Re: [eigen] Enhanced AlignedBox

[Manuel Yguel <manuel.yguel@xxxxxxxxx>]

Here are the new patches for AlignedBox taking into account your
comments (I was unaware of the cast politic, which seems to me very
clever).
For the moment I made lowest and highest template functions.
As soon as I finish the things with the polynomial solver I will make
NumTraits<foo> inherits std::numeric_limits (that is exactly what the
guys in the boost are doing to define lowest and highest, so it seems
to be a general good idea)
and add dummy_precision and perhaps something about the fpclassify, I
always wanted to have something clear about that in such a class.

Thanks for the patient reviews !


- Cheers,

Manuel

# HG changeset patch
# User Manuel Yguel <manuel.yguel@xxxxxxxxx>
# Date 1263995538 -3600
# Node ID 03be9fa3c5b5dda4add62cfbe0bd6016bcffb9b1
# Parent  6f94def20336f220d9551453c7a434222880aa75
Lowest and highest template functions to patch the min, max inconsitent definition in std::numerics for floating and integral types.

diff -r 6f94def20336 -r 03be9fa3c5b5 Eigen/src/Core/MathFunctions.h
--- a/Eigen/src/Core/MathFunctions.h	Wed Jan 20 12:07:46 2010 +0000
+++ b/Eigen/src/Core/MathFunctions.h	Wed Jan 20 14:52:18 2010 +0100
@@ -51,9 +51,21 @@
   return p * ei_sqrt(T(1) + qp*qp);
 }
 
+
+template<typename T> inline T highest();
+template<typename T> inline T lowest();
+
+template<typename T> inline T ei_default_float_highest(){ return std::numeric_limits<T>::max(); }
+template<typename T> inline T ei_default_float_lowest(){ return static_cast<T>(-std::numeric_limits<T>::max()); }
+template<typename T> inline T ei_default_integral_highest(){ return std::numeric_limits<T>::max(); }
+template<typename T> inline T ei_default_integral_lowest(){ return std::numeric_limits<T>::min(); }
+
 /**************
 ***   int   ***
 **************/
+
+template<> inline int highest<int>() { return ei_default_integral_highest<int>(); }
+template<> inline int lowest<int>() { return ei_default_integral_lowest<int>(); }
 
 template<> inline int dummy_precision<int>() { return 0; }
 inline int ei_real(int x)  { return x; }
@@ -108,6 +120,8 @@
 /**************
 *** float   ***
 **************/
+template<> inline float highest<float>() { return ei_default_float_highest<float>(); }
+template<> inline float lowest<float>() { return ei_default_float_lowest<float>(); }
 
 template<> inline float dummy_precision<float>() { return 1e-5f; }
 inline float ei_real(float x)  { return x; }
@@ -156,6 +170,8 @@
 /**************
 *** double  ***
 **************/
+template<> inline double highest<double>() { return ei_default_float_highest<double>(); }
+template<> inline double lowest<double>() { return ei_default_float_lowest<double>(); }
 
 template<> inline double dummy_precision<double>() { return 1e-12; }
 
@@ -205,6 +221,10 @@
 /*********************
 *** complex<float> ***
 *********************/
+template<> inline std::complex<float> highest<std::complex<float> >() {
+  return std::complex<float>( ei_default_float_highest<float>(), ei_default_float_highest<float>() ); }
+template<> inline std::complex<float> lowest<std::complex<float> >() {
+  return std::complex<float>( ei_default_float_lowest<float>(),ei_default_float_lowest<float>() ); }
 
 template<> inline float dummy_precision<std::complex<float> >() { return dummy_precision<float>(); }
 inline float ei_real(const std::complex<float>& x) { return std::real(x); }
@@ -243,6 +263,10 @@
 /**********************
 *** complex<double> ***
 **********************/
+template<> inline std::complex<double> highest<std::complex<double> >() {
+  return std::complex<double>( ei_default_float_highest<double>(), ei_default_float_highest<double>() ); }
+template<> inline std::complex<double> lowest<std::complex<double> >() {
+  return std::complex<double>( ei_default_float_lowest<double>(),ei_default_float_lowest<double>() ); }
 
