[eigen] Enhanced AlignedBox

[Manuel Yguel <manuel.yguel@xxxxxxxxx>]

Hello,
I have written some small pieces of codes to enhance AlignedBox.
The following changes I propose are as follow:

1) Define some new functions:
Scalar size( size_t k ) --> returns the size of the k-th side
Vector sizes() --> returns a vector with all the sides
Vector corner( CornerType t ) --> defines some enum and return the
corresponding corner for 1D,2D and 3D boundingBox
Scalar squaredDiagonale()
Real diagonal()
Scalar volume()
Vector sample() --> sample a point in the boundingBox volume with a
uniform distribution

2) Add the function isEmpty (I do not like very much the isNull name,
it is a matter of taste, so if it does not fit you, let me know...)

3) Semantic: I think that it is usefull to have bounding boxes with
integers: in this case the min and the max are considered inside the
bounding box and a side of the bounding box is max - min + 1 instead
of max - min.
This is a complex semantic problem, but I think it is the more natural choice.

4) Following that line, I have changed the code for the distances
functions such that non-negative integers types are safely handled and
I trust the compiler to produce as optimized code as the one that Gael
has written.
I know that such types are not natively handled by Eigen, but I think
that it is a safe change.


What do you think about those proposals?

If you agree with that lines, I plan to write an OrientedBox class
with almost same interface.
Also, I would like to launch a topic about the way random numbers are
generated because when writing sample(), I found that we can enhance
the way it is done.
Is this already an active topic ?

- best regards,

Manuel

# HG changeset patch
# User Manuel Yguel <manuel.yguel@xxxxxxxxx>
# Date 1261346899 -3600
# Node ID 8d31bd6406a8f9302d977172fb5a3d7d0172110e
# Parent  550cdad8b2a2a6c0a9df4d7a45c8f6aea5ac33a0
Enhanced AlignedBox: takes into account integer AlignedBox and add methods for side, diagonal, volume and corners for 1D, 2D and 3D cases.

diff -r 550cdad8b2a2 -r 8d31bd6406a8 Eigen/src/Geometry/AlignedBox.h
--- a/Eigen/src/Geometry/AlignedBox.h	Tue Dec 15 08:09:14 2009 +0100
+++ b/Eigen/src/Geometry/AlignedBox.h	Sun Dec 20 23:08:19 2009 +0100
@@ -43,9 +43,25 @@
 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 */
+	BottomLeft=0, BottomRight=1,
+
+	/** Added names for 2D */
+	TopLeft=2, TopRight=3,
+
+	/** Added names for 3D */
+	BottomLeftCeil=4, BottomRightCeil=5,
+	TopLeftCeil=6, TopRightCeil=7
+  } CornerType;
+
 
   /** Default constructor initializing a null box. */
   inline explicit AlignedBox()
@@ -53,13 +69,15 @@
 
   /** 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 OtherVectorType>
+  inline explicit AlignedBox(const OtherVectorType& p) : m_min(p), m_max(p) {}
 
   ~AlignedBox() {}
 
@@ -76,6 +94,17 @@
     m_max.setConstant(-std::numeric_limits<Scalar>::max());
   }
 
+  /** \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());
+  }
+
+
   /** \returns the minimal corner */
   inline const VectorType& min() const { return m_min; }
   /** \returns a non const reference to the minimal corner */
@@ -88,63 +117,163 @@
   /** \returns the center of the box */
   inline VectorType center() const { return (m_min + m_max) / 2; }
 
+  /** \returns the k-th coordinate of the center of the
+   * bounding box as (max()[k]+min()[k])/2 */
+  inline Scalar center( size_t k ) const { return (m_min[k]+m_max[k])/2; }
+
+  /** \returns the length of the k-th side of the bounding box
+   * Note that this function does not get the same
+   * result for integral or floating scalar types:
+   *   - floating types: max()[k]-min()[k]
+   *   - integral types: max()[k]-min()[k]+1
+   *
+   */
+  Scalar side( size_t k ) const;
+
+  /** \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
+   */
+  VectorType sides() const;
+
+  /** \returns the length of the largest side of the bounding box */
+  inline Scalar maxSide() const {
+	  return sides().maxCoeff(); }
+
+  /** \returns the length of the smallest side of the bounding box */
+  inline Scalar minSide() const {
+	  return sides().minCoeff(); }
+
+  /** \returns the volume of the bounding box */
+  inline Scalar volume() const {
+	  return sides().prod(); }
+
+  /** \returns the squared length of the bounding box diagonal */
+  inline Scalar squaredDiagonal() const {
+	  return sides().squaredNorm(); }
+
+  /** \returns the length of the bounding box diagonal */
+  inline FloatingPoint diagonal() const {
+	  return ei_sqrt(FloatingPoint(squaredDiagonal())); }
+
+  /** \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
+  template<typename OtherVectorType>
+  inline bool contains(const OtherVectorType& p) const
   { 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
+  template<typename Os, int Od>
+  inline bool contains(const AlignedBox<Os,Od>& 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)
+  template<typename OtherVectorType>
+  inline AlignedBox& extend(const OtherVectorType& p)
   { 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)
+  template<typename Os, int Od>
+  inline AlignedBox& extend(const AlignedBox<Os,Od>& 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)
+  template<typename Os, int Od>
+  inline AlignedBox& clamp(const AlignedBox<Os,Od>& 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
+  template<typename Os, int Od>
+  inline AlignedBox intersection(const AlignedBox<Os,Od> &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
+  template<typename Os, int Od>
+  inline AlignedBox merged(const AlignedBox<Os,Od> &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)
+  template<typename OtherVectorType>
+  inline AlignedBox& translate(const OtherVectorType& t)
   { 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 OtherVectorType>
+  inline Scalar squaredExteriorDistance(const OtherVectorType& 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;
+  template<typename Os,int Od>
+  inline Scalar squaredExteriorDistance(const AlignedBox<Os,Od>& 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 OtherVectorType>
+  inline FloatingPoint exteriorDistance(const OtherVectorType& 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)); }
+  template<typename Os, int Od>
+  inline FloatingPoint exteriorDistance(const AlignedBox<Os,Od>& b) const
+  { return ei_sqrt(FloatingPoint(squaredExteriorDistance(b))); }
 
