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 (at) 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 #ifndef EIGEN_ALIGNEDBOX_H 11 #define EIGEN_ALIGNEDBOX_H 12 13 namespace Eigen { 14 15 /** \geometry_module \ingroup Geometry_Module 16 * 17 * 18 * \class AlignedBox 19 * 20 * \brief An axis aligned box 21 * 22 * \tparam _Scalar the type of the scalar coefficients 23 * \tparam _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic. 24 * 25 * This class represents an axis aligned box as a pair of the minimal and maximal corners. 26 * \warning The result of most methods is undefined when applied to an empty box. You can check for empty boxes using isEmpty(). 27 * \sa alignedboxtypedefs 28 */ 29 template <typename _Scalar, int _AmbientDim> 30 class AlignedBox 31 { 32 public: 33 EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim) 34 enum { AmbientDimAtCompileTime = _AmbientDim }; 35 typedef _Scalar Scalar; 36 typedef NumTraits<Scalar> ScalarTraits; 37 typedef DenseIndex Index; 38 typedef typename ScalarTraits::Real RealScalar; 39 typedef typename ScalarTraits::NonInteger NonInteger; 40 typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType; 41 42 /** Define constants to name the corners of a 1D, 2D or 3D axis aligned bounding box */ 43 enum CornerType 44 { 45 /** 1D names @{ */ 46 Min=0, Max=1, 47 /** @} */ 48 49 /** Identifier for 2D corner @{ */ 50 BottomLeft=0, BottomRight=1, 51 TopLeft=2, TopRight=3, 52 /** @} */ 53 54 /** Identifier for 3D corner @{ */ 55 BottomLeftFloor=0, BottomRightFloor=1, 56 TopLeftFloor=2, TopRightFloor=3, 57 BottomLeftCeil=4, BottomRightCeil=5, 58 TopLeftCeil=6, TopRightCeil=7 59 /** @} */ 60 }; 61 62 63 /** Default constructor initializing a null box. */ 64 inline AlignedBox() 65 { if (AmbientDimAtCompileTime!=Dynamic) setEmpty(); } 66 67 /** Constructs a null box with \a _dim the dimension of the ambient space. */ 68 inline explicit AlignedBox(Index _dim) : m_min(_dim), m_max(_dim) 69 { setEmpty(); } 70 71 /** Constructs a box with extremities \a _min and \a _max. 72 * \warning If either component of \a _min is larger than the same component of \a _max, the constructed box is empty. */ 73 template<typename OtherVectorType1, typename OtherVectorType2> 74 inline AlignedBox(const OtherVectorType1& _min, const OtherVectorType2& _max) : m_min(_min), m_max(_max) {} 75 76 /** Constructs a box containing a single point \a p. */ 77 template<typename Derived> 78 inline explicit AlignedBox(const MatrixBase<Derived>& p) : m_min(p), m_max(m_min) 79 { } 80 81 ~AlignedBox() {} 82 83 /** \returns the dimension in which the box holds */ 84 inline Index dim() const { return AmbientDimAtCompileTime==Dynamic ? m_min.size() : Index(AmbientDimAtCompileTime); } 85 86 /** \deprecated use isEmpty() */ 87 inline bool isNull() const { return isEmpty(); } 88 89 /** \deprecated use setEmpty() */ 90 inline void setNull() { setEmpty(); } 91 92 /** \returns true if the box is empty. 93 * \sa setEmpty */ 94 inline bool isEmpty() const { return (m_min.array() > m_max.array()).any(); } 95 96 /** Makes \c *this an empty box. 97 * \sa isEmpty */ 98 inline void setEmpty() 99 { 100 m_min.setConstant( ScalarTraits::highest() ); 101 m_max.setConstant( ScalarTraits::lowest() ); 102 } 103 104 /** \returns the minimal corner */ 105 inline const VectorType& (min)() const { return m_min; } 106 /** \returns a non const reference to the minimal corner */ 107 inline VectorType& (min)() { return m_min; } 108 /** \returns the maximal corner */ 109 inline const VectorType& (max)() const { return m_max; } 110 /** \returns a non const reference to the maximal corner */ 111 inline VectorType& (max)() { return m_max; } 112 113 /** \returns the center of the box */ 114 inline const CwiseUnaryOp<internal::scalar_quotient1_op<Scalar>, 115 const CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const VectorType, const VectorType> > 116 center() const 117 { return (m_min+m_max)/2; } 118 119 /** \returns the lengths of the sides of the bounding box. 120 * Note that this function does not get the same 121 * result for integral or floating scalar types: see 122 */ 123 inline const CwiseBinaryOp< internal::scalar_difference_op<Scalar>, const VectorType, const VectorType> sizes() const 124 { return m_max - m_min; } 125 126 /** \returns the volume of the bounding box */ 127 inline Scalar volume() const 128 { return sizes().prod(); } 129 130 /** \returns an expression for the bounding box diagonal vector 131 * if the length of the diagonal is needed: diagonal().norm() 132 * will provide it. 133 */ 134 inline CwiseBinaryOp< internal::scalar_difference_op<Scalar>, const VectorType, const VectorType> diagonal() const 135 { return sizes(); } 136 137 /** \returns the vertex of the bounding box at the corner defined by 138 * the corner-id corner. It works only for a 1D, 2D or 3D bounding box. 139 * For 1D bounding boxes corners are named by 2 enum constants: 140 * BottomLeft and BottomRight. 141 * For 2D bounding boxes, corners are named by 4 enum constants: 142 * BottomLeft, BottomRight, TopLeft, TopRight. 143 * For 3D bounding boxes, the following names are added: 144 * BottomLeftCeil, BottomRightCeil, TopLeftCeil, TopRightCeil. 145 */ 146 inline VectorType corner(CornerType corner) const 147 { 148 EIGEN_STATIC_ASSERT(_AmbientDim <= 3, THIS_METHOD_IS_ONLY_FOR_VECTORS_OF_A_SPECIFIC_SIZE); 149 150 VectorType res; 151 152 Index mult = 1; 153 for(Index d=0; d<dim(); ++d) 154 { 155 if( mult & corner ) res[d] = m_max[d]; 156 else res[d] = m_min[d]; 157 mult *= 2; 158 } 159 return res; 160 } 161 162 /** \returns a random point inside the bounding box sampled with 163 * a uniform distribution */ 164 inline VectorType sample() const 165 { 166 VectorType r; 167 for(Index d=0; d<dim(); ++d) 168 { 169 if(!ScalarTraits::IsInteger) 170 { 171 r[d] = m_min[d] + (m_max[d]-m_min[d]) 172 * internal::random<Scalar>(Scalar(0), Scalar(1)); 173 } 174 else 175 r[d] = internal::random(m_min[d], m_max[d]); 176 } 177 return r; 178 } 179 180 /** \returns true if the point \a p is inside the box \c *this. */ 181 template<typename Derived> 182 inline bool contains(const MatrixBase<Derived>& p) const 183 { 184 typename internal::nested<Derived,2>::type p_n(p.derived()); 185 return (m_min.array()<=p_n.array()).all() && (p_n.array()<=m_max.array()).all(); 186 } 187 188 /** \returns true if the box \a b is entirely inside the box \c *this. */ 189 inline bool contains(const AlignedBox& b) const 190 { return (m_min.array()<=(b.min)().array()).all() && ((b.max)().array()<=m_max.array()).all(); } 191 192 /** \returns true if the box \a b is intersecting the box \c *this. 193 * \sa intersection, clamp */ 194 inline bool intersects(const AlignedBox& b) const 195 { return (m_min.array()<=(b.max)().array()).all() && ((b.min)().array()<=m_max.array()).all(); } 196 197 /** Extends \c *this such that it contains the point \a p and returns a reference to \c *this. 198 * \sa extend(const