AlignedBox.h (18939B)
1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. 3 // 4 // Copyright (C) 2008 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 // Function void Eigen::AlignedBox::transform(const Transform& transform) 11 // is provided under the following license agreement: 12 // 13 // Software License Agreement (BSD License) 14 // 15 // Copyright (c) 2011-2014, Willow Garage, Inc. 16 // Copyright (c) 2014-2015, Open Source Robotics Foundation 17 // All rights reserved. 18 // 19 // Redistribution and use in source and binary forms, with or without 20 // modification, are permitted provided that the following conditions 21 // are met: 22 // 23 // * Redistributions of source code must retain the above copyright 24 // notice, this list of conditions and the following disclaimer. 25 // * Redistributions in binary form must reproduce the above 26 // copyright notice, this list of conditions and the following 27 // disclaimer in the documentation and/or other materials provided 28 // with the distribution. 29 // * Neither the name of Open Source Robotics Foundation nor the names of its 30 // contributors may be used to endorse or promote products derived 31 // from this software without specific prior written permission. 32 // 33 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS 34 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT 35 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS 36 // FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 37 // COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, 38 // INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, 39 // BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; 40 // LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER 41 // CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 42 // LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN 43 // ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 44 // POSSIBILITY OF SUCH DAMAGE. 45 46 #ifndef EIGEN_ALIGNEDBOX_H 47 #define EIGEN_ALIGNEDBOX_H 48 49 namespace Eigen { 50 51 /** \geometry_module \ingroup Geometry_Module 52 * 53 * 54 * \class AlignedBox 55 * 56 * \brief An axis aligned box 57 * 58 * \tparam _Scalar the type of the scalar coefficients 59 * \tparam _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic. 60 * 61 * This class represents an axis aligned box as a pair of the minimal and maximal corners. 62 * \warning The result of most methods is undefined when applied to an empty box. You can check for empty boxes using isEmpty(). 63 * \sa alignedboxtypedefs 64 */ 65 template <typename _Scalar, int _AmbientDim> 66 class AlignedBox 67 { 68 public: 69 EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim) 70 enum { AmbientDimAtCompileTime = _AmbientDim }; 71 typedef _Scalar Scalar; 72 typedef NumTraits<Scalar> ScalarTraits; 73 typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3 74 typedef typename ScalarTraits::Real RealScalar; 75 typedef typename ScalarTraits::NonInteger NonInteger; 76 typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType; 77 typedef CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const VectorType, const VectorType> VectorTypeSum; 78 79 /** Define constants to name the corners of a 1D, 2D or 3D axis aligned bounding box */ 80 enum CornerType 81 { 82 /** 1D names @{ */ 83 Min=0, Max=1, 84 /** @} */ 85 86 /** Identifier for 2D corner @{ */ 87 BottomLeft=0, BottomRight=1, 88 TopLeft=2, TopRight=3, 89 /** @} */ 90 91 /** Identifier for 3D corner @{ */ 92 BottomLeftFloor=0, BottomRightFloor=1, 93 TopLeftFloor=2, TopRightFloor=3, 94 BottomLeftCeil=4, BottomRightCeil=5, 95 TopLeftCeil=6, TopRightCeil=7 96 /** @} */ 97 }; 98 99 100 /** Default constructor initializing a null box. */ 101 EIGEN_DEVICE_FUNC inline AlignedBox() 102 { if (EIGEN_CONST_CONDITIONAL(AmbientDimAtCompileTime!