Merge pull request #3 from saurabhb17/master

secondary files

1 files changed, 1905 insertions, 0 deletions

diff --git a/include/geometry/rtree.h b/include/geometry/rtree.h
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+++ b/include/geometry/rtree.h
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+//TITLE
+//
+//    R-TREES: A DYNAMIC INDEX STRUCTURE FOR SPATIAL SEARCHING
+//
+//DESCRIPTION
+//
+//    A C++ templated version of the RTree algorithm.
+//    For more information please read the comments in RTree.h
+//
+//AUTHORS
+//
+//    * 1983 Original algorithm and test code by Antonin Guttman and Michael Stonebraker, UC Berkely
+//    * 1994 ANCI C ported from original test code by Melinda Green - melinda@superliminal.com
+//    * 1995 Sphere volume fix for degeneracy problem submitted by Paul Brook
+//    * 2004 Templated C++ port by Greg Douglas
+//    * 2013 CERN (www.cern.ch)
+//
+//LICENSE:
+//
+//    Entirely free for all uses. Enjoy!
+
+#ifndef RTREE_H
+#define RTREE_H
+
+// NOTE This file compiles under MSVC 6 SP5 and MSVC .Net 2003 it may not work on other compilers without modification.
+
+// NOTE These next few lines may be win32 specific, you may need to modify them to compile on other platform
+#include <stdio.h>
+#include <math.h>
+#include <assert.h>
+#include <stdlib.h>
+
+#define ASSERT assert    // RTree uses ASSERT( condition )
+#ifndef rMin
+  #define rMin std::min
+#endif    // rMin
+#ifndef rMax
+  #define rMax std::max
+#endif    // rMax
+
+//
+// RTree.h
+//
+
+#define RTREE_TEMPLATE          template <class DATATYPE, class ELEMTYPE, int NUMDIMS, \
+    class ELEMTYPEREAL, int TMAXNODES, int TMINNODES>
+#define RTREE_SEARCH_TEMPLATE   template <class DATATYPE, class ELEMTYPE, int NUMDIMS, \
+    class ELEMTYPEREAL, int TMAXNODES, int TMINNODES, class VISITOR>
+#define RTREE_QUAL              RTree<DATATYPE, ELEMTYPE, NUMDIMS, ELEMTYPEREAL, TMAXNODES, \
+    TMINNODES>
+#define RTREE_SEARCH_QUAL       RTree<DATATYPE, ELEMTYPE, NUMDIMS, ELEMTYPEREAL, TMAXNODES, \
+    TMINNODES, VISITOR>
+
+#define RTREE_DONT_USE_MEMPOOLS     // This version does not contain a fixed memory allocator, fill in lines with EXAMPLE to implement one.
+#define RTREE_USE_SPHERICAL_VOLUME  // Better split classification, may be slower on some systems
+
+// Fwd decl
+class RTFileStream;    // File I/O helper class, look below for implementation and notes.
+
+
+/// \class RTree
+/// Implementation of RTree, a multidimensional bounding rectangle tree.
+/// Example usage: For a 3-dimensional tree use RTree<Object*, float, 3> myTree;
+///
+/// This modified, templated C++ version by Greg Douglas at Auran (http://www.auran.com)
+///
+/// DATATYPE Referenced data, should be int, void*, obj* etc. no larger than sizeof<void*> and simple type
+/// ELEMTYPE Type of element such as int or float
+/// NUMDIMS Number of dimensions such as 2 or 3
+/// ELEMTYPEREAL Type of element that allows fractional and large values such as float or double, for use in volume calcs
+///
+/// NOTES: Inserting and removing data requires the knowledge of its constant Minimal Bounding Rectangle.
+///        This version uses new/delete for nodes, I recommend using a fixed size allocator for efficiency.
+///        Instead of using a callback function for returned results, I recommend and efficient pre-sized, grow-only memory
+///        array similar to MFC CArray or STL Vector for returning search query result.
+///
+template <class DATATYPE, class ELEMTYPE, int NUMDIMS,
+          class ELEMTYPEREAL = ELEMTYPE, int TMAXNODES = 8, int TMINNODES = TMAXNODES / 2>
+class RTree
+{
+protected:
+
+    struct Node; // Fwd decl.  Used by other internal structs and iterator
+public:
+
+    // These constant must be declared after Branch and before Node struct
+    // Stuck up here for MSVC 6 compiler.  NSVC .NET 2003 is much happier.
