xref: /aosp_15_r20/external/eigen/test/geo_alignedbox.cpp (revision bf2c37156dfe67e5dfebd6d394bad8b2ab5804d4)
1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2008-2009 Gael Guennebaud <[email protected]>
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 
13 using namespace std;
14 
15 // NOTE the following workaround was needed on some 32 bits builds to kill extra precision of x87 registers.
16 // It seems that it is not needed anymore, but let's keep it here, just in case...
17 
18 template<typename T> EIGEN_DONT_INLINE
kill_extra_precision(T &)19 void kill_extra_precision(T& /* x */) {
20   // This one worked but triggered a warning:
21   /* eigen_assert((void*)(&x) != (void*)0); */
22   // An alternative could be:
23   /* volatile T tmp = x; */
24   /* x = tmp; */
25 }
26 
27 
alignedbox(const BoxType & box)28 template<typename BoxType> void alignedbox(const BoxType& box)
29 {
30   /* this test covers the following files:
31      AlignedBox.h
32   */
33   typedef typename BoxType::Scalar Scalar;
34   typedef NumTraits<Scalar> ScalarTraits;
35   typedef typename ScalarTraits::Real RealScalar;
36   typedef Matrix<Scalar, BoxType::AmbientDimAtCompileTime, 1> VectorType;
37 
38   const Index dim = box.dim();
39 
40   VectorType p0 = VectorType::Random(dim);
41   VectorType p1 = VectorType::Random(dim);
42   while( p1 == p0 ){
43       p1 =  VectorType::Random(dim); }
44   RealScalar s1 = internal::random<RealScalar>(0,1);
45 
46   BoxType b0(dim);
47   BoxType b1(VectorType::Random(dim),VectorType::Random(dim));
48   BoxType b2;
49 
50   kill_extra_precision(b1);
51   kill_extra_precision(p0);
52   kill_extra_precision(p1);
53 
54   b0.extend(p0);
55   b0.extend(p1);
56   VERIFY(b0.contains(p0*s1+(Scalar(1)-s1)*p1));
57   VERIFY(b0.contains(b0.center()));
58   VERIFY_IS_APPROX(b0.center(),(p0+p1)/Scalar(2));
59 
60   (b2 = b0).extend(b1);
61   VERIFY(b2.contains(b0));
62   VERIFY(b2.contains(b1));
63   VERIFY_IS_APPROX(b2.clamp(b0), b0);
64 
65   // intersection
66   BoxType box1(VectorType::Random(dim));
67   box1.extend(VectorType::Random(dim));
68   BoxType box2(VectorType::Random(dim));
69   box2.extend(VectorType::Random(dim));
70 
71   VERIFY(box1.intersects(box2) == !box1.intersection(box2).isEmpty());
72 
73   // alignment -- make sure there is no memory alignment assertion
74   BoxType *bp0 = new BoxType(dim);
75   BoxType *bp1 = new BoxType(dim);
76   bp0->extend(*bp1);
77   delete bp0;
78   delete bp1;
79 
80   // sampling
81   for( int i=0; i<10; ++i )
82   {
83       VectorType r = b0.sample();
84       VERIFY(b0.contains(r));
85   }
86 
87 }
88 
alignedboxTranslatable(const BoxType & box)89 template<typename BoxType> void alignedboxTranslatable(const BoxType& box)
90 {
91   typedef typename BoxType::Scalar Scalar;
92   typedef Matrix<Scalar, BoxType::AmbientDimAtCompileTime, 1> VectorType;
93   typedef Transform<Scalar, BoxType::AmbientDimAtCompileTime, Isometry> IsometryTransform;
94   typedef Transform<Scalar, BoxType::AmbientDimAtCompileTime, Affine> AffineTransform;
95 
96   alignedbox(box);
97 
98   const VectorType Ones = VectorType::Ones();