=Dynamic)) setEmpty(); } 103 104 /** Constructs a null box with \a _dim the dimension of the ambient space. */ 105 EIGEN_DEVICE_FUNC inline explicit AlignedBox(Index _dim) : m_min(_dim), m_max(_dim) 106 { setEmpty(); } 107 108 /** Constructs a box with extremities \a _min and \a _max. 109 * \warning If either component of \a _min is larger than the same component of \a _max, the constructed box is empty. */ 110 template<typename OtherVectorType1, typename OtherVectorType2> 111 EIGEN_DEVICE_FUNC inline AlignedBox(const OtherVectorType1& _min, const OtherVectorType2& _max) : m_min(_min), m_max(_max) {} 112 113 /** Constructs a box containing a single point \a p. */ 114 template<typename Derived> 115 EIGEN_DEVICE_FUNC inline explicit AlignedBox(const MatrixBase<Derived>& p) : m_min(p), m_max(m_min) 116 { } 117 118 EIGEN_DEVICE_FUNC ~AlignedBox() {} 119 120 /** \returns the dimension in which the box holds */ 121 EIGEN_DEVICE_FUNC inline Index dim() const { return AmbientDimAtCompileTime==Dynamic ? m_min.size() : Index(AmbientDimAtCompileTime); } 122 123 /** \deprecated use isEmpty() */ 124 EIGEN_DEVICE_FUNC inline bool isNull() const { return isEmpty(); } 125 126 /** \deprecated use setEmpty() */ 127 EIGEN_DEVICE_FUNC inline void setNull() { setEmpty(); } 128 129 /** \returns true if the box is empty. 130 * \sa setEmpty */ 131 EIGEN_DEVICE_FUNC inline bool isEmpty() const { return (m_min.array() > m_max.array()).any(); } 132 133 /** Makes \c *this an empty box. 134 * \sa isEmpty */ 135 EIGEN_DEVICE_FUNC inline void setEmpty() 136 { 137 m_min.setConstant( ScalarTraits::highest() ); 138 m_max.setConstant( ScalarTraits::lowest() ); 139 } 140 141 /** \returns the minimal corner */ 142 EIGEN_DEVICE_FUNC inline const VectorType& (min)() const { return m_min; } 143 /** \returns a non const reference to the minimal corner */ 144 EIGEN_DEVICE_FUNC inline VectorType& (min)() { return m_min; } 145 /** \returns the maximal corner */ 146 EIGEN_DEVICE_FUNC inline const VectorType& (max)() const { return m_max; } 147 /** \returns a non const reference to the maximal corner */ 148 EIGEN_DEVICE_FUNC inline VectorType& (max)() { return m_max; } 149 150 /** \returns the center of the box */ 151 EIGEN_DEVICE_FUNC inline const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(VectorTypeSum, RealScalar, quotient) 152 center() const 153 { return (m_min+m_max)/RealScalar(2); } 154 155 /** \returns the lengths of the sides of the bounding box. 156 * Note that this function does not get the same 157 * result for integral or floating scalar types: see 158 */ 159 EIGEN_DEVICE_FUNC inline const CwiseBinaryOp< internal::scalar_difference_op<Scalar,Scalar>, const VectorType, const VectorType> sizes() const 160 { return m_max - m_min; } 161 162 /** \returns the volume of the bounding box */ 163 EIGEN_DEVICE_FUNC inline Scalar volume() const 164 { return sizes().prod(); } 165 166 /** \returns an expression for the bounding box diagonal vector 167 * if the length of the diagonal is needed: diagonal().norm() 168 * will provide it. 169 */ 170 EIGEN_DEVICE_FUNC inline CwiseBinaryOp< internal::scalar_difference_op<Scalar,Scalar>, const VectorType, const VectorType> diagonal() const 171 { return sizes(); } 172 173 /** \returns the vertex of the bounding box at the corner defined by 174 * the corner-id corner. It works only for a 1D, 2D or 3D bounding box. 175 * For 1D bounding boxes corners are named by 2 enum constants: 176 * BottomLeft and BottomRight. 177 * For 2D bounding boxes, corners are named by 4 enum constants: 178 * BottomLeft, BottomRight, TopLeft, TopRight. 179 * For 3D bounding boxes, the following names are added: 180 * BottomLeftCeil, BottomRightCeil, TopLeftCeil, TopRightCeil. 