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 #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 17 template<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, Matrix3(AngleAxisx(ea[0], Vector3::Unit##X()) * AngleAxisx(ea[1], Vector3::Unit##Y()) * AngleAxisx(ea[2], Vector3::Unit##Z()))); \ 398 } 399 VERIFY_EULER(0,1,2, X,Y,Z); 400 VERIFY_EULER(0,1,0, X,Y,X); 401 VERIFY_EULER(0,2,1, X,Z,Y); 402 VERIFY_EULER(0,2,0, X,Z,X); 403 404 VERIFY_EULER(1,2,0, Y,Z,X); 405 VERIFY_EULER(1,2,1, Y,Z,Y); 406 VERIFY_EULER(1,0,2, Y,X,Z); 407 VERIFY_EULER(1,0,1, Y,X,Y); 408 409 VERIFY_EULER(2,0,1, Z,X,Y); 410 VERIFY_EULER(2,0,2, Z,X,Z); 411 VERIFY_EULER(2,1,0, Z,Y,X); 412 VERIFY_EULER(2,1,2, Z,Y,Z); 413 414 // colwise/rowwise cross product 415 mat3.setRandom(); 416 Vector3 vec3 = Vector3::Random(); 417 Matrix3 mcross; 418 int i = ei_random<int>(0,2); 419 mcross = mat3.colwise().cross(vec3); 420 VERIFY_IS_APPROX(mcross.col(i), mat3.col(i).cross(vec3)); 421 mcross = mat3.rowwise().cross(vec3); 422 VERIFY_IS_APPROX(mcross.row(i), mat3.row(i).cross(vec3)); 423 424 425 } 426 427 void test_eigen2_geometry_with_eigen2_prefix() 428 { 429 std::cout << "eigen2 support: " << EIGEN2_SUPPORT_STAGE << std::endl; 430 for(int i = 0; i < g_repeat; i++) { 431 CALL_SUBTEST_1( geometry<float>() ); 432 CALL_SUBTEST_2( geometry<double>() ); 433 } 434 } 435