 template<> inline double dummy_precision<std::complex<double> >() { return dummy_precision<double>(); }
 inline double ei_real(const std::complex<double>& x) { return std::real(x); }
@@ -282,6 +306,8 @@
 /******************
 *** long double ***
 ******************/
+template<> inline long double highest<long double>() { return ei_default_float_highest<long double>(); }
+template<> inline long double lowest<long double>() { return ei_default_float_lowest<long double>(); }
 
 template<> inline long double dummy_precision<long double>() { return dummy_precision<double>(); }
 inline long double ei_real(long double x)  { return x; }
@@ -322,6 +348,8 @@
 /**************
 ***  bool  ***
 **************/
+template<> inline bool highest<bool>() { return ei_default_integral_highest<bool>(); }
+template<> inline bool lowest<bool>() { return ei_default_integral_lowest<bool>(); }
 
 template<> inline bool dummy_precision<bool>() { return 0; }
 inline bool ei_real(bool x)  { return x; }

# HG changeset patch
# User Manuel Yguel <manuel.yguel@xxxxxxxxx>
# Date 1263995630 -3600
# Node ID 7d8260fae2cf3469af2303652b6c694c25a4da4e
# Parent  03be9fa3c5b5dda4add62cfbe0bd6016bcffb9b1
Enhance AlignedBox to accept integral types and add some usefull methods: diagonal, volume, sample.

diff -r 03be9fa3c5b5 -r 7d8260fae2cf Eigen/src/Geometry/AlignedBox.h
--- a/Eigen/src/Geometry/AlignedBox.h	Wed Jan 20 14:52:18 2010 +0100
+++ b/Eigen/src/Geometry/AlignedBox.h	Wed Jan 20 14:53:50 2010 +0100
@@ -43,23 +43,49 @@
 public:
 EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
   enum { AmbientDimAtCompileTime = _AmbientDim };
-  typedef _Scalar Scalar;
-  typedef typename NumTraits<Scalar>::Real RealScalar;
-  typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType;
+  typedef _Scalar                                   Scalar;
+  typedef typename NumTraits<Scalar>::Real          RealScalar;
+  typedef typename NumTraits<Scalar>::FloatingPoint FloatingPoint;
+  typedef Matrix<Scalar,AmbientDimAtCompileTime,1>  VectorType;
+
+  /** Define constants to name the corners of a 1D, 2D or 3D axis aligned bounding box */
+  typedef enum
+  {
+  /** 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
+  } CornerType;
+
 
   /** 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() {}
 
@@ -67,14 +93,21 @@
   inline int dim() const { return AmbientDimAtCompileTime==Dynamic ? m_min.size()-1 : AmbientDimAtCompileTime; }
 
   /** \returns true if the box is null, i.e, empty. */
-  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. */
-  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_max.setConstant(-std::numeric_limits<Scalar>::max());
+    m_min.setConstant( highest<Scalar>() );
+    m_max.setConstant( lowest<Scalar>() );
   }
+
 
   /** \returns the minimal corner */
   inline const VectorType& min() const { return m_min; }
@@ -86,65 +119,155 @@
   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( NumTraits<Scalar>::HasFloatingPoint )
+      {
+        r[d] = m_min[d] + (m_max[d]-m_min[d])
+            * ( ei_random<Scalar>() + ei_random_amplitude<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
-  { return (m_min.array()<=p.array()).all() && (p.array()<=m_max.array()).all(); }
+  template<typename Derived>
+  inline bool contains(const MatrixBase<Derived>& a_p) const
+  {
+    const typename ei_nested<Derived,2>::type p(a_p.derived());
+    return (m_min.cwise()<=p).all() && (p.cwise()<=m_max).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(); }
+  inline bool contains(const AlignedBox<_Scalar,_AmbientDim>& b) const
+  { return (m_min.cwise()<=b.min()).all() && (b.max().cwise()<=m_max).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)
-  { m_min = m_min.cwiseMin(p); m_max = m_max.cwiseMax(p); return *this; }
+  template<typename Derived>
+  inline AlignedBox& extend(const MatrixBase<Derived>& a_p)
+  {
+    const typename ei_nested<Derived,2>::type p(a_p.derived());
+    m_min = m_min.cwise().min(p); m_max = m_max.cwise().max(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; }
+  inline AlignedBox& extend(const AlignedBox<_Scalar,_AmbientDim>& b)
+  { m_min = m_min.cwise().min(b.m_min); m_max = m_max.cwise().max(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; }
+  inline AlignedBox& clamp(const AlignedBox<_Scalar,_AmbientDim>& b)
+  { m_min = m_min.cwise().max(b.m_min); m_max = m_max.cwise().min(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
-  { return AlignedBox(m_min.cwiseMax(b.m_min), m_max.cwiseMin(b.m_max)); }
+  inline AlignedBox intersection(const AlignedBox<_Scalar,_AmbientDim>& b) const
+  { return AlignedBox(m_min.cwise().max(b.m_min), m_max.cwise().min(b.m_max)); }
 
