0));
276  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
277
278
279  t0.setIdentity();
280  t0.scale(s0).translate(v0);
281  t1 = Eigen::Scaling(s0) * Translation3(v0);
282  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
283  t0.prescale(s0);
284  t1 = Eigen::Scaling(s0) * t1;
285  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
286
287  t0 = t3;
288  t0.scale(s0);
289  t1 = t3 * Eigen::Scaling(s0,s0,s0);
290  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
291  t0.prescale(s0);
292  t1 = Eigen::Scaling(s0,s0,s0) * t1;
293  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
294
295
296  t0.setIdentity();
297  t0.prerotate(q1).prescale(v0).pretranslate(v0);
298  // translation * aligned scaling and transformation * mat
299  t1 = (Translation3(v0) * AlignedScaling3(v0)) * Transform3(q1);
300  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
301  // scaling * mat and translation * mat
302  t1 = Translation3(v0) * (AlignedScaling3(v0) * Transform3(q1));
303  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
304
305  t0.setIdentity();
306  t0.scale(v0).translate(v0).rotate(q1);
307  // translation * mat and aligned scaling * transformation
308  t1 = AlignedScaling3(v0) * (Translation3(v0) * Transform3(q1));
309  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
310  // transformation * aligned scaling
311  t0.scale(v0);
312  t1 *= AlignedScaling3(v0);
313  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
314  // transformation * translation
315  t0.translate(v0);
316  t1 = t1 * Translation3(v0);
317  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
318  // translation * transformation
319  t0.pretranslate(v0);
320  t1 = Translation3(v0) * t1;
321  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
322
323  // transform * quaternion
324  t0.rotate(q1);
325  t1 = t1 * q1;
326  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
327
328  // translation * quaternion
329  t0.translate(v1).rotate(q1);
330  t1 = t1 * (Translation3(v1) * q1);
331  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
332
333  // aligned scaling * quaternion
334  t0.scale(v1).rotate(q1);
335  t1 = t1 * (AlignedScaling3(v1) * q1);
336  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
337
338  // quaternion * transform
339  t0.prerotate(q1);
340  t1 = q1 * t1;
341  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
342
343  // quaternion * translation
344  t0.rotate(q1).translate(v1);
345  t1 = t1 * (q1 * Translation3(v1));
346  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
347
348  // quaternion * aligned scaling
349  t0.rotate(q1).scale(v1);
350  t1 = t1 * (q1 * AlignedScaling3(v1));
351  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
352
353  // test transform inversion
354  t0.setIdentity();
355  t0.translate(v0);
356  t0.linear().setRandom();
357  Matrix4 t044 = Matrix4::Zero();
358  t044(3,3) = 1;
359  t044.block(0,0,t0.matrix().rows(),4) = t0.matrix();
360  VERIFY_IS_APPROX(t0.inverse(Affine).matrix(), t044.inverse().block(0,0,t0.matrix().rows(),4));
361  t0.setIdentity();
362  t0.translate(v0).rotate(q1);
363  t044 = Matrix4::Zero();
364  t044(3,3) = 1;
365  t044.block(0,0,t0.matrix().rows(),4) = t0.matrix();
366  VERIFY_IS_APPROX(t0.inverse(Isometry).matrix(), t044.inverse().block(0,0,t0.matrix().rows(),4));
367
368  Matrix3 mat_rotation, mat_scaling;
369  t0.setIdentity();
370  t0.translate(v0).rotate(q1).scale(v1);
371  t0.computeRotationScaling(&mat_rotation, &mat_scaling);
372  VERIFY_IS_APPROX(t0.linear(), mat_rotation * mat_scaling);
373  VERIFY_IS_APPROX(mat_rotation*mat_rotation.adjoint(), Matrix3::Identity());
374  VERIFY_IS_APPROX(mat_rotation.determinant(), Scalar(1));
375  t0.computeScalingRotation(&mat_scaling, &mat_rotation);
376  VERIFY_IS_APPROX(t0.linear(), mat_scaling * mat_rotation);
377  VERIFY_IS_APPROX(mat_rotation*mat_rotation.adjoint(), Matrix3::Identity());
378  VERIFY_IS_APPROX(mat_rotation.determinant(), Scalar(1));
379
380  // test casting
381  Transform<float,3,Mode> t1f = t1.template cast<float>();
382  VERIFY_IS_APPROX(t1f.template cast<Scalar>(),t1);
383  Transform<double,3,Mode> t1d = t1.template cast<double>();
384  VERIFY_IS_APPROX(t1d.template cast<Scalar>(),t1);