   /** \returns \c *this with scalar type casted to \a NewScalarType
     *
@@ -171,7 +300,7 @@
     * 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 +308,72 @@
   VectorType m_min, m_max;
 };
 
+
+template<typename Scalar>
+struct ei_computeBoxSideOp EIGEN_EMPTY_STRUCT
+{
+  typedef Scalar result_type;
+  inline
+  Scalar operator()(const Scalar& max, const Scalar& min) const
+  {
+	  if( NumTraits<Scalar>::HasFloatingPoint ){ return max - min; }
+	  else{ return max - min + 1; }
+  }
+};
+
+
 template<typename Scalar,int AmbiantDim>
-inline Scalar AlignedBox<Scalar,AmbiantDim>::squaredExteriorDistance(const VectorType& p) const
+inline Scalar AlignedBox<Scalar,AmbiantDim>::side( size_t k ) const {
+	return ei_computeBoxSideOp<Scalar>()( m_max[k], m_min[k] ); }
+
+template<typename Scalar,int AmbiantDim>
+inline
+typename AlignedBox<Scalar,AmbiantDim>::VectorType
+AlignedBox<Scalar,AmbiantDim>::sides() const
+{
+	return m_max.binaryExpr(m_min, ei_computeBoxSideOp<Scalar>() );
+}
+
+template<typename Scalar,int AmbiantDim>
+template<typename OtherVectorType>
+inline Scalar AlignedBox<Scalar,AmbiantDim>::squaredExteriorDistance(const OtherVectorType& p) const
 {
   Scalar dist2 = 0.;
   Scalar aux;
   for (int k=0; k<dim(); ++k)
   {
-    if ((aux = (p[k]-m_min[k]))<0.)
-      dist2 += aux*aux;
-    else if ( (aux = (m_max[k]-p[k]))<0. )
-      dist2 += aux*aux;
+    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 AmbiantDim>
-inline Scalar AlignedBox<Scalar,AmbiantDim>::squaredExteriorDistance(const AlignedBox& b) const
+template<typename Os, int Od>
+inline Scalar AlignedBox<Scalar,AmbiantDim>::squaredExteriorDistance(const AlignedBox<Os,Od>& 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;
+	  if( m_min[k] > b.m_max[k] )
+	  {
+		  aux = m_min[k] - b.m_max[k];
+		  dist2 += aux*aux;
+	  }
+	  else if( b.m_min[k] > m_max[k] )
+	  {
+		  aux = b.m_min[k] - m_max[k];
+		  dist2 += aux*aux;
+	  }
   }
   return dist2;
 }

# HG changeset patch
# User Manuel Yguel <manuel.yguel@xxxxxxxxx>
# Date 1261346995 -3600
# Node ID 1932912e81d040cae27a40f3f0627629d15df977
# Parent  8d31bd6406a8f9302d977172fb5a3d7d0172110e
Tests modified for the enhanced AlignedBox + (one bug fix in the tests for bounding boxes with one side that is less than 1).

diff -r 8d31bd6406a8 -r 1932912e81d0 test/geo_alignedbox.cpp
--- a/test/geo_alignedbox.cpp	Sun Dec 20 23:08:19 2009 +0100
+++ b/test/geo_alignedbox.cpp	Sun Dec 20 23:09:55 2009 +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 +68,119 @@
   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.sides() );
+    VERIFY_IS_APPROX(sides[1], box.side(1) );
+    VERIFY_IS_APPROX(sides[1], box.maxSide() );
+    VERIFY_IS_APPROX(sides[0], box.minSide() );
+
+    VERIFY_IS_APPROX( 14.0f, box.volume() );
+    VERIFY_IS_APPROX( 53.0f, box.squaredDiagonal() );
+    VERIFY_IS_APPROX( ei_sqrt( 53.0f ), box.diagonal() );
+
+    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 + Vector3i(1,1,1);
+    VERIFY_IS_APPROX(sides, box.sides() );
+    VERIFY_IS_APPROX(sides[1], box.side(1) );
+    VERIFY_IS_APPROX(sides[1], box.maxSide() );
+    VERIFY_IS_APPROX(sides[0], box.minSide() );
+
+    VERIFY_IS_APPROX( 96, box.volume() );
+    VERIFY_IS_APPROX( 89, box.squaredDiagonal() );
+    VERIFY_IS_APPROX( ei_sqrt( 89.0 ), box.diagonal() );
+
+    VERIFY_IS_APPROX( m, box.corner( BoxType::BottomLeft ) );
+    VERIFY_IS_APPROX( M, box.corner( BoxType::TopRightCeil ) );
+    Vector3i bottomRight; bottomRight << M[0], m[1], m[2];
+    Vector3i topLeft; topLeft << m[0], M[1], m[2];
+    VERIFY_IS_APPROX( bottomRight, box.corner( BoxType::BottomRight ) );
+    VERIFY_IS_APPROX( topLeft, box.corner( BoxType::TopLeft ) );
+
+}
+
 
 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() );
 }