AlignedBox&) */ 199 template<typename Derived> 200 inline AlignedBox& extend(const MatrixBase<Derived>& p) 201 { 202 typename internal::nested<Derived,2>::type p_n(p.derived()); 203 m_min = m_min.cwiseMin(p_n); 204 m_max = m_max.cwiseMax(p_n); 205 return *this; 206 } 207 208 /** Extends \c *this such that it contains the box \a b and returns a reference to \c *this. 209 * \sa merged, extend(const MatrixBase&) */ 210 inline AlignedBox& extend(const AlignedBox& b) 211 { 212 m_min = m_min.cwiseMin(b.m_min); 213 m_max = m_max.cwiseMax(b.m_max); 214 return *this; 215 } 216 217 /** Clamps \c *this by the box \a b and returns a reference to \c *this. 218 * \note If the boxes don't intersect, the resulting box is empty. 219 * \sa intersection(), intersects() */ 220 inline AlignedBox& clamp(const AlignedBox& b) 221 { 222 m_min = m_min.cwiseMax(b.m_min); 223 m_max = m_max.cwiseMin(b.m_max); 224 return *this; 225 } 226 227 /** Returns an AlignedBox that is the intersection of \a b and \c *this 228 * \note If the boxes don't intersect, the resulting box is empty. 229 * \sa intersects(), clamp, contains() */ 230 inline AlignedBox intersection(const AlignedBox& b) const 231 {return AlignedBox(m_min.cwiseMax(b.m_min), m_max.cwiseMin(b.m_max)); } 232 233 /** Returns an AlignedBox that is the union of \a b and \c *this. 234 * \note Merging with an empty box may result in a box bigger than \c *this. 235 * \sa extend(const AlignedBox&) */ 236 inline AlignedBox merged(const AlignedBox& b) const 237 { return AlignedBox(m_min.cwiseMin(b.m_min), m_max.cwiseMax(b.m_max)); } 238 239 /** Translate \c *this by the vector \a t and returns a reference to \c *this. */ 240 template<typename Derived> 241 inline AlignedBox& translate(const MatrixBase<Derived>& a_t) 242 { 243 const typename internal::nested<Derived,2>::type t(a_t.derived()); 244 m_min += t; 245 m_max += t; 246 return *this; 247 } 248 249 /** \returns the squared distance between the point \a p and the box \c *this, 250 * and zero if \a p is inside the box. 251 * \sa exteriorDistance(const MatrixBase&), squaredExteriorDistance(const AlignedBox&) 252 */ 253 template<typename Derived> 254 inline Scalar squaredExteriorDistance(const MatrixBase<Derived>& p) const; 255 256 /** \returns the squared distance between the boxes \a b and \c *this, 257 * and zero if the boxes intersect. 258 * \sa exteriorDistance(const AlignedBox&), squaredExteriorDistance(const MatrixBase&) 259 */ 260 inline Scalar squaredExteriorDistance(const AlignedBox& b) const; 261 262 /** \returns the distance between the point \a p and the box \c *this, 263 * and zero if \a p is inside the box. 264 * \sa squaredExteriorDistance(const MatrixBase&), exteriorDistance(const AlignedBox&) 265 */ 266 template<typename Derived> 267 inline NonInteger exteriorDistance(const MatrixBase<Derived>& p) const 268 { using std::sqrt; return sqrt(NonInteger(squaredExteriorDistance(p))); } 269 270 /** \returns the distance between the boxes \a b and \c *this, 271 * and zero if the boxes intersect. 