+    enum {
+        MAXNODES = TMAXNODES,                       ///< Max elements in node
+        MINNODES = TMINNODES,                       ///< Min elements in node
+    };
+
+    struct Statistics {
+        int maxDepth;
+        int avgDepth;
+
+        int maxNodeLoad;
+        int avgNodeLoad;
+        int totalItems;
+    };
+
+public:
+
+    RTree();
+    virtual ~RTree();
+
+    /// Insert entry
+    /// \param a_min Min of bounding rect
+    /// \param a_max Max of bounding rect
+    /// \param a_dataId Positive Id of data.  Maybe zero, but negative numbers not allowed.
+    void Insert( const ELEMTYPE     a_min[NUMDIMS],
+                 const ELEMTYPE     a_max[NUMDIMS],
+                 const DATATYPE&    a_dataId );
+
+    /// Remove entry
+    /// \param a_min Min of bounding rect
+    /// \param a_max Max of bounding rect
+    /// \param a_dataId Positive Id of data.  Maybe zero, but negative numbers not allowed.
+    void Remove( const ELEMTYPE     a_min[NUMDIMS],
+                 const ELEMTYPE     a_max[NUMDIMS],
+                 const DATATYPE&    a_dataId );
+
+    /// Find all within search rectangle
+    /// \param a_min Min of search bounding rect
+    /// \param a_max Max of search bounding rect
+    /// \param a_resultCallback Callback function to return result.  Callback should return 'true' to continue searching
+    /// \param a_context User context to pass as parameter to a_resultCallback
+    /// \return Returns the number of entries found
+    int Search( const ELEMTYPE a_min[NUMDIMS],
+                const ELEMTYPE a_max[NUMDIMS],
+                bool a_resultCallback( DATATYPE a_data, void* a_context ),
+                void* a_context );
+
+    template <class VISITOR>
+    int Search( const ELEMTYPE a_min[NUMDIMS], const ELEMTYPE a_max[NUMDIMS], VISITOR& a_visitor )
+    {
+  #ifdef _DEBUG
+
+        for( int index = 0; index<NUMDIMS; ++index )
+        {
+            ASSERT( a_min[index] <= a_max[index] );
+        }
+
+  #endif    // _DEBUG
+
+        Rect rect;
+
+        for( int axis = 0; axis<NUMDIMS; ++axis )
+        {
+            rect.m_min[axis]    = a_min[axis];
+            rect.m_max[axis]    = a_max[axis];
+        }
+
+
+        // NOTE: May want to return search result another way, perhaps returning the number of found elements here.
+        int cnt;
+
+        Search( m_root, &rect, a_visitor, cnt );
+
+        return cnt;
+    }
+
+    /// Calculate Statistics
+
+    Statistics CalcStats();
+
+    /// Remove all entries from tree
+    void    RemoveAll();
+
+    /// Count the data elements in this container.  This is slow as no internal counter is maintained.
+    int     Count();
+
+    /// Load tree contents from file
+    bool    Load( const char* a_fileName );
+
+    /// Load tree contents from stream
+    bool    Load( RTFileStream& a_stream );
+
+
+    /// Save tree contents to file
+    bool    Save( const char* a_fileName );
+
+    /// Save tree contents to stream
+    bool    Save( RTFileStream& a_stream );
+
+    /// Find the nearest neighbor of a specific point.
+    /// It uses the MINDIST method, simplifying the one from "R-Trees: Theory and Applications" by Yannis Manolopoulos et al.
+    /// The bounding rectangle is used to calculate the distance to the DATATYPE.
+    /// \param a_point point to start the search
+    /// \return Returns the DATATYPE located closest to a_point, 0 if the tree is empty.
+    DATATYPE NearestNeighbor( const ELEMTYPE a_point[NUMDIMS] );
+
+    /// Find the nearest neighbor of a specific point.
+    /// It uses the MINDIST method, simplifying the one from "R-Trees: Theory and Applications" by Yannis Manolopoulos et al.
+    /// It receives a callback function to calculate the distance to a DATATYPE object, instead of using the bounding rectangle.
+    /// \param a_point point to start the search
+    /// \param a_squareDistanceCallback function that performs the square distance calculation for the selected DATATYPE.
+    /// \param a_squareDistance Pointer in which the square distance to the nearest neighbour will be returned.
+    /// \return Returns the DATATYPE located closest to a_point, 0 if the tree is empty.
+    DATATYPE NearestNeighbor( const ELEMTYPE a_point[NUMDIMS],
+                              ELEMTYPE a_squareDistanceCallback( const ELEMTYPE a_point[NUMDIMS], DATATYPE a_data ),
+                              ELEMTYPE* a_squareDistance );
+
+    /// Iterator is not remove safe.
+    class Iterator
+    {
+    private:
+
+        enum { MAX_STACK = 32 }; // Max stack size. Allows almost n^32 where n is number of branches in node
+
+        struct StackElement
+        {
+            Node*   m_node;
+            int     m_branchIndex;
+        };
+    public:
+
+        Iterator()                                    { Init(); }
+
+        ~Iterator()                                   { }
+
+        /// Is iterator invalid
+        bool IsNull()                                 { return m_tos <= 0;  }
+
+        /// Is iterator pointing to valid data
+        bool IsNotNull()                              { return m_tos > 0;  }
+
+        /// Access the current data element. Caller must be sure iterator is not NULL first.