99   const VectorType UnitX = VectorType::UnitX();
100   const Index dim = box.dim();
101 
102   // box((-1, -1, -1), (1, 1, 1))
103   BoxType a(-Ones, Ones);
104 
105   VERIFY_IS_APPROX(a.sizes(), Ones * Scalar(2));
106 
107   BoxType b = a;
108   VectorType translate = Ones;
109   translate[0] = Scalar(2);
110   b.translate(translate);
111   // translate by (2, 1, 1) -> box((1, 0, 0), (3, 2, 2))
112 
113   VERIFY_IS_APPROX(b.sizes(), Ones * Scalar(2));
114   VERIFY_IS_APPROX((b.min)(), UnitX);
115   VERIFY_IS_APPROX((b.max)(), Ones * Scalar(2) + UnitX);
116 
117   // Test transform
118 
119   IsometryTransform tf = IsometryTransform::Identity();
120   tf.translation() = -translate;
121 
122   BoxType c = b.transformed(tf);
123   // translate by (-2, -1, -1) -> box((-1, -1, -1), (1, 1, 1))
124   VERIFY_IS_APPROX(c.sizes(), a.sizes());
125   VERIFY_IS_APPROX((c.min)(), (a.min)());
126   VERIFY_IS_APPROX((c.max)(), (a.max)());
127 
128   c.transform(tf);
129   // translate by (-2, -1, -1) -> box((-3, -2, -2), (-1, 0, 0))
130   VERIFY_IS_APPROX(c.sizes(), a.sizes());
131   VERIFY_IS_APPROX((c.min)(), Ones * Scalar(-2) - UnitX);
132   VERIFY_IS_APPROX((c.max)(), -UnitX);
133 
134   // Scaling
135 
136   AffineTransform atf = AffineTransform::Identity();
137   atf.scale(Scalar(3));
138   c.transform(atf);
139   // scale by 3 -> box((-9, -6, -6), (-3, 0, 0))
140   VERIFY_IS_APPROX(c.sizes(), Scalar(3) * a.sizes());
141   VERIFY_IS_APPROX((c.min)(), Ones * Scalar(-6) - UnitX * Scalar(3));
142   VERIFY_IS_APPROX((c.max)(), UnitX * Scalar(-3));
143 
144   atf = AffineTransform::Identity();
145   atf.scale(Scalar(-3));
146   c.transform(atf);
147   // scale by -3 -> box((27, 18, 18), (9, 0, 0))
148   VERIFY_IS_APPROX(c.sizes(), Scalar(9) * a.sizes());
149   VERIFY_IS_APPROX((c.min)(), UnitX * Scalar(9));
150   VERIFY_IS_APPROX((c.max)(), Ones * Scalar(18) + UnitX * Scalar(9));
151 
152   // Check identity transform within numerical precision.
153   BoxType transformedC = c.transformed(IsometryTransform::Identity());
154   VERIFY_IS_APPROX(transformedC, c);
155 
156   for (size_t i = 0; i < 10; ++i)
157   {
158     VectorType minCorner;
159     VectorType maxCorner;
160     for (Index d = 0; d < dim; ++d)
161     {
162       minCorner[d] = internal::random<Scalar>(-10,10);
163       maxCorner[d] = minCorner[d] + internal::random<Scalar>(0, 10);
164     }
165 
166     c = BoxType(minCorner, maxCorner);
167 
168     translate = VectorType::Random();
169     c.translate(translate);
170 
171     VERIFY_IS_APPROX((c.min)(), minCorner + translate);
172     VERIFY_IS_APPROX((c.max)(), maxCorner + translate);
173   }
174 }
175 
176 template<typename Scalar, typename Rotation>
rotate2D(Scalar angle)177 Rotation rotate2D(Scalar angle) {
178   return Rotation2D<Scalar>(angle);
179 }
180 
181 template<typename Scalar, typename Rotation>
rotate2DIntegral(typename NumTraits<Scalar>::NonInteger angle)182 Rotation rotate2DIntegral(typename NumTraits<Scalar>::NonInteger angle) {
183   typedef typename NumTraits<Scalar>::NonInteger NonInteger;
184   return Rotation2D<NonInteger>(angle).toRotationMatrix().