272 * \sa squaredExteriorDistance(const AlignedBox&), exteriorDistance(const MatrixBase&) 273 */ 274 inline NonInteger exteriorDistance(const AlignedBox& b) const 275 { using std::sqrt; return sqrt(NonInteger(squaredExteriorDistance(b))); } 276 277 /** \returns \c *this with scalar type casted to \a NewScalarType 278 * 279 * Note that if \a NewScalarType is equal to the current scalar type of \c *this 280 * then this function smartly returns a const reference to \c *this. 281 */ 282 template<typename NewScalarType> 283 inline typename internal::cast_return_type<AlignedBox, 284 AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type cast() const 285 { 286 return typename internal::cast_return_type<AlignedBox, 287 AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type(*this); 288 } 289 290 /** Copy constructor with scalar type conversion */ 291 template<typename OtherScalarType> 292 inline explicit AlignedBox(const AlignedBox<OtherScalarType,AmbientDimAtCompileTime>& other) 293 { 294 m_min = (other.min)().template cast<Scalar>(); 295 m_max = (other.max)().template cast<Scalar>(); 296 } 297 298 /** \returns \c true if \c *this is approximately equal to \a other, within the precision 299 * determined by \a prec. 300 * 301 * \sa MatrixBase::isApprox() */ 302 bool isApprox(const AlignedBox& other, const RealScalar& prec = ScalarTraits::dummy_precision()) const 303 { return m_min.isApprox(other.m_min, prec) && m_max.isApprox(other.m_max, prec); } 304 305 protected: 306 307 VectorType m_min, m_max; 308 }; 309 310 311 312 template<typename Scalar,int AmbientDim> 313 template<typename Derived> 314 inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance(const MatrixBase<Derived>& a_p) const 315 { 316 typename internal::nested<Derived,2*AmbientDim>::type p(a_p.derived()); 317 Scalar dist2(0); 318 Scalar aux; 319 for (Index k=0; k<dim(); ++k) 320 { 321 if( m_min[k] > p[k] ) 322 { 323 aux = m_min[k] - p[k]; 324 dist2 += aux*aux; 325 } 326 else if( p[k] > m_max[k] ) 327 { 328 aux = p[k] - m_max[k]; 329 dist2 += aux*aux; 330 } 331 } 332 return dist2; 333 } 334 335 template<typename Scalar,int AmbientDim> 336 inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance(const AlignedBox& b) const 337 { 338 Scalar dist2(0); 339 Scalar aux; 340 for (Index k=0; k<dim(); ++k) 341 { 342 if( m_min[k] > b.m_max[k] ) 343 { 344 aux = m_min[k] - b.m_max[k]; 345 dist2 += aux*aux; 346 } 347 else if( b.m_min[k] > m_max[k] ) 348 { 349 aux = b.m_min[k] - m_max[k]; 350 dist2 += aux*aux; 351 } 352 } 353 return dist2; 354 } 355 356 /** \defgroup alignedboxtypedefs Global aligned box typedefs 357 * 358 * \ingroup Geometry_Module 359 * 360 * Eigen defines several typedef shortcuts for most common aligned box types. 361 * 362 * The general patterns are the following: 363 * 364 * \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, 365 * and where \c Type can be \c i for integer, \c f for float, \c d for double. 366 * 367 * 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. 368 * 369 * \sa class AlignedBox 370 */ 371 372 #define EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix) \ 373 /** \ingroup alignedboxtypedefs */ \ 374 typedef AlignedBox<Type, Size> AlignedBox##SizeSuffix##TypeSuffix; 375 376 #define EIGEN_MAKE_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \ 377 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 1, 1) \ 378 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 2, 2) \ 379 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 3, 3) \ 380 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 4, 4) \ 381 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Dynamic, X) 382 383 EIGEN_MAKE_TYPEDEFS_ALL_SIZES(int, i) 384 EIGEN_MAKE_TYPEDEFS_ALL_SIZES(float, f) 385 EIGEN_MAKE_TYPEDEFS_ALL_SIZES(double, d) 386 387 #undef EIGEN_MAKE_TYPEDEFS_ALL_SIZES 388 #undef EIGEN_MAKE_TYPEDEFS 389 390 } // end namespace Eigen 391 392 #endif // EIGEN_ALIGNEDBOX_H 393