181 */ 182 EIGEN_DEVICE_FUNC inline VectorType corner(CornerType corner) const 183 { 184 EIGEN_STATIC_ASSERT(_AmbientDim <= 3, THIS_METHOD_IS_ONLY_FOR_VECTORS_OF_A_SPECIFIC_SIZE); 185 186 VectorType res; 187 188 Index mult = 1; 189 for(Index d=0; d<dim(); ++d) 190 { 191 if( mult & corner ) res[d] = m_max[d]; 192 else res[d] = m_min[d]; 193 mult *= 2; 194 } 195 return res; 196 } 197 198 /** \returns a random point inside the bounding box sampled with 199 * a uniform distribution */ 200 EIGEN_DEVICE_FUNC inline VectorType sample() const 201 { 202 VectorType r(dim()); 203 for(Index d=0; d<dim(); ++d) 204 { 205 if(!ScalarTraits::IsInteger) 206 { 207 r[d] = m_min[d] + (m_max[d]-m_min[d]) 208 * internal::random<Scalar>(Scalar(0), Scalar(1)); 209 } 210 else 211 r[d] = internal::random(m_min[d], m_max[d]); 212 } 213 return r; 214 } 215 216 /** \returns true if the point \a p is inside the box \c *this. */ 217 template<typename Derived> 218 EIGEN_DEVICE_FUNC inline bool contains(const MatrixBase<Derived>& p) const 219 { 220 typename internal::nested_eval<Derived,2>::type p_n(p.derived()); 221 return (m_min.array()<=p_n.array()).all() && (p_n.array()<=m_max.array()).all(); 222 } 223 224 /** \returns true if the box \a b is entirely inside the box \c *this. */ 225 EIGEN_DEVICE_FUNC inline bool contains(const AlignedBox& b) const 226 { return (m_min.array()<=(b.min)().array()).all() && ((b.max)().array()<=m_max.array()).all(); } 227 228 /** \returns true if the box \a b is intersecting the box \c *this. 229 * \sa intersection, clamp */ 230 EIGEN_DEVICE_FUNC inline bool intersects(const AlignedBox& b) const 231 { return (m_min.array()<=(b.max)().array()).all() && ((b.min)().array()<=m_max.array()).all(); } 232 233 /** Extends \c *this such that it contains the point \a p and returns a reference to \c *this. 234 * \sa extend(const AlignedBox&) */ 235 template<typename Derived> 236 EIGEN_DEVICE_FUNC inline AlignedBox& extend(const MatrixBase<Derived>& p) 237 { 238 typename internal::nested_eval<Derived,2>::type p_n(p.derived()); 239 m_min = m_min.cwiseMin(p_n); 240 m_max = m_max.cwiseMax(p_n); 241 return *this; 242 } 243 244 /** Extends \c *this such that it contains the box \a b and returns a reference to \c *this. 245 * \sa merged, extend(const MatrixBase&) */ 246 EIGEN_DEVICE_FUNC inline AlignedBox& extend(const AlignedBox& b) 247 { 248 m_min = m_min.cwiseMin(b.m_min); 249 m_max = m_max.cwiseMax(b.m_max); 250 return *this; 251 } 252 253 /** Clamps \c *this by the box \a b and returns a reference to \c *this. 254 * \note If the boxes don't intersect, the resulting box is empty. 255 * \sa intersection(), intersects() */ 256 EIGEN_DEVICE_FUNC inline AlignedBox& clamp(const AlignedBox& b) 257 { 258 m_min = m_min.cwiseMax(b.m_min); 259 m_max = m_max.cwiseMin(b.m_max); 260 return *this; 261 } 262 263 /** Returns an AlignedBox that is the intersection of \a b and \c *this 264 * \note If the boxes don't intersect, the resulting box is empty. 265 * \sa intersects(), clamp, contains() */ 266 EIGEN_DEVICE_FUNC inline AlignedBox intersection(const AlignedBox& b) const 267 {return AlignedBox(m_min.cwiseMax(b.m_min), m_max.cwiseMin(b.m_max)); } 268 269 /** Returns an AlignedBox that is the union of \a b and \c *this. 270 * \note Merging with an empty box may result in a box bigger than \c *this. 271 * \sa extend(const AlignedBox&) */ 272 EIGEN_DEVICE_FUNC inline AlignedBox merged(const AlignedBox& b) const 273 { return AlignedBox(m_min.cwiseMin(b.m_min), m_max.cwiseMax(b.m_max)); } 274 275 /** Translate \c *this by the vector \a t and returns a reference to \c *this. */ 276 template<typename Derived> 277 EIGEN_DEVICE_FUNC inline AlignedBox& translate(const MatrixBase<Derived>& a_t) 278 { 279 const typename internal::nested_eval<Derived,2>::type t(a_t.derived()); 280 m_min += t; 281 m_max += t; 282 return *this; 283 } 284 285 /** \returns a copy of \c *this translated by the