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AlignedBox.h
00001 // This file is part of Eigen, a lightweight C++ template library 00002 // for linear algebra. 00003 // 00004 // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr> 00005 // 00006 // This Source Code Form is subject to the terms of the Mozilla 00007 // Public License v. 2.0. If a copy of the MPL was not distributed 00008 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 00009 00010 #ifndef EIGEN_ALIGNEDBOX_H 00011 #define EIGEN_ALIGNEDBOX_H 00012 00013 namespace Eigen { 00014 00015 /** \geometry_module \ingroup Geometry_Module 00016 * 00017 * 00018 * \class AlignedBox 00019 * 00020 * \brief An axis aligned box 00021 * 00022 * \tparam _Scalar the type of the scalar coefficients 00023 * \tparam _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic. 00024 * 00025 * This class represents an axis aligned box as a pair of the minimal and maximal corners. 00026 * \warning The result of most methods is undefined when applied to an empty box. You can check for empty boxes using isEmpty(). 00027 * \sa alignedboxtypedefs 00028 */ 00029 template <typename _Scalar, int _AmbientDim> 00030 class AlignedBox 00031 { 00032 public: 00033 EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim) 00034 enum { AmbientDimAtCompileTime = _AmbientDim }; 00035 typedef _Scalar Scalar; 00036 typedef NumTraits<Scalar> ScalarTraits; 00037 typedef DenseIndex Index; 00038 typedef typename ScalarTraits::Real RealScalar; 00039 typedef typename ScalarTraits::NonInteger NonInteger; 00040 typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType ; 00041 00042 /** Define constants to name the corners of a 1D, 2D or 3D axis aligned bounding box */ 00043 enum CornerType 00044 { 00045 /** 1D names @{ */ 00046 Min=0, Max=1, 00047 /** @} */ 00048 00049 /** Identifier for 2D corner @{ */ 00050 BottomLeft=0, BottomRight=1, 00051 TopLeft=2, TopRight=3, 00052 /** @} */ 00053 00054 /** Identifier for 3D corner @{ */ 00055 BottomLeftFloor=0, BottomRightFloor=1, 00056 TopLeftFloor=2, TopRightFloor=3, 00057 BottomLeftCeil=4, BottomRightCeil=5, 00058 TopLeftCeil=6, TopRightCeil=7 00059 /** @} */ 00060 }; 00061 00062 00063 /** Default constructor initializing a null box. */ 00064 inline AlignedBox() 00065 { if (AmbientDimAtCompileTime!=Dynamic) setEmpty(); } 00066 00067 /** Constructs a null box with \a _dim the dimension of the ambient space. */ 00068 inline explicit AlignedBox(Index _dim) : m_min(_dim), m_max(_dim) 00069 { setEmpty(); } 00070 00071 /** Constructs a box with extremities \a _min and \a _max. 00072 * \warning If either component of \a _min is larger than the same component of \a _max, the constructed box is empty. */ 00073 template<typename OtherVectorType1, typename OtherVectorType2> 00074 inline AlignedBox(const OtherVectorType1& _min, const OtherVectorType2& _max) : m_min(_min), m_max(_max) {} 00075 00076 /** Constructs a box containing a single point \a p. */ 00077 template<typename Derived> 00078 inline explicit AlignedBox(const MatrixBase<Derived>& p) : m_min(p), m_max(m_min) 00079 { } 00080 00081 ~AlignedBox () {} 00082 00083 /** \returns the dimension in which the box holds */ 00084 inline Index dim () const { return AmbientDimAtCompileTime==Dynamic ? m_min.size() : Index(AmbientDimAtCompileTime); } 00085 00086 /** \deprecated use isEmpty() */ 00087 inline bool isNull () const { return isEmpty (); } 00088 00089 /** \deprecated use setEmpty() */ 00090 inline void setNull () { setEmpty(); } 00091 00092 /** \returns true if the box is empty. 