+        DATATYPE& operator*()
+        {
+            ASSERT( IsNotNull() );
+            StackElement& curTos = m_stack[m_tos - 1];
+            return curTos.m_node->m_branch[curTos.m_branchIndex].m_data;
+        }
+
+        /// Access the current data element. Caller must be sure iterator is not NULL first.
+        const DATATYPE& operator*() const
+        {
+            ASSERT( IsNotNull() );
+            StackElement& curTos = m_stack[m_tos - 1];
+            return curTos.m_node->m_branch[curTos.m_branchIndex].m_data;
+        }
+
+        /// Find the next data element
+        bool operator++()                             { return FindNextData(); }
+
+        /// Get the bounds for this node
+        void GetBounds( ELEMTYPE a_min[NUMDIMS], ELEMTYPE a_max[NUMDIMS] )
+        {
+            ASSERT( IsNotNull() );
+            StackElement&   curTos = m_stack[m_tos - 1];
+            Branch&         curBranch = curTos.m_node->m_branch[curTos.m_branchIndex];
+
+            for( int index = 0; index < NUMDIMS; ++index )
+            {
+                a_min[index]    = curBranch.m_rect.m_min[index];
+                a_max[index]    = curBranch.m_rect.m_max[index];
+            }
+        }
+
+    private:
+
+        /// Reset iterator
+        void Init()                                   { m_tos = 0; }
+
+        /// Find the next data element in the tree (For internal use only)
+        bool FindNextData()
+        {
+            for( ; ; )
+            {
+                if( m_tos <= 0 )
+                {
+                    return false;
+                }
+
+                StackElement curTos = Pop(); // Copy stack top cause it may change as we use it
+
+                if( curTos.m_node->IsLeaf() )
+                {
+                    // Keep walking through data while we can
+                    if( curTos.m_branchIndex + 1 < curTos.m_node->m_count )
+                    {
+                        // There is more data, just point to the next one
+                        Push( curTos.m_node, curTos.m_branchIndex + 1 );
+                        return true;
+                    }
+
+                    // No more data, so it will fall back to previous level
+                }
+                else
+                {
+                    if( curTos.m_branchIndex + 1 < curTos.m_node->m_count )
+                    {
+                        // Push sibling on for future tree walk
+                        // This is the 'fall back' node when we finish with the current level
+                        Push( curTos.m_node, curTos.m_branchIndex + 1 );
+                    }
+
+                    // Since cur node is not a leaf, push first of next level to get deeper into the tree
+                    Node* nextLevelnode = curTos.m_node->m_branch[curTos.m_branchIndex].m_child;
+                    Push( nextLevelnode, 0 );
+
+                    // If we pushed on a new leaf, exit as the data is ready at TOS
+                    if( nextLevelnode->IsLeaf() )
+                    {
+                        return true;
+                    }
+                }
+            }
+        }
+
+        /// Push node and branch onto iteration stack (For internal use only)
+        void Push( Node* a_node, int a_branchIndex )
+        {
+            m_stack[m_tos].m_node = a_node;
+            m_stack[m_tos].m_branchIndex = a_branchIndex;
+            ++m_tos;
+            ASSERT( m_tos <= MAX_STACK );
+        }
+
+        /// Pop element off iteration stack (For internal use only)
+        StackElement& Pop()
+        {
+            ASSERT( m_tos > 0 );
+            --m_tos;
+            return m_stack[m_tos];
+        }
+
+        StackElement    m_stack[MAX_STACK]; ///< Stack as we are doing iteration instead of recursion
+        int             m_tos;              ///< Top Of Stack index
+
+        friend class RTree;                 // Allow hiding of non-public functions while allowing manipulation by logical owner
+    };
+
+
+    /// Get 'first' for iteration
+    void GetFirst( Iterator& a_it )
+    {
+        a_it.Init();
+        Node* first = m_root;
+
+        while( first )
+        {
+            if( first->IsInternalNode() && first->m_count > 1 )
+            {
+                a_it.Push( first, 1 ); // Descend sibling branch later
+            }
+            else if( first->IsLeaf() )
+            {
+                if( first->m_count )
+                {
+                    a_it.Push( first, 0 );
+                }
+
+                break;
+            }
+
+            first = first->m_branch[0].m_child;
+        }
+    }
+
+    /// Get Next for iteration
+    void GetNext( Iterator& a_it )                    { ++a_it; }
+
+    /// Is iterator NULL, or at end?