vector \a t. */ 286 template<typename Derived> 287 EIGEN_DEVICE_FUNC inline AlignedBox translated(const MatrixBase<Derived>& a_t) const 288 { 289 AlignedBox result(m_min, m_max); 290 result.translate(a_t); 291 return result; 292 } 293 294 /** \returns the squared distance between the point \a p and the box \c *this, 295 * and zero if \a p is inside the box. 296 * \sa exteriorDistance(const MatrixBase&), squaredExteriorDistance(const AlignedBox&) 297 */ 298 template<typename Derived> 299 EIGEN_DEVICE_FUNC inline Scalar squaredExteriorDistance(const MatrixBase<Derived>& p) const; 300 301 /** \returns the squared distance between the boxes \a b and \c *this, 302 * and zero if the boxes intersect. 303 * \sa exteriorDistance(const AlignedBox&), squaredExteriorDistance(const MatrixBase&) 304 */ 305 EIGEN_DEVICE_FUNC inline Scalar squaredExteriorDistance(const AlignedBox& b) const; 306 307 /** \returns the distance between the point \a p and the box \c *this, 308 * and zero if \a p is inside the box. 309 * \sa squaredExteriorDistance(const MatrixBase&), exteriorDistance(const AlignedBox&) 310 */ 311 template<typename Derived> 312 EIGEN_DEVICE_FUNC inline NonInteger exteriorDistance(const MatrixBase<Derived>& p) const 313 { EIGEN_USING_STD(sqrt) return sqrt(NonInteger(squaredExteriorDistance(p))); } 314 315 /** \returns the distance between the boxes \a b and \c *this, 316 * and zero if the boxes intersect. 317 * \sa squaredExteriorDistance(const AlignedBox&), exteriorDistance(const MatrixBase&) 318 */ 319 EIGEN_DEVICE_FUNC inline NonInteger exteriorDistance(const AlignedBox& b) const 320 { EIGEN_USING_STD(sqrt) return sqrt(NonInteger(squaredExteriorDistance(b))); } 321 322 /** 323 * Specialization of transform for pure translation. 324 */ 325 template<int Mode, int Options> 326 EIGEN_DEVICE_FUNC inline void transform( 327 const typename Transform<Scalar, AmbientDimAtCompileTime, Mode, Options>::TranslationType& translation) 328 { 329 this->translate(translation); 330 } 331 332 /** 333 * Transforms this box by \a transform and recomputes it to 334 * still be an axis-aligned box. 335 * 336 * \note This method is provided under BSD license (see the top of this file). 337 */ 338 template<int Mode, int Options> 339 EIGEN_DEVICE_FUNC inline void transform(const Transform<Scalar, AmbientDimAtCompileTime, Mode, Options>& transform) 340 { 341 // Only Affine and Isometry transforms are currently supported. 342 EIGEN_STATIC_ASSERT(Mode == Affine || Mode == AffineCompact || Mode == Isometry, THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS); 343 344 // Method adapted from FCL src/shape/geometric_shapes_utility.cpp#computeBV<AABB, Box>(...) 345 // https://github.com/flexible-collision-library/fcl/blob/fcl-0.4/src/shape/geometric_shapes_utility.cpp#L292 346 // 347 // Here's a nice explanation why it works: https://zeuxcg.org/2010/10/17/aabb-from-obb-with-component-wise-abs/ 348 349 // two times rotated extent 350 const VectorType rotated_extent_2 = transform.linear().cwiseAbs() * sizes(); 351 // two times new center 352 const VectorType rotated_center_2 = transform.linear() * (this->m_max + this->m_min) + 353 Scalar(2) * transform.translation(); 354 355 this->m_max = (rotated_center_2 + rotated_extent_2) / Scalar(2); 356 this->m_min = (rotated_center_2 - rotated_extent_2) / Scalar(2); 357 } 358 359 /** 360 * \returns a copy of \c *this transformed by \a transform and recomputed to 361 * still be an axis-aligned box. 362 */ 363 template<int Mode, int Options> 364 EIGEN_DEVICE_FUNC AlignedBox transformed(const Transform<Scalar, AmbientDimAtCompileTime, Mode, Options>& transform) const 365 { 366 AlignedBox result(m_min, m_max); 367 result.transform(transform); 368 return result; 369 } 370 371 /** \returns \c *this with scalar type casted to \a NewScalarType 372 * 373 * Note