185       template cast<Scalar>();
186 }
187 
188 template<typename Scalar, typename Rotation>
rotate3DZAxis(Scalar angle)189 Rotation rotate3DZAxis(Scalar angle) {
190   return AngleAxis<Scalar>(angle, Matrix<Scalar, 3, 1>(0, 0, 1));
191 }
192 
193 template<typename Scalar, typename Rotation>
rotate3DZAxisIntegral(typename NumTraits<Scalar>::NonInteger angle)194 Rotation rotate3DZAxisIntegral(typename NumTraits<Scalar>::NonInteger angle) {
195   typedef typename NumTraits<Scalar>::NonInteger NonInteger;
196   return AngleAxis<NonInteger>(angle, Matrix<NonInteger, 3, 1>(0, 0, 1)).
197       toRotationMatrix().template cast<Scalar>();
198 }
199 
200 template<typename Scalar, typename Rotation>
rotate4DZWAxis(Scalar angle)201 Rotation rotate4DZWAxis(Scalar angle) {
202   Rotation result = Matrix<Scalar, 4, 4>::Identity();
203   result.block(0, 0, 3, 3) = rotate3DZAxis<Scalar, AngleAxisd>(angle).toRotationMatrix();
204   return result;
205 }
206 
207 template <typename MatrixType>
randomRotationMatrix()208 MatrixType randomRotationMatrix()
209 {
210   // algorithm from
211   // https://www.isprs-ann-photogramm-remote-sens-spatial-inf-sci.net/III-7/103/2016/isprs-annals-III-7-103-2016.pdf
212   const MatrixType rand = MatrixType::Random();
213   const MatrixType q = rand.householderQr().householderQ();
214   const JacobiSVD<MatrixType> svd = q.jacobiSvd(ComputeFullU | ComputeFullV);
215   const typename MatrixType::Scalar det = (svd.matrixU() * svd.matrixV().transpose()).determinant();
216   MatrixType diag = rand.Identity();
217   diag(MatrixType::RowsAtCompileTime - 1, MatrixType::ColsAtCompileTime - 1) = det;
218   const MatrixType rotation = svd.matrixU() * diag * svd.matrixV().transpose();
219   return rotation;
220 }
221 
222 template <typename Scalar, int Dim>
boxGetCorners(const Matrix<Scalar,Dim,1> & min_,const Matrix<Scalar,Dim,1> & max_)223 Matrix<Scalar, Dim, (1<<Dim)> boxGetCorners(const Matrix<Scalar, Dim, 1>& min_, const Matrix<Scalar, Dim, 1>& max_)
224 {
225   Matrix<Scalar, Dim, (1<<Dim) > result;
226   for(Index i=0; i<(1<<Dim); ++i)
227   {
228     for(Index j=0; j<Dim; ++j)
229       result(j,i) = (i & (1<<j)) ? min_(j) : max_(j);
230   }
231   return result;
232 }
233 
alignedboxRotatable(const BoxType & box,Rotation (* rotate)(typename NumTraits<typename BoxType::Scalar>::NonInteger))234 template<typename BoxType, typename Rotation> void alignedboxRotatable(
235     const BoxType& box,
236     Rotation (*rotate)(typename NumTraits<typename BoxType::Scalar>::NonInteger /*_angle*/))
237 {
238   alignedboxTranslatable(box);
239 
240   typedef typename BoxType::Scalar Scalar;
241   typedef typename NumTraits<Scalar>::NonInteger NonInteger;
242   typedef Matrix<Scalar, BoxType::AmbientDimAtCompileTime, 1> VectorType;
243   typedef Transform<Scalar, BoxType::AmbientDimAtCompileTime, Isometry> IsometryTransform;
