Improved patch from Manuel Yguel:

Enhance AlignedBox to accept integral types and add some usefull methods: diagonal, volume, sample.

Eigen/src/Core/NumTraits.h

@@ -54,8 +54,8 @@ template<typename T> struct NumTraits;
 template<typename T> struct ei_default_float_numtraits
   : std::numeric_limits<T>
 {
-  inline static T higest() { return  std::numeric_limits<T>::max(); }
+  inline static T highest() { return  std::numeric_limits<T>::max(); }
-  inline static T lowest() { return -std::numeric_limits<T>::max(); }
+  inline static T lowest()  { return -std::numeric_limits<T>::max(); }
 };
 
 template<typename T> struct ei_default_integral_numtraits

Eigen/src/Geometry/AlignedBox.h

@@ -43,37 +43,70 @@ class AlignedBox
 public:
 EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
   enum { AmbientDimAtCompileTime = _AmbientDim };
-  typedef _Scalar Scalar;
+  typedef _Scalar                                   Scalar;
-  typedef typename NumTraits<Scalar>::Real RealScalar;
+  typedef NumTraits<Scalar>                         ScalarTraits;
-  typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType;
+  typedef typename ScalarTraits::Real               RealScalar;
+  typedef typename ScalarTraits::FloatingPoint      FloatingPoint;
+  typedef Matrix<Scalar,AmbientDimAtCompileTime,1>  VectorType;
+
+  /** Define constants to name the corners of a 1D, 2D or 3D axis aligned bounding box */
+  enum CornerType
+  {
+    /** 1D names */
+    Min=0, Max=1,
+
+    /** Added names for 2D */
+    BottomLeft=0, BottomRight=1,
+    TopLeft=2, TopRight=3,
+
+    /** Added names for 3D */
+    BottomLeftFloor=0, BottomRightFloor=1,
+    TopLeftFloor=2, TopRightFloor=3,
+    BottomLeftCeil=4, BottomRightCeil=5,
+    TopLeftCeil=6, TopRightCeil=7
+  };
+
 
   /** Default constructor initializing a null box. */
   inline explicit AlignedBox()
-  { if (AmbientDimAtCompileTime!=Dynamic) setNull(); }
+  { if (AmbientDimAtCompileTime!=Dynamic) setEmpty(); }
 
   /** Constructs a null box with \a _dim the dimension of the ambient space. */
   inline explicit AlignedBox(int _dim) : m_min(_dim), m_max(_dim)
-  { setNull(); }
+  { setEmpty(); }
 
   /** Constructs a box with extremities \a _min and \a _max. */
-  inline AlignedBox(const VectorType& _min, const VectorType& _max) : m_min(_min), m_max(_max) {}
+  template<typename OtherVectorType1, typename OtherVectorType2>
+  inline AlignedBox(const OtherVectorType1& _min, const OtherVectorType2& _max) : m_min(_min), m_max(_max) {}
 
   /** Constructs a box containing a single point \a p. */
-  inline explicit AlignedBox(const VectorType& p) : m_min(p), m_max(p) {}
+  template<typename Derived>
+  inline explicit AlignedBox(const MatrixBase<Derived>& a_p)
+  {
+    const typename ei_nested<Derived,2>::type p(a_p.derived());
+    m_min = p;
+    m_max = p;
+  }
 
   ~AlignedBox() {}
 
   /** \returns the dimension in which the box holds */
   inline int dim() const { return AmbientDimAtCompileTime==Dynamic ? m_min.size()-1 : AmbientDimAtCompileTime; }
 
-  /** \returns true if the box is null, i.e, empty. */
+  /** \deprecated use isEmpty */
-  inline bool isNull() const { return (m_min.array() > m_max.array()).any(); }
+  inline bool isNull() const { return isEmpty(); }
 
-  /** Makes \c *this a null/empty box. */
+  /** \deprecated use setEmpty */
-  inline void setNull()
+  inline void setNull() { setEmpty(); }
+
+  /** \returns true if the box is empty. */
+  inline bool isEmpty() const { return (m_min.cwise() > m_max).any(); }
+
+  /** Makes \c *this an empty box. */
+  inline void setEmpty()
   {
-    m_min.setConstant( std::numeric_limits<Scalar>::max());
+    m_min.setConstant( ScalarTraits::highest() );
-    m_max.setConstant(-std::numeric_limits<Scalar>::max());
+    m_max.setConstant( ScalarTraits::lowest() );
   }
 
   /** \returns the minimal corner */
@@ -86,45 +119,135 @@ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
   inline VectorType& max() { return m_max; }
 