00093 * \sa setEmpty */ 00094 inline bool isEmpty () const { return (m_min.array() > m_max.array()).any(); } 00095 00096 /** Makes \c *this an empty box. 00097 * \sa isEmpty */ 00098 inline void setEmpty() 00099 { 00100 m_min.setConstant( ScalarTraits::highest() ); 00101 m_max.setConstant( ScalarTraits::lowest() ); 00102 } 00103 00104 /** \returns the minimal corner */ 00105 inline const VectorType & (min )() const { return m_min; } 00106 /** \returns a non const reference to the minimal corner */ 00107 inline VectorType & (min )() { return m_min; } 00108 /** \returns the maximal corner */ 00109 inline const VectorType & (max )() const { return m_max; } 00110 /** \returns a non const reference to the maximal corner */ 00111 inline VectorType & (max )() { return m_max; } 00112 00113 /** \returns the center of the box */ 00114 inline const CwiseUnaryOp<internal::scalar_quotient1_op<Scalar>, 00115 const CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const VectorType, const VectorType> > 00116 center () const 00117 { return (m_min+m_max)/2; } 00118 00119 /** \returns the lengths of the sides of the bounding box. 00120 * Note that this function does not get the same 00121 * result for integral or floating scalar types: see 00122 */ 00123 inline const CwiseBinaryOp< internal::scalar_difference_op<Scalar>, const VectorType , const VectorType > sizes () const 00124 { return m_max - m_min; } 00125 00126 /** \returns the volume of the bounding box */ 00127 inline Scalar volume () const 00128 { return sizes ().prod(); } 00129 00130 /** \returns an expression for the bounding box diagonal vector 00131 * if the length of the diagonal is needed: diagonal().norm() 00132 * will provide it. 00133 */ 00134 inline CwiseBinaryOp< internal::scalar_difference_op<Scalar>, const VectorType , const VectorType > diagonal () const 00135 { return sizes (); } 00136 00137 /** \returns the vertex of the bounding box at the corner defined by 00138 * the corner-id corner. It works only for a 1D, 2D or 3D bounding box. 00139 * For 1D bounding boxes corners are named by 2 enum constants: 00140 * BottomLeft and BottomRight. 00141 * For 2D bounding boxes, corners are named by 4 enum constants: 00142 * BottomLeft, BottomRight, TopLeft, TopRight. 00143 * For 3D bounding boxes, the following names are added: 00144 * BottomLeftCeil, BottomRightCeil, TopLeftCeil, TopRightCeil. 00145 */ 00146 inline VectorType corner (CornerType corner ) const 00147 { 00148 EIGEN_STATIC_ASSERT(_AmbientDim <= 3, THIS_METHOD_IS_ONLY_FOR_VECTORS_OF_A_SPECIFIC_SIZE); 00149 00150 VectorType res; 00151 00152 Index mult = 1; 00153 for(Index d=0; d<dim (); ++d) 00154 { 00155 if( mult & corner ) res[d] = m_max[d]; 00156 else res[d] = m_min[d]; 00157 mult *= 2; 00158 } 00159 return res; 00160 } 00161 00162 /** \returns a random point inside the bounding box sampled with 00163 * a uniform distribution */ 00164 inline VectorType sample () const 00165 { 00166 VectorType r(dim ()); 00167 for(Index d=0; d<dim (); ++d) 00168 { 00169 if(!ScalarTraits::IsInteger) 00170 { 00171 r[d] = m_min[d] + (m_max[d]-m_min[d]) 00172 * internal::random<Scalar>(Scalar(0), Scalar(1)); 00173 } 00174 else 00175 r[d] = internal::random(m_min[d], m_max[d]); 00176 } 00177 return r; 00178 } 00179 00180 /** \returns true if the point \a p is inside the box \c *this. */ 00181 template<typename Derived> 00182 inline bool contains (const MatrixBase<Derived>& p) const 00183 { 00184 typename internal::nested<Derived,2>::type p_n(p.derived()); 00185 return (m_min.array()<=p_n.array()).all() && (p_n.array()<=m_max.array()).all(); 00186 } 00187 00188 /** \returns true if the box \a b is entirely inside the box \c *this. */ 00189 inline bool contains (const AlignedBox & b) const 00190 { return (m_min.array()<=(b.min )().array()).all() && ((b.max )().array()<=m_max.array()).all(); } 00191 00192 /** \returns true if the box \a b is intersecting the box \c *this. 00193 * \sa intersection, clamp */ 00194 inline bool intersects (const AlignedBox & b) const 00195 { return (m_min.array()<=(b.max )().array()).all() && ((b.min )().array()<=m_max.array()).all(); } 00196 00197 /** Extends \c *this such that it contains the point \a p and returns a reference to \c *this. 00198 * \sa extend(const AlignedBox&) */ 00199 template<typename Derived> 00200 inline AlignedBox & extend(const MatrixBase<Derived>& p) 00201 { 00202 typename internal::nested<Derived,2>::type p_n(p.derived()); 00203 m_min = m_min.cwiseMin(p_n); 00204 m_max = m_max.cwiseMax(p_n); 00205 return *this; 00206 } 00207 00208 /** Extends \c *this such that it contains the box \a b and returns a reference to \c *this. 00209 * \sa merged, extend(const MatrixBase&) */ 00210 inline AlignedBox & extend(const AlignedBox & b) 00211 { 00212 m_min = m_min.cwiseMin(b.m_min); 00213 m_max = m_max.cwiseMax(b.m_max); 00214 return *this; 00215 } 00216 00217 /** Clamps \c *this by the box \a b and returns a reference to \c *this. 00218 * \note If the boxes don't intersect, the resulting box is empty. 00219 * \sa intersection(), intersects() */ 00220 inline AlignedBox & clamp(const AlignedBox & b) 00221 { 00222 m_min = m_min.cwiseMax(b.m_min); 00223 m_max = m_max.cwiseMin(b.m_max); 00224 return *this; 00225 } 00226 00227 /** Returns an AlignedBox that is the intersection of \a b and \c *this 00228 * \note If the boxes don't intersect, the resulting box is empty. 00229 * \sa intersects(), clamp, contains() */ 00230 inline AlignedBox intersection(const AlignedBox & b) const 00231 {return AlignedBox(m_min.cwiseMax(b.m_min), m_max.cwiseMin(b.m_max)); } 00232 00233 /** Returns an AlignedBox that is the union of \a b and \c *this. 00234 * \note Merging with an empty box may result in a box bigger than \c *this. 00235 * \sa extend(const AlignedBox&) */ 00236 inline AlignedBox merged(const AlignedBox & b) const 00237 { return AlignedBox(m_min.cwiseMin(b.m_min), m_max.cwiseMax(b.m_max)); } 00238 00239 /** Translate \c *this by the vector \a t and returns a reference to \c *this. */ 00240 template<typename Derived> 00241 inline AlignedBox & translate(const MatrixBase<Derived>& a_t) 00242 { 00243 const typename internal::nested<Derived,2>::type t(a_t.derived()); 00244 m_min += t; 00245 m_max += t; 00246 return *this; 00247 } 00248 00249 /** \returns the squared distance between the point \a p and the box \c *this, 00250 * and zero if \a p is inside the box. 00251 * \sa exteriorDistance(const MatrixBase&), squaredExteriorDistance(const AlignedBox&) 00252 */ 00253 template<typename Derived> 00254 inline Scalar squaredExteriorDistance (const MatrixBase<Derived>& p) const; 00255 00256 /** \returns the squared distance between the boxes \a b and \c *this, 00257 * and zero if the boxes intersect. 00258 * \sa exteriorDistance(const AlignedBox&), squaredExteriorDistance(const MatrixBase&) 00259 */ 00260 inline Scalar squaredExteriorDistance (const AlignedBox & b) const; 00261 00262 /** \returns the distance between the point \a p and the box \c *this, 00263 * and zero if \a p is inside the box. 00264 * \sa squaredExteriorDistance(const MatrixBase&), exteriorDistance(const AlignedBox&) 00265 */ 00266 template<typename Derived> 00267 inline NonInteger exteriorDistance (const MatrixBase<Derived>& p) const 00268 { using std::sqrt; return sqrt(NonInteger(squaredExteriorDistance (p))); } 00269 00270 /** \returns the distance between the boxes \a b and \c *this, 00271 * and zero if the boxes intersect. 