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 (at) 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 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, m1); \ 396 VERIFY_IS_APPROX(m, Matrix3(AngleAxisx(ea[0], Vector3::Unit##X()) * AngleAxisx(ea[1], Vector3::Unit##Y()) * AngleAxisx(ea[2], Vector3::Unit##Z()))); \ 397 } 398 VERIFY_EULER(0,1,2, X,Y,Z); 399 VERIFY_EULER(0,1,0, X,Y,X); 400 VERIFY_EULER(0,2,1, X,Z,Y); 401 VERIFY_EULER(0,2,0, X,Z,X); 402 403 VERIFY_EULER(1,2,0, Y,Z,X); 404 VERIFY_EULER(1,2,1, Y,Z,Y); 405 VERIFY_EULER(1,0,2, Y,X,Z); 406 VERIFY_EULER(1,0,1, Y,X,Y); 407 408 VERIFY_EULER(2,0,1, Z,X,Y); 409 VERIFY_EULER(2,0,2, Z,X,Z); 410 VERIFY_EULER(2,1,0, Z,Y,X); 411 VERIFY_EULER(2,1,2, Z,Y,Z); 412 413 // colwise/rowwise cross product 414 mat3.setRandom(); 415 Vector3 vec3 = Vector3::Random(); 416 Matrix3 mcross; 417 int i = ei_random<int>(0,2); 418 mcross = mat3.colwise().cross(vec3); 419 VERIFY_IS_APPROX(mcross.col(i), mat3.col(i).cross(vec3)); 420 mcross = mat3.rowwise().cross(vec3); 421 VERIFY_IS_APPROX(mcross.row(i), mat3.row(i).cross(vec3)); 422 423 424 } 425 426 void test_eigen2_geometry() 427 { 428 for(int i = 0; i < g_repeat; i++) { 429 CALL_SUBTEST_1( geometry<float>() ); 430 CALL_SUBTEST_2( geometry<double>() ); 431 } 432 } 433
