source: pacpussensors/trunk/Vislab/lib3dv/eigen/test/geo_transformations.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//
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,3,1> Vector3;
21 typedef Quaternion<Scalar> Quaternionx;
22 typedef AngleAxis<Scalar> AngleAxisx;
23 typedef Transform<Scalar,3,Mode,Options> Transform3;
24 typedef DiagonalMatrix<Scalar,3> AlignedScaling3;
25 typedef Translation<Scalar,3> Translation3;
26
27 Vector3 v0 = Vector3::Random(),
28 v1 = Vector3::Random();
29
30 Transform3 t0, t1, t2;
31
32 Scalar a = internal::random<Scalar>(-Scalar(M_PI), Scalar(M_PI));
33
34 Quaternionx q1, q2;
35
36 q1 = AngleAxisx(a, v0.normalized());
37
38 t0 = Transform3::Identity();
39 VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());
40
41 t0.linear() = q1.toRotationMatrix();
42
43 v0 << 50, 2, 1;
44 t0.scale(v0);
45
46 VERIFY_IS_APPROX( (t0 * Vector3(1,0,0)).template head<3>().norm(), v0.x());
47
48 t0.setIdentity();
49 t1.setIdentity();
50 v1 << 1, 2, 3;
51 t0.linear() = q1.toRotationMatrix();
52 t0.pretranslate(v0);
53 t0.scale(v1);
54 t1.linear() = q1.conjugate().toRotationMatrix();
55 t1.prescale(v1.cwiseInverse());
56 t1.translate(-v0);
57
58 VERIFY((t0 * t1).matrix().isIdentity(test_precision<Scalar>()));
59
60 t1.fromPositionOrientationScale(v0, q1, v1);
61 VERIFY_IS_APPROX(t1.matrix(), t0.matrix());
62 VERIFY_IS_APPROX(t1*v1, t0*v1);
63
64 // translation * vector
65 t0.setIdentity();
66 t0.translate(v0);
67 VERIFY_IS_APPROX((t0 * v1).template head<3>(), Translation3(v0) * v1);
68
69 // AlignedScaling * vector
70 t0.setIdentity();
71 t0.scale(v0);
72 VERIFY_IS_APPROX((t0 * v1).template head<3>(), AlignedScaling3(v0) * v1);
73}
74
75template<typename Scalar, int Mode, int Options> void transformations()
76{
77 /* this test covers the following files:
78 Cross.h Quaternion.h, Transform.cpp
79 */
80 using std::cos;
81 using std::abs;
82 typedef Matrix<Scalar,3,3> Matrix3;
83 typedef Matrix<Scalar,4,4> Matrix4;
84 typedef Matrix<Scalar,2,1> Vector2;
85 typedef Matrix<Scalar,3,1> Vector3;
86 typedef Matrix<Scalar,4,1> Vector4;
87 typedef Quaternion<Scalar> Quaternionx;
88 typedef AngleAxis<Scalar> AngleAxisx;
89 typedef Transform<Scalar,2,Mode,Options> Transform2;
90 typedef Transform<Scalar,3,Mode,Options> Transform3;
91 typedef typename Transform3::MatrixType MatrixType;
92 typedef DiagonalMatrix<Scalar,3> AlignedScaling3;
93 typedef Translation<Scalar,2> Translation2;
94 typedef Translation<Scalar,3> Translation3;
95
96 Vector3 v0 = Vector3::Random(),
97 v1 = Vector3::Random();
98 Matrix3 matrot1, m;
99
100 Scalar a = internal::random<Scalar>(-Scalar(M_PI), Scalar(M_PI));
101 Scalar s0 = internal::random<Scalar>(),
102 s1 = internal::random<Scalar>();
103
104 while(v0.norm() < test_precision<Scalar>()) v0 = Vector3::Random();
105 while(v1.norm() < test_precision<Scalar>()) v1 = Vector3::Random();
106
107
108 VERIFY_IS_APPROX(v0, AngleAxisx(a, v0.normalized()) * v0);
109 VERIFY_IS_APPROX(-v0, AngleAxisx(Scalar(M_PI), v0.unitOrthogonal()) * v0);
110 if(abs(cos(a)) > test_precision<Scalar>())
111 {