   /** \returns the center of the box */
-  inline VectorType center() const { return (m_min + m_max) / 2; }
+  inline const CwiseUnaryOp<ei_scalar_quotient1_op<Scalar>,
+                            CwiseBinaryOp<ei_scalar_sum_op<Scalar>, VectorType, VectorType> >
+  center() const
+  { return (m_min+m_max)/2; }
+
+  /** \returns the lengths of the sides of the bounding box.
+    * Note that this function does not get the same
+    * result for integral or floating scalar types: see
+    */
+  inline const CwiseBinaryOp< ei_scalar_difference_op<Scalar>, VectorType, VectorType> sizes() const
+  { return m_max - m_min; }
+
+  /** \returns the volume of the bounding box */
+  inline Scalar volume() const
+  { return sizes().prod(); }
+
+  /** \returns an expression for the bounding box diagonal vector
+    * if the length of the diagonal is needed: diagonal().norm()
+    * will provide it.
+    */
+  inline CwiseBinaryOp< ei_scalar_difference_op<Scalar>, VectorType, VectorType> diagonal() const
+  { return sizes(); }
+
+  /** \returns the vertex of the bounding box at the corner defined by
+    * the corner-id corner. It works only for a 1D, 2D or 3D bounding box.
+    * For 1D bounding boxes corners are named by 2 enum constants:
+    * BottomLeft and BottomRight.
+    * For 2D bounding boxes, corners are named by 4 enum constants:
+    * BottomLeft, BottomRight, TopLeft, TopRight.
+    * For 3D bounding boxes, the following names are added:
+    * BottomLeftCeil, BottomRightCeil, TopLeftCeil, TopRightCeil.
+    */
+  inline VectorType corner(CornerType corner) const
+  {
+    EIGEN_STATIC_ASSERT(_AmbientDim <= 3, THIS_METHOD_IS_ONLY_FOR_VECTORS_OF_A_SPECIFIC_SIZE);
+
+    VectorType res;
+
+    int mult = 1;
+    for(int d=0; d<dim(); ++d)
+    {
+      if( mult & corner ) res[d] = m_max[d];
+      else                res[d] = m_min[d];
+      mult *= 2;
+    }
+    return res;
+  }
+
+  /** \returns a random point inside the bounding box sampled with
+   * a uniform distribution */
+  inline VectorType sample() const
+  {
+    VectorType r;
+    for(int d=0; d<dim(); ++d)
+    {
+      if(ScalarTraits::HasFloatingPoint)
+      {
+        r[d] = m_min[d] + (m_max[d]-m_min[d])
+             * (ei_random<Scalar>() + ei_random_amplitude<Scalar>())
+             / (Scalar(2)*ei_random_amplitude<Scalar>() );
+      }
+      else
+        r[d] = ei_random(m_min[d], m_max[d]);
+    }
+    return r;
+  }
 
   /** \returns true if the point \a p is inside the box \c *this. */
-  inline bool contains(const VectorType& p) const
+  template<typename Derived>
-  { return (m_min.array()<=p.array()).all() && (p.array()<=m_max.array()).all(); }
+  inline bool contains(const MatrixBase<Derived>& a_p) const
+  {
+    const typename ei_nested<Derived,2>::type p(a_p.derived());
+    return (m_min.array()<=p.array()).all() && (p.array()<=m_max.array()).all();
+  }
 
   /** \returns true if the box \a b is entirely inside the box \c *this. */
   inline bool contains(const AlignedBox& b) const
   { return (m_min.array()<=b.min().array()).all() && (b.max().array()<=m_max.array()).all(); }
 
   /** Extends \c *this such that it contains the point \a p and returns a reference to \c *this. */
-  inline AlignedBox& extend(const VectorType& p)
+  template<typename Derived>
-  { m_min = m_min.cwiseMin(p); m_max = m_max.cwiseMax(p); return *this; }
+  inline AlignedBox& extend(const MatrixBase<Derived>& a_p)
+  {
+    const typename ei_nested<Derived,2>::type p(a_p.derived());
+    m_min = m_min.cwiseMin(p);
+    m_max = m_max.cwiseMax(p);
+    return *this;
+  }
 
   /** Extends \c *this such that it contains the box \a b and returns a reference to \c *this. */
   inline AlignedBox& extend(const AlignedBox& b)
-  { m_min = m_min.cwiseMin(b.m_min); m_max = m_max.cwiseMax(b.m_max); return *this; }
+  {
+    m_min = m_min.cwiseMin(b.m_min);
+    m_max = m_max.cwiseMax(b.m_max);
+    return *this;
+  }
 
   /** Clamps \c *this by the box \a b and returns a reference to \c *this. */
   inline AlignedBox& clamp(const AlignedBox& b)
-  { m_min = m_min.cwiseMax(b.m_min); m_max = m_max.cwiseMin(b.m_max); return *this; }
+  {
+    m_min = m_min.cwiseMax(b.m_min);
+    m_max = m_max.cwiseMin(b.m_max);
+    return *this;
+  }
 
   /** Returns an AlignedBox that is the intersection of \a b and \c *this */
-  inline AlignedBox intersection(const AlignedBox &b) const
+  inline AlignedBox intersection(const AlignedBox& b) const
-  { return AlignedBox(m_min.cwiseMax(b.m_min), m_max.cwiseMin(b.m_max)); }
+  {return AlignedBox(m_min.cwiseMax(b.m_min), m_max.cwiseMin(b.m_max)); }
 