   /** Returns an AlignedBox that is the union of \a b and \c *this */
-  inline AlignedBox merged(const AlignedBox &b) const
-  { return AlignedBox(m_min.cwiseMin(b.m_min), m_max.cwiseMax(b.m_max)); }
+  inline AlignedBox merged(const AlignedBox<_Scalar,_AmbientDim>& b) const
+  { return AlignedBox(m_min.cwise().min(b.m_min), m_max.cwise().max(b.m_max)); }
 
   /** Translate \c *this by the vector \a t and returns a reference to \c *this. */
-  inline AlignedBox& translate(const VectorType& t)
-  { m_min += t; m_max += t; return *this; }
+  template<typename Derived>
+  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.
     * \sa exteriorDistance()
     */
-  inline Scalar squaredExteriorDistance(const AlignedBox& b) const;
+  inline Scalar squaredExteriorDistance(const AlignedBox<_Scalar,_AmbientDim>& b) const;
 
   /** \returns the distance between the point \a p and the box \c *this,
     * and zero if \a p is inside the box.
     * \sa squaredExteriorDistance()
     */
-  inline Scalar exteriorDistance(const VectorType& p) const
-  { return ei_sqrt(squaredExteriorDistance(p)); }
+  template<typename Derived>
+  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
-  { return ei_sqrt(squaredExteriorDistance(b)); }
+  inline FloatingPoint exteriorDistance(const AlignedBox<_Scalar,_AmbientDim>& b) const
+  { return ei_sqrt(FloatingPoint(squaredExteriorDistance(b))); }
 
   /** \returns \c *this with scalar type casted to \a NewScalarType
     *
@@ -171,7 +294,7 @@
     * determined by \a prec.
     *
     * \sa MatrixBase::isApprox() */
-  bool isApprox(const AlignedBox& other, typename NumTraits<Scalar>::Real prec = dummy_precision<Scalar>()) const
+  bool isApprox(const AlignedBox& other, RealScalar prec = dummy_precision<Scalar>()) const
   { return m_min.isApprox(other.m_min, prec) && m_max.isApprox(other.m_max, prec); }
 
 protected:
@@ -179,32 +302,50 @@
   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( m_min[k] > p[k] )
+    {
+      aux = m_min[k] - p[k];
+      dist2 += aux*aux;
+    }
+    else if( p[k] > m_max[k] )
+    {
+      aux = p[k] - m_max[k];
+      dist2 += aux*aux;
+    }
+  }
+  return dist2;
+}
+
+template<typename _Scalar,int _AmbientDim>
+inline _Scalar AlignedBox<_Scalar,_AmbientDim>::squaredExteriorDistance(
+    const AlignedBox<_Scalar,_AmbientDim>& b) const
 {
   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] > b.m_max[k] )
+    {
+      aux = m_min[k] - b.m_max[k];
       dist2 += aux*aux;
-    else if ( (aux = (m_max[k]-p[k]))<Scalar(0) )
+    }
+    else if( b.m_min[k] > m_max[k] )
+    {
+      aux = b.m_min[k] - m_max[k];
       dist2 += aux*aux;
-  }
-  return dist2;
-}
-
-template<typename Scalar,int AmbiantDim>
-inline Scalar AlignedBox<Scalar,AmbiantDim>::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.)
-      dist2 += aux*aux;
-    else if ( (aux = (m_min[k]-b.m_max[k]))>0. )
-      dist2 += aux*aux;
+    }
   }
   return dist2;
 }