112 VERIFY_IS_APPROX(cos(a)*v0.squaredNorm(), v0.dot(AngleAxisx(a, v0.unitOrthogonal()) * v0));
113 }
114 m = AngleAxisx(a, v0.normalized()).toRotationMatrix().adjoint();
115 VERIFY_IS_APPROX(Matrix3::Identity(), m * AngleAxisx(a, v0.normalized()));
116 VERIFY_IS_APPROX(Matrix3::Identity(), AngleAxisx(a, v0.normalized()) * m);
117
118 Quaternionx q1, q2;
119 q1 = AngleAxisx(a, v0.normalized());
120 q2 = AngleAxisx(a, v1.normalized());
121
122 // rotation matrix conversion
123 matrot1 = AngleAxisx(Scalar(0.1), Vector3::UnitX())
124 * AngleAxisx(Scalar(0.2), Vector3::UnitY())
125 * AngleAxisx(Scalar(0.3), Vector3::UnitZ());
126 VERIFY_IS_APPROX(matrot1 * v1,
127 AngleAxisx(Scalar(0.1), Vector3(1,0,0)).toRotationMatrix()
128 * (AngleAxisx(Scalar(0.2), Vector3(0,1,0)).toRotationMatrix()
129 * (AngleAxisx(Scalar(0.3), Vector3(0,0,1)).toRotationMatrix() * v1)));
130
131 // angle-axis conversion
132 AngleAxisx aa = AngleAxisx(q1);
133 VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1);
134
135 if(abs(aa.angle()) > NumTraits<Scalar>::dummy_precision())
136 {
137 VERIFY( !(q1 * v1).isApprox(Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1) );
138 }
139
140 aa.fromRotationMatrix(aa.toRotationMatrix());
141 VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1);
142 if(abs(aa.angle()) > NumTraits<Scalar>::dummy_precision())
143 {
144 VERIFY( !(q1 * v1).isApprox(Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1) );
145 }
146
147 // AngleAxis
148 VERIFY_IS_APPROX(AngleAxisx(a,v1.normalized()).toRotationMatrix(),
149 Quaternionx(AngleAxisx(a,v1.normalized())).toRotationMatrix());
150
151 AngleAxisx aa1;
152 m = q1.toRotationMatrix();
153 aa1 = m;
154 VERIFY_IS_APPROX(AngleAxisx(m).toRotationMatrix(),
155 Quaternionx(m).toRotationMatrix());
156
157 // Transform
158 // TODO complete the tests !
159 a = 0;
160 while (abs(a)<Scalar(0.1))
161 a = internal::random<Scalar>(-Scalar(0.4)*Scalar(M_PI), Scalar(0.4)*Scalar(M_PI));
162 q1 = AngleAxisx(a, v0.normalized());
163 Transform3 t0, t1, t2;
164
165 // first test setIdentity() and Identity()
166 t0.setIdentity();
167 VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());
168 t0.matrix().setZero();
169 t0 = Transform3::Identity();
170 VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());
171
172 t0.setIdentity();
173 t1.setIdentity();
174 v1 << 1, 2, 3;
175 t0.linear() = q1.toRotationMatrix();
176 t0.pretranslate(v0);
177 t0.scale(v1);
178 t1.linear() = q1.conjugate().toRotationMatrix();
179 t1.prescale(v1.cwiseInverse());
180 t1.translate(-v0);
181
182 VERIFY((t0 * t1).matrix().isIdentity(test_precision<Scalar>()));
183
184 t1.fromPositionOrientationScale(v0, q1, v1);
185 VERIFY_IS_APPROX(t1.matrix(), t0.matrix());
186
187 t0.setIdentity(); t0.scale(v0).rotate(q1.toRotationMatrix());
188 t1.setIdentity(); t1.scale(v0).rotate(q1);
189 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
190
191 t0.setIdentity(); t0.scale(v0).rotate(AngleAxisx(q1));
192 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
193
194 VERIFY_IS_APPROX(t0.scale(a).matrix(), t1.scale(Vector3::Constant(a)).matrix());
195 VERIFY_IS_APPROX(t0.prescale(a).matrix(), t1.prescale(Vector3::Constant(a)).matrix());