+    bool IsNull( Iterator& a_it )                     { return a_it.IsNull(); }
+
+    /// Get object at iterator position
+    DATATYPE& GetAt( Iterator& a_it )                 { return *a_it; }
+protected:
+
+    /// Minimal bounding rectangle (n-dimensional)
+    struct Rect
+    {
+        ELEMTYPE    m_min[NUMDIMS];                 ///< Min dimensions of bounding box
+        ELEMTYPE    m_max[NUMDIMS];                 ///< Max dimensions of bounding box
+    };
+
+    /// May be data or may be another subtree
+    /// The parents level determines this.
+    /// If the parents level is 0, then this is data
+    struct Branch
+    {
+        Rect m_rect;                              ///< Bounds
+        union
+        {
+            Node*       m_child;                    ///< Child node
+            DATATYPE    m_data;                     ///< Data Id or Ptr
+        };
+    };
+
+    /// Node for each branch level
+    struct Node
+    {
+        bool    IsInternalNode()                         { return m_level > 0;  }   // Not a leaf, but a internal node
+        bool    IsLeaf()                                 { return m_level == 0;  }  // A leaf, contains data
+
+        int     m_count;                            ///< Count
+        int     m_level;                            ///< Leaf is zero, others positive
+        Branch  m_branch[MAXNODES];                 ///< Branch
+    };
+
+    /// A link list of nodes for reinsertion after a delete operation
+    struct ListNode
+    {
+        ListNode*   m_next;                         ///< Next in list
+        Node*       m_node;                         ///< Node
+    };
+
+    /// Variables for finding a split partition
+    struct PartitionVars
+    {
+        int             m_partition[MAXNODES + 1];
+        int             m_total;
+        int             m_minFill;
+        int             m_taken[MAXNODES + 1];
+        int             m_count[2];
+        Rect            m_cover[2];
+        ELEMTYPEREAL    m_area[2];
+
+        Branch          m_branchBuf[MAXNODES + 1];
+        int             m_branchCount;
+        Rect            m_coverSplit;
+        ELEMTYPEREAL    m_coverSplitArea;
+    };
+
+    /// Data structure used for Nearest Neighbor search implementation
+    struct NNNode
+    {
+        Branch m_branch;
+        ELEMTYPE minDist;
+        bool isLeaf;
+    };
+
+    Node*           AllocNode();
+    void            FreeNode( Node* a_node );
+    void            InitNode( Node* a_node );
+    void            InitRect( Rect* a_rect );
+    bool            InsertRectRec( Rect*            a_rect,
+                                   const DATATYPE&  a_id,
+                                   Node*            a_node,
+                                   Node**           a_newNode,
+                                   int              a_level );
+    bool            InsertRect( Rect* a_rect, const DATATYPE& a_id, Node** a_root, int a_level );
+    Rect            NodeCover( Node* a_node );
+    bool            AddBranch( Branch* a_branch, Node* a_node, Node** a_newNode );
+    void            DisconnectBranch( Node* a_node, int a_index );
+    int             PickBranch( Rect* a_rect, Node* a_node );
+    Rect            CombineRect( Rect* a_rectA, Rect* a_rectB );
+    void            SplitNode( Node* a_node, Branch* a_branch, Node** a_newNode );
+    ELEMTYPEREAL    RectSphericalVolume( Rect* a_rect );
+    ELEMTYPEREAL    RectVolume( Rect* a_rect );
+    ELEMTYPEREAL    CalcRectVolume( Rect* a_rect );
+    void            GetBranches( Node* a_node, Branch* a_branch, PartitionVars* a_parVars );
+    void            ChoosePartition( PartitionVars* a_parVars, int a_minFill );
+    void            LoadNodes( Node* a_nodeA, Node* a_nodeB, PartitionVars* a_parVars );
+    void            InitParVars( PartitionVars* a_parVars, int a_maxRects, int a_minFill );
+    void            PickSeeds( PartitionVars* a_parVars );
+    void            Classify( int a_index, int a_group, PartitionVars* a_parVars );
+    bool            RemoveRect( Rect* a_rect, const DATATYPE& a_id, Node** a_root );
+    bool            RemoveRectRec( Rect*            a_rect,
+                                   const DATATYPE&  a_id,
