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