196
197 // More transform constructors, operator=, operator*=
198
199 Matrix3 mat3 = Matrix3::Random();
200 Matrix4 mat4;
201 mat4 << mat3 , Vector3::Zero() , Vector4::Zero().transpose();
202 Transform3 tmat3(mat3), tmat4(mat4);
203 if(Mode!=int(AffineCompact))
204 tmat4.matrix()(3,3) = Scalar(1);
205 VERIFY_IS_APPROX(tmat3.matrix(), tmat4.matrix());
206
207 Scalar a3 = internal::random<Scalar>(-Scalar(M_PI), Scalar(M_PI));
208 Vector3 v3 = Vector3::Random().normalized();
209 AngleAxisx aa3(a3, v3);
210 Transform3 t3(aa3);
211 Transform3 t4;
212 t4 = aa3;
213 VERIFY_IS_APPROX(t3.matrix(), t4.matrix());
214 t4.rotate(AngleAxisx(-a3,v3));
215 VERIFY_IS_APPROX(t4.matrix(), MatrixType::Identity());
216 t4 *= aa3;
217 VERIFY_IS_APPROX(t3.matrix(), t4.matrix());
218
219 v3 = Vector3::Random();
220 Translation3 tv3(v3);
221 Transform3 t5(tv3);
222 t4 = tv3;
223 VERIFY_IS_APPROX(t5.matrix(), t4.matrix());
224 t4.translate(-v3);
225 VERIFY_IS_APPROX(t4.matrix(), MatrixType::Identity());
226 t4 *= tv3;
227 VERIFY_IS_APPROX(t5.matrix(), t4.matrix());
228
229 AlignedScaling3 sv3(v3);
230 Transform3 t6(sv3);
231 t4 = sv3;
232 VERIFY_IS_APPROX(t6.matrix(), t4.matrix());
233 t4.scale(v3.cwiseInverse());
234 VERIFY_IS_APPROX(t4.matrix(), MatrixType::Identity());
235 t4 *= sv3;
236 VERIFY_IS_APPROX(t6.matrix(), t4.matrix());
237
238 // matrix * transform
239 VERIFY_IS_APPROX((t3.matrix()*t4).matrix(), (t3*t4).matrix());
240
241 // chained Transform product
242 VERIFY_IS_APPROX(((t3*t4)*t5).matrix(), (t3*(t4*t5)).matrix());
243
244 // check that Transform product doesn't have aliasing problems
245 t5 = t4;
246 t5 = t5*t5;
247 VERIFY_IS_APPROX(t5, t4*t4);
248
249 // 2D transformation
250 Transform2 t20, t21;
251 Vector2 v20 = Vector2::Random();
252 Vector2 v21 = Vector2::Random();
253 for (int k=0; k<2; ++k)
254 if (abs(v21[k])<Scalar(1e-3)) v21[k] = Scalar(1e-3);
255 t21.setIdentity();
256 t21.linear() = Rotation2D<Scalar>(a).toRotationMatrix();
257 VERIFY_IS_APPROX(t20.fromPositionOrientationScale(v20,a,v21).matrix(),
258 t21.pretranslate(v20).scale(v21).matrix());
259
260 t21.setIdentity();
261 t21.linear() = Rotation2D<Scalar>(-a).toRotationMatrix();
262 VERIFY( (t20.fromPositionOrientationScale(v20,a,v21)
263 * (t21.prescale(v21.cwiseInverse()).translate(-v20))).matrix().isIdentity(test_precision<Scalar>()) );
264
265 // Transform - new API
266 // 3D
267 t0.setIdentity();
268 t0.rotate(q1).scale(v0).translate(v0);
269 // mat * aligned scaling and mat * translation
270 t1 = (Matrix3(q1) * AlignedScaling3(v0)) * Translation3(v0);
271 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
272 t1 = (Matrix3(q1) * Eigen::Scaling(v0)) * Translation3(v0);
273 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
274 t1 = (q1 * Eigen::Scaling(v0)) * Translation3(v0);
275 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
276 // mat * transformation and aligned scaling * translation
277 t1 = Matrix3(q1) * (AlignedScaling3(v0) * Translation3(v0));
278 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
279
280
281 t0.setIdentity();
282 t0.scale(s0).translate(v0);