that if \a NewScalarType is equal to the current scalar type of \c *this 374 * then this function smartly returns a const reference to \c *this. 375 */ 376 template<typename NewScalarType> 377 EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<AlignedBox, 378 AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type cast() const 379 { 380 return typename internal::cast_return_type<AlignedBox, 381 AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type(*this); 382 } 383 384 /** Copy constructor with scalar type conversion */ 385 template<typename OtherScalarType> 386 EIGEN_DEVICE_FUNC inline explicit AlignedBox(const AlignedBox<OtherScalarType,AmbientDimAtCompileTime>& other) 387 { 388 m_min = (other.min)().template cast<Scalar>(); 389 m_max = (other.max)().template cast<Scalar>(); 390 } 391 392 /** \returns \c true if \c *this is approximately equal to \a other, within the precision 393 * determined by \a prec. 394 * 395 * \sa MatrixBase::isApprox() */ 396 EIGEN_DEVICE_FUNC bool isApprox(const AlignedBox& other, const RealScalar& prec = ScalarTraits::dummy_precision()) const 397 { return m_min.isApprox(other.m_min, prec) && m_max.isApprox(other.m_max, prec); } 398 399 protected: 400 401 VectorType m_min, m_max; 402 }; 403 404 405 406 template<typename Scalar,int AmbientDim> 407 template<typename Derived> 408 EIGEN_DEVICE_FUNC inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance(const MatrixBase<Derived>& a_p) const 409 { 410 typename internal::nested_eval<Derived,2*AmbientDim>::type p(a_p.derived()); 411 Scalar dist2(0); 412 Scalar aux; 413 for (Index k=0; k<dim(); ++k) 414 { 415 if( m_min[k] > p[k] ) 416 { 417 aux = m_min[k] - p[k]; 418 dist2 += aux*aux; 419 } 420 else if( p[k] > m_max[k] ) 421 { 422 aux = p[k] - m_max[k]; 423 dist2 += aux*aux; 424 } 425 } 426 return dist2; 427 } 428 429 template<typename Scalar,int AmbientDim> 430 EIGEN_DEVICE_FUNC inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance(const AlignedBox& b) const 431 { 432 Scalar dist2(0); 433 Scalar aux; 434 for (Index k=0; k<dim(); ++k) 435 { 436 if( m_min[k] > b.m_max[k] ) 437 { 438 aux = m_min[k] - b.m_max[k]; 439 dist2 += aux*aux; 440 } 441 else if( b.m_min[k] > m_max[k] ) 442 { 443 aux = b.m_min[k] - m_max[k]; 444 dist2 += aux*aux; 445 } 446 } 447 return dist2; 448 } 449 450 /** \defgroup alignedboxtypedefs Global aligned box typedefs 451 * 452 * \ingroup Geometry_Module 453 * 454 * Eigen defines several typedef shortcuts for most common aligned box types. 455 * 456 * The general patterns are the following: 457 * 458 * \c AlignedBoxSizeType where \c Size can be \c 1, \c 2,\c 3,\c 4 for fixed size boxes or \c X for dynamic size, 459 * and where \c Type can be \c i for integer, \c f for float, \c d for double. 460 * 461 * For example, \c AlignedBox3d is a fixed-size 3x3 aligned box type of doubles, and \c AlignedBoxXf is a dynamic-size aligned box of floats. 462 * 463 * \sa class AlignedBox 464 */ 465 466 #define EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix) \ 467 /** \ingroup alignedboxtypedefs */ \ 468 typedef AlignedBox<Type, Size> AlignedBox##SizeSuffix##TypeSuffix; 469 470 #define EIGEN_MAKE_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \ 471 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 1, 1) \ 472 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 2, 2) \ 473 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 3, 3) \ 474 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 4, 4) \ 475 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Dynamic, X) 476 477 EIGEN_MAKE_TYPEDEFS_ALL_SIZES(int, i) 478 EIGEN_MAKE_TYPEDEFS_ALL_SIZES(float, f) 479 EIGEN_MAKE_TYPEDEFS_ALL_SIZES(double, d) 480 481 #undef EIGEN_MAKE_TYPEDEFS_ALL_SIZES 482 #undef EIGEN_MAKE_TYPEDEFS 483 484 } // end namespace Eigen 485 486 #endif // EIGEN_ALIGNEDBOX_H