+                                   Node*            a_node,
+                                   ListNode**       a_listNode );
+    ListNode*       AllocListNode();
+    void            FreeListNode( ListNode* a_listNode );
+    bool            Overlap( Rect* a_rectA, Rect* a_rectB );
+    void            ReInsert( Node* a_node, ListNode** a_listNode );
+    ELEMTYPE        MinDist( const ELEMTYPE a_point[NUMDIMS], Rect* a_rect );
+    void            InsertNNListSorted( std::vector<NNNode*>* nodeList, NNNode* newNode );
+
+    bool Search( Node * a_node, Rect * a_rect, int& a_foundCount, bool a_resultCallback(
+                     DATATYPE a_data,
+                     void* a_context ), void* a_context );
+
+    template <class VISITOR>
+    bool Search( Node* a_node, Rect* a_rect, VISITOR& a_visitor, int& a_foundCount )
+    {
+        ASSERT( a_node );
+        ASSERT( a_node->m_level >= 0 );
+        ASSERT( a_rect );
+
+        if( a_node->IsInternalNode() ) // This is an internal node in the tree
+        {
+            for( int index = 0; index < a_node->m_count; ++index )
+            {
+                if( Overlap( a_rect, &a_node->m_branch[index].m_rect ) )
+                {
+                    if( !Search( a_node->m_branch[index].m_child, a_rect, a_visitor, a_foundCount ) )
+                    {
+                        return false; // Don't continue searching
+                    }
+                }
+            }
+        }
+        else // This is a leaf node
+        {
+            for( int index = 0; index < a_node->m_count; ++index )
+            {
+                if( Overlap( a_rect, &a_node->m_branch[index].m_rect ) )
+                {
+                    DATATYPE& id = a_node->m_branch[index].m_data;
+
+                    if( !a_visitor( id ) )
+                        return false;
+
+                    a_foundCount++;
+                }
+            }
+        }
+
+        return true; // Continue searching
+    }
+
+    void    RemoveAllRec( Node* a_node );
+    void    Reset();
+    void    CountRec( Node* a_node, int& a_count );
+
+    bool    SaveRec( Node* a_node, RTFileStream& a_stream );
+    bool    LoadRec( Node* a_node, RTFileStream& a_stream );
+
+    Node*           m_root;                         ///< Root of tree
+    ELEMTYPEREAL    m_unitSphereVolume;             ///< Unit sphere constant for required number of dimensions
+};
+
+
+// Because there is not stream support, this is a quick and dirty file I/O helper.
+// Users will likely replace its usage with a Stream implementation from their favorite API.
+class RTFileStream
+{
+    FILE* m_file;
+public:
+
+
+    RTFileStream()
+    {
+        m_file = NULL;
+    }
+
+    ~RTFileStream()
+    {
+        Close();
+    }
+
+    bool OpenRead( const char* a_fileName )
+    {
+        m_file = fopen( a_fileName, "rb" );
+
+        if( !m_file )
+        {
+            return false;
+        }
+
+        return true;
+    }
+
+    bool OpenWrite( const char* a_fileName )
+    {
+        m_file = fopen( a_fileName, "wb" );
+
+        if( !m_file )
+        {
+            return false;
+        }
+
+        return true;
+    }
+
+    void Close()
+    {
+        if( m_file )
+        {
+            fclose( m_file );
+            m_file = NULL;
+        }
+    }
+
+    template <typename TYPE>
+    size_t Write( const TYPE& a_value )
+    {
+        ASSERT( m_file );
+        return fwrite( (void*) &a_value, sizeof(a_value), 1, m_file );
+    }
+
+    template <typename TYPE>
+    size_t WriteArray( const TYPE* a_array, int a_count )
+    {
+        ASSERT( m_file );
+        return fwrite( (void*) a_array, sizeof(TYPE) * a_count, 1, m_file );
+    }
+
+    template <typename TYPE>
+    size_t Read( TYPE& a_value )
+    {
+        ASSERT( m_file );
+        return fread( (void*) &a_value, sizeof(a_value), 1, m_file );
+    }
+
+    template <typename TYPE>
+    size_t ReadArray( TYPE* a_array, int a_count )
+    {
+        ASSERT( m_file );
+        return fread( (void*) a_array, sizeof(TYPE) * a_count, 1, m_file );
+    }
+};
+
+
+RTREE_TEMPLATE RTREE_QUAL::RTree()
+{
+    ASSERT( MAXNODES > MINNODES );
+    ASSERT( MINNODES > 0 );
+
+
+    // We only support machine word size simple data type eg. integer index or object pointer.