283 t1 = Eigen::Scaling(s0) * Translation3(v0);
284 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
285 t0.prescale(s0);
286 t1 = Eigen::Scaling(s0) * t1;
287 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
288
289 t0 = t3;
290 t0.scale(s0);
291 t1 = t3 * Eigen::Scaling(s0,s0,s0);
292 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
293 t0.prescale(s0);
294 t1 = Eigen::Scaling(s0,s0,s0) * t1;
295 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
296
297 t0 = t3;
298 t0.scale(s0);
299 t1 = t3 * Eigen::Scaling(s0);
300 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
301 t0.prescale(s0);
302 t1 = Eigen::Scaling(s0) * t1;
303 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
304
305 t0.setIdentity();
306 t0.prerotate(q1).prescale(v0).pretranslate(v0);
307 // translation * aligned scaling and transformation * mat
308 t1 = (Translation3(v0) * AlignedScaling3(v0)) * Transform3(q1);
309 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
310 // scaling * mat and translation * mat
311 t1 = Translation3(v0) * (AlignedScaling3(v0) * Transform3(q1));
312 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
313
314 t0.setIdentity();
315 t0.scale(v0).translate(v0).rotate(q1);
316 // translation * mat and aligned scaling * transformation
317 t1 = AlignedScaling3(v0) * (Translation3(v0) * Transform3(q1));
318 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
319 // transformation * aligned scaling
320 t0.scale(v0);
321 t1 *= AlignedScaling3(v0);
322 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
323 // transformation * translation
324 t0.translate(v0);
325 t1 = t1 * Translation3(v0);
326 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
327 // translation * transformation
328 t0.pretranslate(v0);
329 t1 = Translation3(v0) * t1;
330 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
331
332 // transform * quaternion
333 t0.rotate(q1);
334 t1 = t1 * q1;
335 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
336
337 // translation * quaternion
338 t0.translate(v1).rotate(q1);
339 t1 = t1 * (Translation3(v1) * q1);
340 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
341
342 // aligned scaling * quaternion
343 t0.scale(v1).rotate(q1);
344 t1 = t1 * (AlignedScaling3(v1) * q1);
345 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
346
347 // quaternion * transform
348 t0.prerotate(q1);
349 t1 = q1 * t1;
350 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
351
352 // quaternion * translation
353 t0.rotate(q1).translate(v1);
354 t1 = t1 * (q1 * Translation3(v1));
355 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
356
357 // quaternion * aligned scaling
358 t0.rotate(q1).scale(v1);
359 t1 = t1 * (q1 * AlignedScaling3(v1));
360 VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
361
362 // test transform inversion
363 t0.setIdentity();
364 t0.translate(v0);
365 do {
366 t0.linear().setRandom();
367 } while(t0.linear().jacobiSvd().singularValues()(2)<test_precision<Scalar>());
368 Matrix4 t044 = Matrix4::Zero();
369 t044(3,3) = 1;
370 t044.block(0,0,t0.matrix().rows(),4) = t0.matrix();