244   typedef Transform<Scalar, BoxType::AmbientDimAtCompileTime, Affine> AffineTransform;
245 
246   const VectorType Zero = VectorType::Zero();
247   const VectorType Ones = VectorType::Ones();
248   const VectorType UnitX = VectorType::UnitX();
249   const VectorType UnitY = VectorType::UnitY();
250   // this is vector (0, 0, -1, -1, -1, ...), i.e. with zeros at first and second dimensions
251   const VectorType UnitZ = Ones - UnitX - UnitY;
252 
253   // in this kind of comments the 3D case values will be illustrated
254   // box((-1, -1, -1), (1, 1, 1))
255   BoxType a(-Ones, Ones);
256 
257   // to allow templating this test for both 2D and 3D cases, we always set all
258   // but the first coordinate to the same value; so basically 3D case works as
259   // if you were looking at the scene from top
260 
261   VectorType minPoint = -2 * Ones;
262   minPoint[0] = -3;
263   VectorType maxPoint = Zero;
264   maxPoint[0] = -1;
265   BoxType c(minPoint, maxPoint);
266   // box((-3, -2, -2), (-1, 0, 0))
267 
268   IsometryTransform tf2 = IsometryTransform::Identity();
269   // for some weird reason the following statement has to be put separate from
270   // the following rotate call, otherwise precision problems arise...
271   Rotation rot = rotate(NonInteger(EIGEN_PI));
272   tf2.rotate(rot);
273 
274   c.transform(tf2);
275   // rotate by 180 deg around origin -> box((1, 0, -2), (3, 2, 0))
276 
277   VERIFY_IS_APPROX(c.sizes(), a.sizes());
278   VERIFY_IS_APPROX((c.min)(), UnitX - UnitZ * Scalar(2));
279   VERIFY_IS_APPROX((c.max)(), UnitX * Scalar(3) + UnitY * Scalar(2));
280 
281   rot = rotate(NonInteger(EIGEN_PI / 2));
282   tf2.setIdentity();
283   tf2.rotate(rot);
284 
285   c.transform(tf2);
286   // rotate by 90 deg around origin ->  box((-2, 1, -2), (0, 3, 0))
287 
288   VERIFY_IS_APPROX(c.sizes(), a.sizes());
289   VERIFY_IS_APPROX((c.min)(), Ones * Scalar(-2) + UnitY * Scalar(3));
290   VERIFY_IS_APPROX((c.max)(), UnitY * Scalar(3));
291 
292   // box((-1, -1, -1), (1, 1, 1))
293   AffineTransform atf = AffineTransform::Identity();
294   atf.linearExt()(0, 1) = Scalar(1);
295   c = BoxType(-Ones, Ones);
296   c.transform(atf);
297   // 45 deg shear in x direction -> box((-2, -1, -1), (2, 1, 1))
298 
299   VERIFY_IS_APPROX(c.sizes(), Ones * Scalar(2) + UnitX * Scalar(2));
300   VERIFY_IS_APPROX((c.min)(), -Ones - UnitX);
301   VERIFY_IS_APPROX((c.max)(), Ones + UnitX);
302 }
303 
alignedboxNonIntegralRotatable(const BoxType & box,Rotation (* rotate)(typename NumTraits<typename BoxType::Scalar>::NonInteger))304 template<typename BoxType, typename Rotation> void alignedboxNonIntegralRotatable(
305     const BoxType& box,
306     Rotation (*rotate)(typename NumTraits<typename BoxType::Scalar>::NonInteger /*_angle*/))
307 {
308   alignedboxRotatable(box, rotate);
309 
310   typedef typename BoxType::Scalar Scalar;