00272 * \sa squaredExteriorDistance(const AlignedBox&), exteriorDistance(const MatrixBase&) 00273 */ 00274 inline NonInteger exteriorDistance (const AlignedBox & b) const 00275 { using std::sqrt; return sqrt(NonInteger(squaredExteriorDistance (b))); } 00276 00277 /** \returns \c *this with scalar type casted to \a NewScalarType 00278 * 00279 * Note that if \a NewScalarType is equal to the current scalar type of \c *this 00280 * then this function smartly returns a const reference to \c *this. 00281 */ 00282 template<typename NewScalarType> 00283 inline typename internal::cast_return_type<AlignedBox, 00284 AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type cast () const 00285 { 00286 return typename internal::cast_return_type<AlignedBox, 00287 AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type(*this); 00288 } 00289 00290 /** Copy constructor with scalar type conversion */ 00291 template<typename OtherScalarType> 00292 inline explicit AlignedBox(const AlignedBox<OtherScalarType,AmbientDimAtCompileTime> & other) 00293 { 00294 m_min = (other.min )().template cast<Scalar>(); 00295 m_max = (other.max )().template cast<Scalar>(); 00296 } 00297 00298 /** \returns \c true if \c *this is approximately equal to \a other, within the precision 00299 * determined by \a prec. 00300 * 00301 * \sa MatrixBase::isApprox() */ 00302 bool isApprox (const AlignedBox & other, const RealScalar& prec = ScalarTraits::dummy_precision()) const 00303 { return m_min.isApprox(other.m_min, prec) && m_max.isApprox(other.m_max, prec); } 00304 00305 protected: 00306 00307 VectorType m_min, m_max; 00308 }; 00309 00310 00311 00312 template<typename Scalar,int AmbientDim> 00313 template<typename Derived> 00314 inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance (const MatrixBase<Derived>& a_p) const 00315 { 00316 typename internal::nested<Derived,2*AmbientDim>::type p(a_p.derived()); 00317 Scalar dist2(0); 00318 Scalar aux; 00319 for (Index k=0; k<dim(); ++k) 00320 { 00321 if( m_min[k] > p[k] ) 00322 { 00323 aux = m_min[k] - p[k]; 00324 dist2 += aux*aux; 00325 } 00326 else if( p[k] > m_max[k] ) 00327 { 00328 aux = p[k] - m_max[k]; 00329 dist2 += aux*aux; 00330 } 00331 } 00332 return dist2; 00333 } 00334 00335 template<typename Scalar,int AmbientDim> 00336 inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance (const AlignedBox & b) const 00337 { 00338 Scalar dist2(0); 00339 Scalar aux; 00340 for (Index k=0; k<dim(); ++k) 00341 { 00342 if( m_min[k] > b.m_max[k] ) 00343 { 00344 aux = m_min[k] - b.m_max[k]; 00345 dist2 += aux*aux; 00346 } 00347 else if( b.m_min[k] > m_max[k] ) 00348 { 00349 aux = b.m_min[k] - m_max[k]; 00350 dist2 += aux*aux; 00351 } 00352 } 00353 return dist2; 00354 } 00355 00356 /** \defgroup alignedboxtypedefs Global aligned box typedefs 00357 * 00358 * \ingroup Geometry_Module 00359 * 00360 * Eigen defines several typedef shortcuts for most common aligned box types. 00361 * 00362 * The general patterns are the following: 00363 * 00364 * \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, 00365 * and where \c Type can be \c i for integer, \c f for float, \c d for double. 00366 * 00367 * 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. 00368 * 00369 * \sa class AlignedBox 00370 */ 00371 00372 #define EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix) \ 00373 /** \ingroup alignedboxtypedefs */ \ 00374 typedef AlignedBox<Type, Size> AlignedBox##SizeSuffix##TypeSuffix; 00375 00376 #define EIGEN_MAKE_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \ 00377 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 1, 1) \ 00378 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 2, 2) \ 00379 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 3, 3) \ 00380 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 4, 4) \ 00381 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Dynamic, X) 00382 00383 EIGEN_MAKE_TYPEDEFS_ALL_SIZES(int, i) 00384 EIGEN_MAKE_TYPEDEFS_ALL_SIZES(float, f) 00385 EIGEN_MAKE_TYPEDEFS_ALL_SIZES(double, d) 00386 00387 #undef EIGEN_MAKE_TYPEDEFS_ALL_SIZES 00388 #undef EIGEN_MAKE_TYPEDEFS 00389 00390 } // end namespace Eigen 00391 00392 #endif // EIGEN_ALIGNEDBOX_H
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