+    // Since we are storing as union with non data branch
+    ASSERT( sizeof(DATATYPE) == sizeof(void*) || sizeof(DATATYPE) == sizeof(int) );
+
+    // Precomputed volumes of the unit spheres for the first few dimensions
+    const float UNIT_SPHERE_VOLUMES[] =
+    {
+        0.000000f, 2.000000f, 3.141593f,    // Dimension  0,1,2
+        4.188790f, 4.934802f, 5.263789f,    // Dimension  3,4,5
+        5.167713f, 4.724766f, 4.058712f,    // Dimension  6,7,8
+        3.298509f, 2.550164f, 1.884104f,    // Dimension  9,10,11
+        1.335263f, 0.910629f, 0.599265f,    // Dimension  12,13,14
+        0.381443f, 0.235331f, 0.140981f,    // Dimension  15,16,17
+        0.082146f, 0.046622f, 0.025807f,    // Dimension  18,19,20
+    };
+
+    m_root = AllocNode();
+    m_root->m_level     = 0;
+    m_unitSphereVolume  = (ELEMTYPEREAL) UNIT_SPHERE_VOLUMES[NUMDIMS];
+}
+
+
+RTREE_TEMPLATE
+RTREE_QUAL::~RTree() {
+    Reset(); // Free, or reset node memory
+}
+
+
+RTREE_TEMPLATE
+void RTREE_QUAL::Insert( const ELEMTYPE     a_min[NUMDIMS],
+                         const ELEMTYPE     a_max[NUMDIMS],
+                         const DATATYPE&    a_dataId )
+{
+#ifdef _DEBUG
+
+    for( int index = 0; index<NUMDIMS; ++index )
+    {
+        ASSERT( a_min[index] <= a_max[index] );
+    }
+
+#endif    // _DEBUG
+
+    Rect rect;
+
+    for( int axis = 0; axis<NUMDIMS; ++axis )
+    {
+        rect.m_min[axis]    = a_min[axis];
+        rect.m_max[axis]    = a_max[axis];
+    }
+
+    InsertRect( &rect, a_dataId, &m_root, 0 );
+}
+
+
+RTREE_TEMPLATE
+void RTREE_QUAL::Remove( const ELEMTYPE     a_min[NUMDIMS],
+                         const ELEMTYPE     a_max[NUMDIMS],
+                         const DATATYPE&    a_dataId )
+{
+#ifdef _DEBUG
+
+    for( int index = 0; index<NUMDIMS; ++index )
+    {
+        ASSERT( a_min[index] <= a_max[index] );
+    }
+
+#endif    // _DEBUG
+
+    Rect rect;
+
+    for( int axis = 0; axis<NUMDIMS; ++axis )
+    {
+        rect.m_min[axis]    = a_min[axis];
+        rect.m_max[axis]    = a_max[axis];
+    }
+
+    RemoveRect( &rect, a_dataId, &m_root );
+}
+
+
+RTREE_TEMPLATE
+int RTREE_QUAL::Search( const ELEMTYPE a_min[NUMDIMS],
+                        const ELEMTYPE a_max[NUMDIMS],
+                        bool a_resultCallback( DATATYPE a_data, void* a_context ),
+                        void* a_context )
+{
+#ifdef _DEBUG
+
+    for( int index = 0; index<NUMDIMS; ++index )
+    {
+        ASSERT( a_min[index] <= a_max[index] );
+    }
+
+#endif    // _DEBUG
+
+    Rect rect;
+
+    for( int axis = 0; axis<NUMDIMS; ++axis )
+    {
+        rect.m_min[axis]    = a_min[axis];
+        rect.m_max[axis]    = a_max[axis];
+    }
+
+    // NOTE: May want to return search result another way, perhaps returning the number of found elements here.
+
+    int foundCount = 0;
+    Search( m_root, &rect, foundCount, a_resultCallback, a_context );
+
+    return foundCount;
+}
+
+
+RTREE_TEMPLATE
+DATATYPE RTREE_QUAL::NearestNeighbor( const ELEMTYPE a_point[NUMDIMS] )
+{
+    return this->NearestNeighbor( a_point, 0, 0 );
+}
+
+
+RTREE_TEMPLATE
+DATATYPE RTREE_QUAL::NearestNeighbor( const ELEMTYPE a_point[NUMDIMS],
+                                      ELEMTYPE a_squareDistanceCallback( const ELEMTYPE a_point[NUMDIMS], DATATYPE a_data ),
+                                      ELEMTYPE* a_squareDistance )
+{
+    typedef typename std::vector<NNNode*>::iterator iterator;
+    std::vector<NNNode*> nodeList;
+    Node* node = m_root;
+    NNNode* closestNode = 0;
+    while( !closestNode || !closestNode->isLeaf )
+    {
+        //check every node on this level
+        for( int index = 0; index < node->m_count; ++index )
+        {
+            NNNode* newNode = new NNNode;
+            newNode->isLeaf = node->IsLeaf();
+            newNode->m_branch = node->m_branch[index];
+            if( newNode->isLeaf && a_squareDistanceCallback )