311   typedef typename NumTraits<Scalar>::NonInteger NonInteger;
312   enum { Dim = BoxType::AmbientDimAtCompileTime };
313   typedef Matrix<Scalar, Dim, 1> VectorType;
314   typedef Matrix<Scalar, Dim, (1 << Dim)> CornersType;
315   typedef Transform<Scalar, Dim, Isometry> IsometryTransform;
316   typedef Transform<Scalar, Dim, Affine> AffineTransform;
317 
318   const Index dim = box.dim();
319   const VectorType Zero = VectorType::Zero();
320   const VectorType Ones = VectorType::Ones();
321 
322   VectorType minPoint = -2 * Ones;
323   minPoint[1] = 1;
324   VectorType maxPoint = Zero;
325   maxPoint[1] = 3;
326   BoxType c(minPoint, maxPoint);
327   // ((-2, 1, -2), (0, 3, 0))
328 
329   VectorType cornerBL = (c.min)();
330   VectorType cornerTR = (c.max)();
331   VectorType cornerBR = (c.min)(); cornerBR[0] = cornerTR[0];
332   VectorType cornerTL = (c.max)(); cornerTL[0] = cornerBL[0];
333 
334   NonInteger angle = NonInteger(EIGEN_PI/3);
335   Rotation rot = rotate(angle);
336   IsometryTransform tf2;
337   tf2.setIdentity();
338   tf2.rotate(rot);
339 
340   c.transform(tf2);
341   // rotate by 60 deg ->  box((-3.59, -1.23, -2), (-0.86, 1.5, 0))
342 
343   cornerBL = tf2 * cornerBL;
344   cornerBR = tf2 * cornerBR;
345   cornerTL = tf2 * cornerTL;
346   cornerTR = tf2 * cornerTR;
347 
348   VectorType minCorner = Ones * Scalar(-2);
349   VectorType maxCorner = Zero;
350   minCorner[0] = (min)((min)(cornerBL[0], cornerBR[0]), (min)(cornerTL[0], cornerTR[0]));
351   maxCorner[0] = (max)((max)(cornerBL[0], cornerBR[0]), (max)(cornerTL[0], cornerTR[0]));
352   minCorner[1] = (min)((min)(cornerBL[1], cornerBR[1]), (min)(cornerTL[1], cornerTR[1]));
353   maxCorner[1] = (max)((max)(cornerBL[1], cornerBR[1]), (max)(cornerTL[1], cornerTR[1]));
354 
355   for (Index d = 2; d < dim; ++d)
356     VERIFY_IS_APPROX(c.sizes()[d], Scalar(2));
357 
358   VERIFY_IS_APPROX((c.min)(), minCorner);
359   VERIFY_IS_APPROX((c.max)(), maxCorner);
360 
361   VectorType minCornerValue = Ones * Scalar(-2);
362   VectorType maxCornerValue = Zero;
363   minCornerValue[0] = Scalar(Scalar(-sqrt(2*2 + 3*3)) * Scalar(cos(Scalar(atan(2.0/3.0)) - angle/2)));
364   minCornerValue[1] = Scalar(Scalar(-sqrt(1*1 + 2*2)) * Scalar(sin(Scalar(atan(2.0/1.0)) - angle/2)));
365   maxCornerValue[0] = Scalar(-sin(angle));
366   maxCornerValue[1] = Scalar(3 * cos(angle));
367   VERIFY_IS_APPROX((c.min)(), minCornerValue);
368   VERIFY_IS_APPROX((c.max)(), maxCornerValue);
369 
370   // randomized test - translate and rotate the box and compare to a box made of transformed vertices
371   for (size_t i = 0; i < 10; ++i)
372   {
373     for (Index d = 0; d < dim; ++d)
374     {
375       minCorner[d] = internal::random<Scalar>(-10,10);
376       maxCorner[d] = minCorner[d] + internal::random<Scalar>(0, 10);
377     }
378 
379     c = BoxType(minCorner, maxCorner);
380 