   /** Returns an AlignedBox that is the union of \a b and \c *this */
-  inline AlignedBox merged(const AlignedBox &b) const
+  inline AlignedBox merged(const AlignedBox& b) const
   { return AlignedBox(m_min.cwiseMin(b.m_min), m_max.cwiseMax(b.m_max)); }
 
   /** Translate \c *this by the vector \a t and returns a reference to \c *this. */
-  inline AlignedBox& translate(const VectorType& t)
+  template<typename Derived>
-  { m_min += t; m_max += t; return *this; }
+  inline AlignedBox& translate(const MatrixBase<Derived>& a_t)
+  {
+    const typename ei_nested<Derived,2>::type t(a_t.derived());
+    m_min += t;
+    m_max += t;
+    return *this;
+  }
 
   /** \returns the squared distance between the point \a p and the box \c *this,
     * and zero if \a p is inside the box.
     * \sa exteriorDistance()
     */
-  inline Scalar squaredExteriorDistance(const VectorType& p) const;
+  template<typename Derived>
+  inline Scalar squaredExteriorDistance(const MatrixBase<Derived>& a_p) const;
 
   /** \returns the squared distance between the boxes \a b and \c *this,
     * and zero if the boxes intersect.
@@ -136,15 +259,16 @@ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
     * and zero if \a p is inside the box.
     * \sa squaredExteriorDistance()
     */
-  inline Scalar exteriorDistance(const VectorType& p) const
+  template<typename Derived>
-  { return ei_sqrt(squaredExteriorDistance(p)); }
+  inline FloatingPoint exteriorDistance(const MatrixBase<Derived>& p) const
+  { return ei_sqrt(FloatingPoint(squaredExteriorDistance(p))); }
 
   /** \returns the distance between the boxes \a b and \c *this,
     * and zero if the boxes intersect.
     * \sa squaredExteriorDistance()
     */
-  inline Scalar exteriorDistance(const AlignedBox& b) const
+  inline FloatingPoint exteriorDistance(const AlignedBox& b) const
-  { return ei_sqrt(squaredExteriorDistance(b)); }
+  { return ei_sqrt(FloatingPoint(squaredExteriorDistance(b))); }
 
   /** \returns \c *this with scalar type casted to \a NewScalarType
     *
@@ -171,7 +295,7 @@ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
     * determined by \a prec.
     *
     * \sa MatrixBase::isApprox() */
-  bool isApprox(const AlignedBox& other, typename NumTraits<Scalar>::Real prec = NumTraits<Scalar>::dummy_precision()) const
+  bool isApprox(const AlignedBox& other, RealScalar prec = ScalarTraits::dummy_precision()) const
   { return m_min.isApprox(other.m_min, prec) && m_max.isApprox(other.m_max, prec); }
 
 protected:
@@ -179,32 +303,48 @@ protected:
   VectorType m_min, m_max;
 };
 
-template<typename Scalar,int AmbiantDim>
+
-inline Scalar AlignedBox<Scalar,AmbiantDim>::squaredExteriorDistance(const VectorType& p) const
+
+template<typename Scalar,int AmbientDim>
+template<typename Derived>
+inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance(const MatrixBase<Derived>& a_p) const
 {
+  const typename ei_nested<Derived,2*AmbientDim>::type p(a_p.derived());
   Scalar dist2 = 0.;
   Scalar aux;
   for (int k=0; k<dim(); ++k)
   {
-    if ((aux = (p[k]-m_min[k]))<Scalar(0))
+    if( m_min[k] > p[k] )
+    {
+      aux = m_min[k] - p[k];
       dist2 += aux*aux;
-    else if ( (aux = (m_max[k]-p[k]))<Scalar(0) )
+    }
+    else if( p[k] > m_max[k] )
+    {
+      aux = p[k] - m_max[k];
       dist2 += aux*aux;
+    }
   }
   return dist2;
 }
 
-template<typename Scalar,int AmbiantDim>
+template<typename Scalar,int AmbientDim>
-inline Scalar AlignedBox<Scalar,AmbiantDim>::squaredExteriorDistance(const AlignedBox& b) const
+inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance(const AlignedBox& b) const
 {
   Scalar dist2 = 0.;
   Scalar aux;
   for (int k=0; k<dim(); ++k)
   {
-    if ((aux = (b.m_min[k]-m_max[k]))>0.)
+    if( m_min[k] > b.m_max[k] )
+    {
+      aux = m_min[k] - b.m_max[k];
       dist2 += aux*aux;
-    else if ( (aux = (m_min[k]-b.m_max[k]))>0. )
+    }
+    else if( b.m_min[k] > m_max[k] )
+    {
+      aux = b.m_min[k] - m_max[k];
       dist2 += aux*aux;
+    }
   }
   return dist2;
 }