+                newNode->minDist = a_squareDistanceCallback( a_point, newNode->m_branch.m_data );
+            else
+                newNode->minDist = this->MinDist( a_point, &(node->m_branch[index].m_rect) );
+
+            //TODO: a custom list could be more efficient than a vector
+            this->InsertNNListSorted( &nodeList, newNode );
+        }
+        if( nodeList.size() == 0 )
+        {
+            return 0;
+        }
+        closestNode = nodeList.back();
+        node = closestNode->m_branch.m_child;
+        nodeList.pop_back();
+        free(closestNode);
+    }
+
+    // free memory used for remaining NNNodes in nodeList
+    for( iterator iter = nodeList.begin(); iter != nodeList.end(); ++iter )
+    {
+        NNNode* node = *iter;
+        free(node);
+    }
+
+    *a_squareDistance = closestNode->minDist;
+    return closestNode->m_branch.m_data;
+}
+
+
+RTREE_TEMPLATE
+int RTREE_QUAL::Count()
+{
+    int count = 0;
+
+    CountRec( m_root, count );
+
+    return count;
+}
+
+
+RTREE_TEMPLATE
+void RTREE_QUAL::CountRec( Node* a_node, int& a_count )
+{
+    if( a_node->IsInternalNode() ) // not a leaf node
+    {
+        for( int index = 0; index < a_node->m_count; ++index )
+        {
+            CountRec( a_node->m_branch[index].m_child, a_count );
+        }
+    }
+    else // A leaf node
+    {
+        a_count += a_node->m_count;
+    }
+}
+
+
+RTREE_TEMPLATE
+bool RTREE_QUAL::Load( const char* a_fileName )
+{
+    RemoveAll(); // Clear existing tree
+
+    RTFileStream stream;
+
+    if( !stream.OpenRead( a_fileName ) )
+    {
+        return false;
+    }
+
+    bool result = Load( stream );
+
+    stream.Close();
+
+    return result;
+};
+
+
+RTREE_TEMPLATE
+bool RTREE_QUAL::Load( RTFileStream& a_stream )
+{
+    // Write some kind of header
+    int _dataFileId         = ('R' << 0) | ('T' << 8) | ('R' << 16) | ('E' << 24);
+    int _dataSize           = sizeof(DATATYPE);
+    int _dataNumDims        = NUMDIMS;
+    int _dataElemSize       = sizeof(ELEMTYPE);
+    int _dataElemRealSize   = sizeof(ELEMTYPEREAL);
+    int _dataMaxNodes       = TMAXNODES;
+    int _dataMinNodes       = TMINNODES;
+
+    int dataFileId          = 0;
+    int dataSize            = 0;
+    int dataNumDims         = 0;
+    int dataElemSize        = 0;
+    int dataElemRealSize    = 0;
+    int dataMaxNodes        = 0;
+    int dataMinNodes        = 0;
+
+    a_stream.Read( dataFileId );
+    a_stream.Read( dataSize );
+    a_stream.Read( dataNumDims );
+    a_stream.Read( dataElemSize );
+    a_stream.Read( dataElemRealSize );
+    a_stream.Read( dataMaxNodes );
+    a_stream.Read( dataMinNodes );
+
+    bool result = false;
+
+    // Test if header was valid and compatible
+    if( (dataFileId == _dataFileId)
+        && (dataSize == _dataSize)
+        && (dataNumDims == _dataNumDims)
+        && (dataElemSize == _dataElemSize)
+        && (dataElemRealSize == _dataElemRealSize)
+        && (dataMaxNodes == _dataMaxNodes)
+        && (dataMinNodes == _dataMinNodes)
+         )
+    {
+        // Recursively load tree
+        result = LoadRec( m_root, a_stream );
+    }
+
+    return result;
+}
+
+
+RTREE_TEMPLATE
+bool RTREE_QUAL::LoadRec( Node* a_node, RTFileStream& a_stream )
+{
+    a_stream.Read( a_node->m_level );
+    a_stream.Read( a_node->m_count );
+
+    if( a_node->IsInternalNode() ) // not a leaf node
+    {
+        for( int index = 0; index < a_node->m_count; ++index )
+        {
+            Branch* curBranch = &a_node->m_branch[index];
+
+            a_stream.ReadArray( curBranch->m_rect.m_min, NUMDIMS );
+            a_stream.ReadArray( curBranch->m_rect.m_max, NUMDIMS );
+
+            curBranch->m_child = AllocNode();
+            LoadRec( curBranch->m_child, a_stream );
+        }
+    }
+    else // A leaf node
+    {
+        for( int index = 0; index < a_node->m_count; ++index )
+        {