381     CornersType corners = boxGetCorners(minCorner, maxCorner);
382 
383     typename AffineTransform::LinearMatrixType rotation =
384         randomRotationMatrix<typename AffineTransform::LinearMatrixType>();
385 
386     tf2.setIdentity();
387     tf2.rotate(rotation);
388     tf2.translate(VectorType::Random());
389 
390     c.transform(tf2);
391     corners = tf2 * corners;
392 
393     minCorner = corners.rowwise().minCoeff();
394     maxCorner = corners.rowwise().maxCoeff();
395 
396     VERIFY_IS_APPROX((c.min)(), minCorner);
397     VERIFY_IS_APPROX((c.max)(), maxCorner);
398   }
399 
400   // randomized test - transform the box with a random affine matrix and compare to a box made of transformed vertices
401   for (size_t i = 0; i < 10; ++i)
402   {
403     for (Index d = 0; d < dim; ++d)
404     {
405       minCorner[d] = internal::random<Scalar>(-10,10);
406       maxCorner[d] = minCorner[d] + internal::random<Scalar>(0, 10);
407     }
408 
409     c = BoxType(minCorner, maxCorner);
410 
411     CornersType corners = boxGetCorners(minCorner, maxCorner);
412 
413     AffineTransform atf = AffineTransform::Identity();
414     atf.linearExt() = AffineTransform::LinearPart::Random();
415     atf.translate(VectorType::Random());
416 
417     c.transform(atf);
418     corners = atf * corners;
419 
420     minCorner = corners.rowwise().minCoeff();
421     maxCorner = corners.rowwise().maxCoeff();
422 
423     VERIFY_IS_APPROX((c.min)(), minCorner);
424     VERIFY_IS_APPROX((c.max)(), maxCorner);
425   }
426 }
427 
428 template<typename BoxType>
alignedboxCastTests(const BoxType & box)429 void alignedboxCastTests(const BoxType& box)
430 {
431   // casting
432   typedef typename BoxType::Scalar Scalar;
433   typedef Matrix<Scalar, BoxType::AmbientDimAtCompileTime, 1> VectorType;
434 
435   const Index dim = box.dim();
436 
437   VectorType p0 = VectorType::Random(dim);
438   VectorType p1 = VectorType::Random(dim);
439 
440   BoxType b0(dim);
441 
442   b0.extend(p0);
443   b0.extend(p1);
444 
445   const int Dim = BoxType::AmbientDimAtCompileTime;
446   typedef typename GetDifferentType<Scalar>::type OtherScalar;
447   AlignedBox<OtherScalar,Dim> hp1f = b0.template cast<OtherScalar>();
448   VERIFY_IS_APPROX(hp1f.template cast<Scalar>(),b0);
449   AlignedBox<Scalar,Dim> hp1d = b0.template cast<Scalar>();
450   VERIFY_IS_APPROX(hp1d.template cast<Scalar>(),b0);
451 }
452 
453 
specificTest1()454 void specificTest1()
455 {
456     Vector2f m; m << -1.0f, -2.0f;
457     Vector2f M; M <<  1.0f,  5.0f;
458 
459     typedef AlignedBox2f  BoxType;
460     BoxType box( m, M );
461 
462     Vector2f sides = M-m;
463     VERIFY_IS_APPROX(sides, box.sizes() );
464     VERIFY_IS_APPROX(sides[1], box.sizes()[1] );
465     VERIFY_IS_APPROX(sides[1], box.sizes().maxCoeff() );
466     VERIFY_IS_APPROX(sides[0], box.sizes().minCoeff() );
467 
468     VERIFY_IS_APPROX( 14.0f, box.volume() );