371 VERIFY_IS_APPROX(t0.inverse(Affine).matrix(), t044.inverse().block(0,0,t0.matrix().rows(),4));
372 t0.setIdentity();
373 t0.translate(v0).rotate(q1);
374 t044 = Matrix4::Zero();
375 t044(3,3) = 1;
376 t044.block(0,0,t0.matrix().rows(),4) = t0.matrix();
377 VERIFY_IS_APPROX(t0.inverse(Isometry).matrix(), t044.inverse().block(0,0,t0.matrix().rows(),4));
378
379 Matrix3 mat_rotation, mat_scaling;
380 t0.setIdentity();
381 t0.translate(v0).rotate(q1).scale(v1);
382 t0.computeRotationScaling(&mat_rotation, &mat_scaling);
383 VERIFY_IS_APPROX(t0.linear(), mat_rotation * mat_scaling);
384 VERIFY_IS_APPROX(mat_rotation*mat_rotation.adjoint(), Matrix3::Identity());
385 VERIFY_IS_APPROX(mat_rotation.determinant(), Scalar(1));
386 t0.computeScalingRotation(&mat_scaling, &mat_rotation);
387 VERIFY_IS_APPROX(t0.linear(), mat_scaling * mat_rotation);
388 VERIFY_IS_APPROX(mat_rotation*mat_rotation.adjoint(), Matrix3::Identity());
389 VERIFY_IS_APPROX(mat_rotation.determinant(), Scalar(1));
390
391 // test casting
392 Transform<float,3,Mode> t1f = t1.template cast<float>();
393 VERIFY_IS_APPROX(t1f.template cast<Scalar>(),t1);
394 Transform<double,3,Mode> t1d = t1.template cast<double>();
395 VERIFY_IS_APPROX(t1d.template cast<Scalar>(),t1);
396
397 Translation3 tr1(v0);
398 Translation<float,3> tr1f = tr1.template cast<float>();
399 VERIFY_IS_APPROX(tr1f.template cast<Scalar>(),tr1);
400 Translation<double,3> tr1d = tr1.template cast<double>();
401 VERIFY_IS_APPROX(tr1d.template cast<Scalar>(),tr1);
402
403 AngleAxis<float> aa1f = aa1.template cast<float>();
404 VERIFY_IS_APPROX(aa1f.template cast<Scalar>(),aa1);
405 AngleAxis<double> aa1d = aa1.template cast<double>();
406 VERIFY_IS_APPROX(aa1d.template cast<Scalar>(),aa1);
407
408 Rotation2D<Scalar> r2d1(internal::random<Scalar>());
409 Rotation2D<float> r2d1f = r2d1.template cast<float>();
410 VERIFY_IS_APPROX(r2d1f.template cast<Scalar>(),r2d1);
411 Rotation2D<double> r2d1d = r2d1.template cast<double>();
412 VERIFY_IS_APPROX(r2d1d.template cast<Scalar>(),r2d1);
413
414 t20 = Translation2(v20) * (Rotation2D<Scalar>(s0) * Eigen::Scaling(s0));
415 t21 = Translation2(v20) * Rotation2D<Scalar>(s0) * Eigen::Scaling(s0);
416 VERIFY_IS_APPROX(t20,t21);
417
418 Rotation2D<Scalar> R0(s0), R1(s1);
419 t20 = Translation2(v20) * (R0 * Eigen::Scaling(s0));
420 t21 = Translation2(v20) * R0 * Eigen::Scaling(s0);
421 VERIFY_IS_APPROX(t20,t21);
422
423 t20 = Translation2(v20) * (R0 * R0.inverse() * Eigen::Scaling(s0));
424 t21 = Translation2(v20) * Eigen::Scaling(s0);
425 VERIFY_IS_APPROX(t20,t21);
426
427 VERIFY_IS_APPROX(s0, (R0.slerp(0, R1)).angle());
428 VERIFY_IS_APPROX(s1, (R0.slerp(1, R1)).angle());
429 VERIFY_IS_APPROX(s0, (R0.slerp(0.5, R0)).angle());
430 VERIFY_IS_APPROX(Scalar(0), (R0.slerp(0.5, R0.inverse())).angle());
431
432 // check basic features
433 {
434 Rotation2D<Scalar> r1; // default ctor
435 r1 = Rotation2D<Scalar>(s0); // copy assignment
436 VERIFY_IS_APPROX(r1.angle(),s0);
437 Rotation2D<Scalar> r2(r1); // copy ctor
438 VERIFY_IS_APPROX(r2.angle(),s0);
439 }
440}
441
442template<typename Scalar> void transform_alignment()
443{