# HG changeset patch
# User Manuel Yguel <manuel.yguel@xxxxxxxxx>
# Date 1263995710 -3600
# Node ID 2de4ff00adb8c8f6d617150d21fe5d62806926ad
# Parent  7d8260fae2cf3469af2303652b6c694c25a4da4e
Updated tests for enhanced AlignedBox with volume, diagonal and better handling of integral types.

diff -r 7d8260fae2cf -r 2de4ff00adb8 test/geo_alignedbox.cpp
--- a/test/geo_alignedbox.cpp	Wed Jan 20 14:53:50 2010 +0100
+++ b/test/geo_alignedbox.cpp	Wed Jan 20 14:55:10 2010 +0100
@@ -27,6 +27,9 @@
 #include <Eigen/LU>
 #include <Eigen/QR>
 
+#include<iostream>
+using namespace std;
+
 template<typename BoxType> void alignedbox(const BoxType& _box)
 {
   /* this test covers the following files:
@@ -40,6 +43,8 @@
 
   VectorType p0 = VectorType::Random(dim);
   VectorType p1 = VectorType::Random(dim);
+  while( p1 == p0 ){
+      p1 =  VectorType::Random(dim); }
   RealScalar s1 = ei_random<RealScalar>(0,1);
 
   BoxType b0(dim);
@@ -49,20 +54,13 @@
   b0.extend(p0);
   b0.extend(p1);
   VERIFY(b0.contains(p0*s1+(Scalar(1)-s1)*p1));
-  VERIFY(!b0.contains(p0 + (1+s1)*(p1-p0)));
+  VERIFY(!b0.contains(p0 + (2+s1)*(p1-p0)));
 
   (b2 = b0).extend(b1);
   VERIFY(b2.contains(b0));
   VERIFY(b2.contains(b1));
   VERIFY_IS_APPROX(b2.clamp(b0), b0);
 
-  // casting
-  const int Dim = BoxType::AmbientDimAtCompileTime;
-  typedef typename GetDifferentType<Scalar>::type OtherScalar;
-  AlignedBox<OtherScalar,Dim> hp1f = b0.template cast<OtherScalar>();
-  VERIFY_IS_APPROX(hp1f.template cast<Scalar>(),b0);
-  AlignedBox<Scalar,Dim> hp1d = b0.template cast<Scalar>();
-  VERIFY_IS_APPROX(hp1d.template cast<Scalar>(),b0);
 