469     VERIFY_IS_APPROX( 53.0f, box.diagonal().squaredNorm() );
470     VERIFY_IS_APPROX( std::sqrt( 53.0f ), box.diagonal().norm() );
471 
472     VERIFY_IS_APPROX( m, box.corner( BoxType::BottomLeft ) );
473     VERIFY_IS_APPROX( M, box.corner( BoxType::TopRight ) );
474     Vector2f bottomRight; bottomRight << M[0], m[1];
475     Vector2f topLeft; topLeft << m[0], M[1];
476     VERIFY_IS_APPROX( bottomRight, box.corner( BoxType::BottomRight ) );
477     VERIFY_IS_APPROX( topLeft, box.corner( BoxType::TopLeft ) );
478 }
479 
480 
specificTest2()481 void specificTest2()
482 {
483     Vector3i m; m << -1, -2, 0;
484     Vector3i M; M <<  1,  5, 3;
485 
486     typedef AlignedBox3i  BoxType;
487     BoxType box( m, M );
488 
489     Vector3i sides = M-m;
490     VERIFY_IS_APPROX(sides, box.sizes() );
491     VERIFY_IS_APPROX(sides[1], box.sizes()[1] );
492     VERIFY_IS_APPROX(sides[1], box.sizes().maxCoeff() );
493     VERIFY_IS_APPROX(sides[0], box.sizes().minCoeff() );
494 
495     VERIFY_IS_APPROX( 42, box.volume() );
496     VERIFY_IS_APPROX( 62, box.diagonal().squaredNorm() );
497 
498     VERIFY_IS_APPROX( m, box.corner( BoxType::BottomLeftFloor ) );
499     VERIFY_IS_APPROX( M, box.corner( BoxType::TopRightCeil ) );
500     Vector3i bottomRightFloor; bottomRightFloor << M[0], m[1], m[2];
501     Vector3i topLeftFloor; topLeftFloor << m[0], M[1], m[2];
502     VERIFY_IS_APPROX( bottomRightFloor, box.corner( BoxType::BottomRightFloor ) );
503     VERIFY_IS_APPROX( topLeftFloor, box.corner( BoxType::TopLeftFloor ) );
504 }
505 
506 
EIGEN_DECLARE_TEST(geo_alignedbox)507 EIGEN_DECLARE_TEST(geo_alignedbox)
508 {
509   for(int i = 0; i < g_repeat; i++)
510   {
511     CALL_SUBTEST_1( (alignedboxNonIntegralRotatable<AlignedBox2f, Rotation2Df>(AlignedBox2f(), &rotate2D)) );
512     CALL_SUBTEST_2( alignedboxCastTests(AlignedBox2f()) );
513 
514     CALL_SUBTEST_3( (alignedboxNonIntegralRotatable<AlignedBox3f, AngleAxisf>(AlignedBox3f(), &rotate3DZAxis)) );
515     CALL_SUBTEST_4( alignedboxCastTests(AlignedBox3f()) );
516 
517     CALL_SUBTEST_5( (alignedboxNonIntegralRotatable<AlignedBox4d, Matrix4d>(AlignedBox4d(), &rotate4DZWAxis)) );
518     CALL_SUBTEST_6( alignedboxCastTests(AlignedBox4d()) );
519 
520     CALL_SUBTEST_7( alignedboxTranslatable(AlignedBox1d()) );
521     CALL_SUBTEST_8( alignedboxCastTests(AlignedBox1d()) );
522 
523     CALL_SUBTEST_9( alignedboxTranslatable(AlignedBox1i()) );
524     CALL_SUBTEST_10( (alignedboxRotatable<AlignedBox2i, Matrix2i>(AlignedBox2i(), &rotate2DIntegral<int, Matrix2i>)) );
525     CALL_SUBTEST_11( (alignedboxRotatable<AlignedBox3i, Matrix3i>(AlignedBox3i(), &rotate3DZAxisIntegral<int, Matrix3i>)) );
526 
527     CALL_SUBTEST_14( alignedbox(AlignedBox<double,Dynamic>(4)) );
528   }
529   CALL_SUBTEST_12( specificTest1() );
530   CALL_SUBTEST_13( specificTest2() );
531 }
532