385
386  Translation3 tr1(v0);
387  Translation<float,3> tr1f = tr1.template cast<float>();
388  VERIFY_IS_APPROX(tr1f.template cast<Scalar>(),tr1);
389  Translation<double,3> tr1d = tr1.template cast<double>();
390  VERIFY_IS_APPROX(tr1d.template cast<Scalar>(),tr1);
391
392  AngleAxis<float> aa1f = aa1.template cast<float>();
393  VERIFY_IS_APPROX(aa1f.template cast<Scalar>(),aa1);
394  AngleAxis<double> aa1d = aa1.template cast<double>();
395  VERIFY_IS_APPROX(aa1d.template cast<Scalar>(),aa1);
396
397  Rotation2D<Scalar> r2d1(internal::random<Scalar>());
398  Rotation2D<float> r2d1f = r2d1.template cast<float>();
399  VERIFY_IS_APPROX(r2d1f.template cast<Scalar>(),r2d1);
400  Rotation2D<double> r2d1d = r2d1.template cast<double>();
401  VERIFY_IS_APPROX(r2d1d.template cast<Scalar>(),r2d1);
402
403  t20 = Translation2(v20) * (Rotation2D<Scalar>(s0) * Scaling(s0));
404  t21 = Translation2(v20) * Rotation2D<Scalar>(s0) * Scaling(s0);
405  VERIFY_IS_APPROX(t20,t21);
406}
407
408template<typename Scalar> void transform_alignment()
409{
410  typedef Transform<Scalar,3,Projective,AutoAlign> Projective3a;
411  typedef Transform<Scalar,3,Projective,DontAlign> Projective3u;
412
413  EIGEN_ALIGN16 Scalar array1[16];
414  EIGEN_ALIGN16 Scalar array2[16];
415  EIGEN_ALIGN16 Scalar array3[16+1];
416  Scalar* array3u = array3+1;
417
418  Projective3a *p1 = ::new(reinterpret_cast<void*>(array1)) Projective3a;
419  Projective3u *p2 = ::new(reinterpret_cast<void*>(array2)) Projective3u;
420  Projective3u *p3 = ::new(reinterpret_cast<void*>(array3u)) Projective3u;
421
422  p1->matrix().setRandom();
423  *p2 = *p1;
424  *p3 = *p1;
425
426  VERIFY_IS_APPROX(p1->matrix(), p2->matrix());
427  VERIFY_IS_APPROX(p1->matrix(), p3->matrix());
428
429  VERIFY_IS_APPROX( (*p1) * (*p1), (*p2)*(*p3));
430
431  #if defined(EIGEN_VECTORIZE) && EIGEN_ALIGN_STATICALLY
432  if(internal::packet_traits<Scalar>::Vectorizable)
433    VERIFY_RAISES_ASSERT((::new(reinterpret_cast<void*>(array3u)) Projective3a));
434  #endif
435}
436
437template<typename Scalar, int Dim, int Options> void transform_products()
438{
439  typedef Matrix<Scalar,Dim+1,Dim+1> Mat;
440  typedef Transform<Scalar,Dim,Projective,Options> Proj;
441  typedef Transform<Scalar,Dim,Affine,Options> Aff;
442  typedef Transform<Scalar,Dim,AffineCompact,Options> AffC;
443
444  Proj p; p.matrix().setRandom();
445  Aff a; a.linear().setRandom(); a.translation().setRandom();
446  AffC ac = a;
447
448  Mat p_m(p.matrix()), a_m(a.matrix());
449
450  VERIFY_IS_APPROX((p*p).matrix(), p_m*p_m);
451  VERIFY_IS_APPROX((a*a).matrix(), a_m*a_m);
452  VERIFY_IS_APPROX((p*a).matrix(), p_m*a_m);
453  VERIFY_IS_APPROX((a*p).matrix(), a_m*p_m);
454  VERIFY_IS_APPROX((ac*a).matrix(), a_m*a_m);
455  VERIFY_IS_APPROX((a*ac).matrix(), a_m*a_m);
456  VERIFY_IS_APPROX((p*ac).matrix(), p_m*a_m);
457  VERIFY_IS_APPROX((ac*p).matrix(), a_m*p_m);
458}
459
460void test_geo_transformations()
461{
462  for(int i = 0; i < g_repeat; i++) {
463    CALL_SUBTEST_1(( transformations<double,Affine,AutoAlign>() ));
464    CALL_SUBTEST_1(( non_projective_only<double,Affine,AutoAlign>() ));
465
466    CALL_SUBTEST_2(( transformations<float,AffineCompact,AutoAlign>() ));
467    CALL_SUBTEST_2(( non_projective_only<float,AffineCompact,AutoAlign>() ));
468    CALL_SUBTEST_2(( transform_alignment<float>() ));
469
470    CALL_SUBTEST_3(( transformations<double,Projective,AutoAlign>() ));
471    CALL_SUBTEST_3(( transformations<double,Projective,DontAlign>() ));
472    CALL_SUBTEST_3(( transform_alignment<double>() ));
473
474    CALL_SUBTEST_4(( transformations<float,Affine,RowMajor|AutoAlign>() ));
475    CALL_SUBTEST_4(( non_projective_only<float,Affine,RowMajor>() ));
476
477    CALL_SUBTEST_5(( transformations<double,AffineCompact,RowMajor|AutoAlign>() ));
478    CALL_SUBTEST_5(( non_projective_only<double,AffineCompact,RowMajor>() ));
479
480    CALL_SUBTEST_6(( transformations<double,Projective,RowMajor|AutoAlign>() ));
481    CALL_SUBTEST_6(( transformations<double,Projective,RowMajor|DontAlign>() ));
482
483
484    CALL_SUBTEST_7(( transform_products<double,3,RowMajor|AutoAlign>() ));
485    CALL_SUBTEST_7(( transform_products<float,2,AutoAlign>() ));
486  }
487}
488