   // alignment -- make sure there is no memory alignment assertion
   BoxType *bp0 = new BoxType(dim);
@@ -70,13 +68,117 @@
   bp0->extend(*bp1);
   delete bp0;
   delete bp1;
+
+  // sampling
+  for( int i=0; i<10; ++i )
+  {
+      VectorType r = b0.sample();
+      VERIFY(b0.contains(r));
+  }
+
 }
+
+
+
+template<typename BoxType>
+void alignedboxCastTests(const BoxType& _box)
+{
+  // casting
+  const int dim = _box.dim();
+  typedef typename BoxType::Scalar Scalar;
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  typedef Matrix<Scalar, BoxType::AmbientDimAtCompileTime, 1> VectorType;
+
+  VectorType p0 = VectorType::Random(dim);
+  VectorType p1 = VectorType::Random(dim);
+
+  BoxType b0(dim);
+
+  b0.extend(p0);
+  b0.extend(p1);
+
+  const int Dim = BoxType::AmbientDimAtCompileTime;
+  typedef typename GetDifferentType<Scalar>::type OtherScalar;
+  AlignedBox<OtherScalar,Dim> hp1f = b0.template cast<OtherScalar>();
+  VERIFY_IS_APPROX(hp1f.template cast<Scalar>(),b0);
+  AlignedBox<Scalar,Dim> hp1d = b0.template cast<Scalar>();
+  VERIFY_IS_APPROX(hp1d.template cast<Scalar>(),b0);
+}
+
+
+void specificTest1()
+{
+    Vector2f m; m << -1.0f, -2.0f;
+    Vector2f M; M <<  1.0f,  5.0f;
+
+    typedef AlignedBox<float,2>  BoxType;
+    BoxType box( m, M );
+
+    Vector2f sides = M-m;
+    VERIFY_IS_APPROX(sides, box.sizes() );
+    VERIFY_IS_APPROX(sides[1], box.sizes()[1] );
+    VERIFY_IS_APPROX(sides[1], box.sizes().maxCoeff() );
+    VERIFY_IS_APPROX(sides[0], box.sizes().minCoeff() );
+
+    VERIFY_IS_APPROX( 14.0f, box.volume() );
+    VERIFY_IS_APPROX( 53.0f, box.diagonal().squaredNorm() );
+    VERIFY_IS_APPROX( ei_sqrt( 53.0f ), box.diagonal().norm() );
+
+    VERIFY_IS_APPROX( m, box.corner( BoxType::BottomLeft ) );
+    VERIFY_IS_APPROX( M, box.corner( BoxType::TopRight ) );
+    Vector2f bottomRight; bottomRight << M[0], m[1];
+    Vector2f topLeft; topLeft << m[0], M[1];
+    VERIFY_IS_APPROX( bottomRight, box.corner( BoxType::BottomRight ) );
+    VERIFY_IS_APPROX( topLeft, box.corner( BoxType::TopLeft ) );
+}
+
+
+void specificTest2()
+{
+    Vector3i m; m << -1, -2, 0;
+    Vector3i M; M <<  1,  5, 3;
+
+    typedef AlignedBox<int,3>  BoxType;
+    BoxType box( m, M );
+
+    Vector3i sides = M-m;
+    VERIFY_IS_APPROX(sides, box.sizes() );
+    VERIFY_IS_APPROX(sides[1], box.sizes()[1] );
+    VERIFY_IS_APPROX(sides[1], box.sizes().maxCoeff() );
+    VERIFY_IS_APPROX(sides[0], box.sizes().minCoeff() );
+
+    VERIFY_IS_APPROX( 42, box.volume() );
+    VERIFY_IS_APPROX( 62, box.diagonal().squaredNorm() );
+
+    VERIFY_IS_APPROX( m, box.corner( BoxType::BottomLeftFloor ) );
+    VERIFY_IS_APPROX( M, box.corner( BoxType::TopRightCeil ) );
+    Vector3i bottomRightFloor; bottomRightFloor << M[0], m[1], m[2];
+    Vector3i topLeftFloor; topLeftFloor << m[0], M[1], m[2];
+    VERIFY_IS_APPROX( bottomRightFloor, box.corner( BoxType::BottomRightFloor ) );
+    VERIFY_IS_APPROX( topLeftFloor, box.corner( BoxType::TopLeftFloor ) );
+}
+
 
 void test_geo_alignedbox()
 {
-  for(int i = 0; i < g_repeat; i++) {
+  for(int i = 0; i < g_repeat; i++)
+  {
     CALL_SUBTEST_1( alignedbox(AlignedBox<float,2>()) );
-    CALL_SUBTEST_2( alignedbox(AlignedBox<float,3>()) );
-    CALL_SUBTEST_3( alignedbox(AlignedBox<double,4>()) );
+    CALL_SUBTEST_2( alignedboxCastTests(AlignedBox<float,2>()) );
+
+    CALL_SUBTEST_3( alignedbox(AlignedBox<float,3>()) );
+    CALL_SUBTEST_4( alignedboxCastTests(AlignedBox<float,3>()) );
+
+    CALL_SUBTEST_5( alignedbox(AlignedBox<double,4>()) );
+    CALL_SUBTEST_6( alignedboxCastTests(AlignedBox<double,4>()) );
+
+    CALL_SUBTEST_7( alignedbox(AlignedBox<double,1>()) );
+    CALL_SUBTEST_8( alignedboxCastTests(AlignedBox<double,1>()) );
+
+    CALL_SUBTEST_9( alignedbox(AlignedBox<int,1>()) );
+    CALL_SUBTEST_10( alignedbox(AlignedBox<int,2>()) );
+    CALL_SUBTEST_11( alignedbox(AlignedBox<int,3>()) );
   }
+  CALL_SUBTEST_12( specificTest1() );
+  CALL_SUBTEST_13( specificTest2() );
 }