Add an axis aligned box in the geometry module.

Some naming questions:
- for "extend" we could also think of: "expand", "union", "add"
- same for "clamp": "crop", "intersect"
- same for "contains": "isInside", "intersect"
=> ah "intersect" is conflicting, so that eliminates this one !

Eigen/Geometry

@@ -33,6 +33,7 @@ namespace Eigen {
 #include "src/Geometry/Scaling.h"
 #include "src/Geometry/Hyperplane.h"
 #include "src/Geometry/ParametrizedLine.h"
+#include "src/Geometry/AlignedBox.h"
 
 } // namespace Eigen
 

Eigen/src/Geometry/AlignedBox.h

@@ -0,0 +1,179 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_ALIGNEDBOX_H
+#define EIGEN_ALIGNEDBOX_H
+
+/** \geometry_module \ingroup GeometryModule
+  *
+  * \class AlignedBox
+  *
+  * \brief A box aligned with a axis
+  *
+  * \param _Scalar the type of the scalar coefficients
+  * \param _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
+  *
+  * This class represents an axis aligned box as the pair of the minimal and maximal corners.
+  */
+template <typename _Scalar, int _AmbientDim>
+class AlignedBox
+  #ifdef EIGEN_VECTORIZE
+  : public ei_with_aligned_operator_new<_Scalar,_AmbientDim==Dynamic ? Dynamic : _AmbientDim+1>
+  #endif
+{
+public:
+
+  enum { AmbientDimAtCompileTime = _AmbientDim };
+  typedef _Scalar Scalar;
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType;
+
+  /** Default constructor initializing a null box. */
+  inline explicit AlignedBox()
+  { if (AmbientDimAtCompileTime!=Dynamic) setNull(); }
+
+  /** 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(); }
+
+  /** Constructs a box with extremities \a _min and \a _max. */
+  inline AlignedBox(const VectorType& _min, const VectorType _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) {}
+
+  ~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. */
+  inline bool isNull() const { return (m_min.cwise() > m_max).any(); }
+
+  /** Makes \c *this a null/empty box. */
+  inline void setNull()
+  {
+    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 */
+  inline VectorType& min() { return m_min; }
+  /** \returns the maximal corner */
+  inline const VectorType& max() const { return m_max; }
+  /** \returns a non const reference to the maximal corner */
+  inline VectorType& max() { return m_max; }
+
+  /** \returns true if the point \a p is inside the box \c *this. */
+  inline bool contains(const VectorType& 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
+  { 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.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.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.cwise().max(b.m_min); m_max = m_max.cwise().min(b.m_max); 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;
+
+  /** \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)); }
+
+  /** 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;
+  }
+
+  /** \returns \c *this with scalar type casted to \a NewScalarType
+    *
+    * Note that if \a NewScalarType is equal to the current scalar type of \c *this
+    * then this function smartly returns a const reference to \c *this.
+    */
+  template<typename NewScalarType>
+  inline typename ei_cast_return_type<AlignedBox,
+           AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type cast() const
+  {
+    return typename ei_cast_return_type<AlignedBox,
+                    AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type(*this);
+  }
+
+  /** Copy constructor with scalar type conversion */
+  template<typename OtherScalarType>
+  inline explicit AlignedBox(const AlignedBox<OtherScalarType,AmbientDimAtCompileTime>& other)
+  {
+    m_min = other.min().template cast<OtherScalarType>();
+    m_max = other.max().template cast<OtherScalarType>();
+  }
+
+  /** \returns \c true if \c *this is approximately equal to \a other, within the precision
+    * determined by \a prec.
+    *
+    * \sa MatrixBase::isApprox() */
+  bool isApprox(const AlignedBox& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
+  { return m_min.isApprox(other.m_min, prec) && m_max.isApprox(other.m_max, prec); }
+
+protected:
+
+  VectorType m_min, m_max;
+};
+
+template<typename Scalar,int AmbiantDim>
+inline Scalar AlignedBox<Scalar,AmbiantDim>::squaredExteriorDistance(const VectorType& 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;
+  }
+  return dist2;
+}
+
+#endif // EIGEN_ALIGNEDBOX_H

Eigen/src/Geometry/Hyperplane.h

@@ -203,7 +203,7 @@ public:
     }
   }
 
-  /** \returns the transformation of \c *this by the transformation matrix \a mat.
+  /** Applies the transformation matrix \a mat to \c *this and returns a reference to \c *this.
     *
     * \param mat the Dim x Dim transformation matrix
     * \param traits specifies whether the matrix \a mat represents an Isometry
@@ -223,7 +223,7 @@ public:
     return *this;
   }
 
-  /** \returns the transformation of \c *this by the transformation \a t
+  /** Applies the transformation \a t to \c *this and returns a reference to \c *this.
     *
     * \param t the transformation of dimension Dim
     * \param traits specifies whether the transformation \a t represents an Isometry

Eigen/src/Geometry/Scaling.h

@@ -35,7 +35,7 @@
   * \param _Dim the  dimension of the space, can be a compile time value or Dynamic
   *
   * \note This class is not aimed to be used to store a scaling transformation,
-  * but rather to make easier the constructions and updates of Transformation object.
+  * but rather to make easier the constructions and updates of Transform objects.
   *
   * \sa class Translation, class Transform
   */

Eigen/src/Geometry/Translation.h

@@ -35,7 +35,7 @@
   * \param _Dim the  dimension of the space, can be a compile time value or Dynamic
   *
   * \note This class is not aimed to be used to store a translation transformation,
-  * but rather to make easier the constructions and updates of Transformation object.
+  * but rather to make easier the constructions and updates of Transform objects.
   *
   * \sa class Scaling, class Transform
   */

test/CMakeLists.txt

@@ -166,6 +166,7 @@ ei_add_test(svd)
 ei_add_test(geometry)
 ei_add_test(hyperplane)
 ei_add_test(parametrizedline)
+ei_add_test(alignedbox)
 ei_add_test(regression)
 ei_add_test(sparse )
 

test/alignedbox.cpp

@@ -0,0 +1,75 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#include "main.h"
+#include <Eigen/Geometry>
+#include <Eigen/LU>
+#include <Eigen/QR>
+
+template<typename BoxType> void alignedbox(const BoxType& _box)
+{
+  /* this test covers the following files:
+     AlignedBox.h
+  */
+
+  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);
+  RealScalar s1 = ei_random<RealScalar>(0,1);
+
+  BoxType b0(dim);
+  BoxType b1(VectorType::Random(dim),VectorType::Random(dim));
+  BoxType b2;
+
+  b0.extend(p0);
+  b0.extend(p1);
+  VERIFY(b0.contains(p0*s1+(1.-s1)*p1));
+  VERIFY(!b0.contains(p0 + (1+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);
+}
+
+void test_alignedbox()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( alignedbox(AlignedBox<float,2>()) );
+    CALL_SUBTEST( alignedbox(AlignedBox<float,3>()) );
+    CALL_SUBTEST( alignedbox(AlignedBox<double,4>()) );
+  }
+}