444 typedef Transform<Scalar,3,Projective,AutoAlign> Projective3a;
445 typedef Transform<Scalar,3,Projective,DontAlign> Projective3u;
446
447 EIGEN_ALIGN16 Scalar array1[16];
448 EIGEN_ALIGN16 Scalar array2[16];
449 EIGEN_ALIGN16 Scalar array3[16+1];
450 Scalar* array3u = array3+1;
451
452 Projective3a *p1 = ::new(reinterpret_cast<void*>(array1)) Projective3a;
453 Projective3u *p2 = ::new(reinterpret_cast<void*>(array2)) Projective3u;
454 Projective3u *p3 = ::new(reinterpret_cast<void*>(array3u)) Projective3u;
455
456 p1->matrix().setRandom();
457 *p2 = *p1;
458 *p3 = *p1;
459
460 VERIFY_IS_APPROX(p1->matrix(), p2->matrix());
461 VERIFY_IS_APPROX(p1->matrix(), p3->matrix());
462
463 VERIFY_IS_APPROX( (*p1) * (*p1), (*p2)*(*p3));
464
465 #if defined(EIGEN_VECTORIZE) && EIGEN_ALIGN_STATICALLY
466 if(internal::packet_traits<Scalar>::Vectorizable)
467 VERIFY_RAISES_ASSERT((::new(reinterpret_cast<void*>(array3u)) Projective3a));
468 #endif
469}
470
471template<typename Scalar, int Dim, int Options> void transform_products()
472{
473 typedef Matrix<Scalar,Dim+1,Dim+1> Mat;
474 typedef Transform<Scalar,Dim,Projective,Options> Proj;
475 typedef Transform<Scalar,Dim,Affine,Options> Aff;
476 typedef Transform<Scalar,Dim,AffineCompact,Options> AffC;
477
478 Proj p; p.matrix().setRandom();
479 Aff a; a.linear().setRandom(); a.translation().setRandom();
480 AffC ac = a;
481
482 Mat p_m(p.matrix()), a_m(a.matrix());
483
484 VERIFY_IS_APPROX((p*p).matrix(), p_m*p_m);
485 VERIFY_IS_APPROX((a*a).matrix(), a_m*a_m);
486 VERIFY_IS_APPROX((p*a).matrix(), p_m*a_m);
487 VERIFY_IS_APPROX((a*p).matrix(), a_m*p_m);
488 VERIFY_IS_APPROX((ac*a).matrix(), a_m*a_m);
489 VERIFY_IS_APPROX((a*ac).matrix(), a_m*a_m);
490 VERIFY_IS_APPROX((p*ac).matrix(), p_m*a_m);
491 VERIFY_IS_APPROX((ac*p).matrix(), a_m*p_m);
492}
493
494void test_geo_transformations()
495{
496 for(int i = 0; i < g_repeat; i++) {
497 CALL_SUBTEST_1(( transformations<double,Affine,AutoAlign>() ));
498 CALL_SUBTEST_1(( non_projective_only<double,Affine,AutoAlign>() ));
499
500 CALL_SUBTEST_2(( transformations<float,AffineCompact,AutoAlign>() ));
501 CALL_SUBTEST_2(( non_projective_only<float,AffineCompact,AutoAlign>() ));
502 CALL_SUBTEST_2(( transform_alignment<float>() ));
503
504 CALL_SUBTEST_3(( transformations<double,Projective,AutoAlign>() ));
505 CALL_SUBTEST_3(( transformations<double,Projective,DontAlign>() ));
506 CALL_SUBTEST_3(( transform_alignment<double>() ));
507
508 CALL_SUBTEST_4(( transformations<float,Affine,RowMajor|AutoAlign>() ));
509 CALL_SUBTEST_4(( non_projective_only<float,Affine,RowMajor>() ));
510
511 CALL_SUBTEST_5(( transformations<double,AffineCompact,RowMajor|AutoAlign>() ));
512 CALL_SUBTEST_5(( non_projective_only<double,AffineCompact,RowMajor>() ));
513
514 CALL_SUBTEST_6(( transformations<double,Projective,RowMajor|AutoAlign>() ));
515 CALL_SUBTEST_6(( transformations<double,Projective,RowMajor|DontAlign>() ));
516
517
518 CALL_SUBTEST_7(( transform_products<double,3,RowMajor|AutoAlign>() ));
519 CALL_SUBTEST_7(( transform_products<float,2,AutoAlign>() ));
520 }
521}
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