+            Branch* curBranch = &a_node->m_branch[index];
+
+            a_stream.ReadArray( curBranch->m_rect.m_min, NUMDIMS );
+            a_stream.ReadArray( curBranch->m_rect.m_max, NUMDIMS );
+
+            a_stream.Read( curBranch->m_data );
+        }
+    }
+
+    return true; // Should do more error checking on I/O operations
+}
+
+
+RTREE_TEMPLATE
+bool RTREE_QUAL::Save( const char* a_fileName )
+{
+    RTFileStream stream;
+
+    if( !stream.OpenWrite( a_fileName ) )
+    {
+        return false;
+    }
+
+    bool result = Save( stream );
+
+    stream.Close();
+
+    return result;
+}
+
+
+RTREE_TEMPLATE
+bool RTREE_QUAL::Save( RTFileStream& a_stream )
+{
+    // Write some kind of header
+    int dataFileId          = ('R' << 0) | ('T' << 8) | ('R' << 16) | ('E' << 24);
+    int dataSize            = sizeof(DATATYPE);
+    int dataNumDims         = NUMDIMS;
+    int dataElemSize        = sizeof(ELEMTYPE);
+    int dataElemRealSize    = sizeof(ELEMTYPEREAL);
+    int dataMaxNodes        = TMAXNODES;
+    int dataMinNodes        = TMINNODES;
+
+    a_stream.Write( dataFileId );
+    a_stream.Write( dataSize );
+    a_stream.Write( dataNumDims );
+    a_stream.Write( dataElemSize );
+    a_stream.Write( dataElemRealSize );
+    a_stream.Write( dataMaxNodes );
+    a_stream.Write( dataMinNodes );
+
+    // Recursively save tree
+    bool result = SaveRec( m_root, a_stream );
+
+    return result;
+}
+
+
+RTREE_TEMPLATE
+bool RTREE_QUAL::SaveRec( Node* a_node, RTFileStream& a_stream )
+{
+    a_stream.Write( a_node->m_level );
+    a_stream.Write( a_node->m_count );
+
+    if( a_node->IsInternalNode() ) // not a leaf node
+    {
+        for( int index = 0; index < a_node->m_count; ++index )
+        {
+            Branch* curBranch = &a_node->m_branch[index];
+
+            a_stream.WriteArray( curBranch->m_rect.m_min, NUMDIMS );
+            a_stream.WriteArray( curBranch->m_rect.m_max, NUMDIMS );
+
+            SaveRec( curBranch->m_child, a_stream );
+        }
+    }
+    else // A leaf node
+    {
+        for( int index = 0; index < a_node->m_count; ++index )
+        {
+            Branch* curBranch = &a_node->m_branch[index];
+
+            a_stream.WriteArray( curBranch->m_rect.m_min, NUMDIMS );
+            a_stream.WriteArray( curBranch->m_rect.m_max, NUMDIMS );
+
+            a_stream.Write( curBranch->m_data );
+        }
+    }
+
+    return true; // Should do more error checking on I/O operations
+}
+
+
+RTREE_TEMPLATE
+void RTREE_QUAL::RemoveAll()
+{
+    // Delete all existing nodes
+    Reset();
+
+    m_root = AllocNode();
+    m_root->m_level = 0;
+}
+
+
+RTREE_TEMPLATE
+void RTREE_QUAL::Reset()
+{
+#ifdef RTREE_DONT_USE_MEMPOOLS
+    // Delete all existing nodes
+    RemoveAllRec( m_root );
+#else    // RTREE_DONT_USE_MEMPOOLS
+    // Just reset memory pools.  We are not using complex types
+    // EXAMPLE
+#endif    // RTREE_DONT_USE_MEMPOOLS
+}
+
+
+RTREE_TEMPLATE
+void RTREE_QUAL::RemoveAllRec( Node* a_node )
+{
+    ASSERT( a_node );
+    ASSERT( a_node->m_level >= 0 );
+
+    if( a_node->IsInternalNode() ) // This is an internal node in the tree
+    {
+        for( int index = 0; index < a_node->m_count; ++index )
+        {
+            RemoveAllRec( a_node->m_branch[index].m_child );
+        }
+    }
+
+    FreeNode( a_node );
+}
+
+
+RTREE_TEMPLATE
+typename RTREE_QUAL::Node* RTREE_QUAL::AllocNode()
+{
+    Node* newNode;
+
+#ifdef RTREE_DONT_USE_MEMPOOLS
+    newNode = new Node;
+#else       // RTREE_DONT_USE_MEMPOOLS
+    // EXAMPLE
+#endif      // RTREE_DONT_USE_MEMPOOLS
+    InitNode( newNode );
+    return newNode;
+}
+
+
+RTREE_TEMPLATE
+void RTREE_QUAL::FreeNode( Node* a_node )
+{
+    ASSERT( a_node );
+
+#ifdef RTREE_DONT_USE_MEMPOOLS
+    delete a_node;
+#else       // RTREE_DONT_USE_MEMPOOLS
+    // EXAMPLE
+#endif      // RTREE_DONT_USE_MEMPOOLS
+}
+
+
+// Allocate space for a node in the list used in DeletRect to
+// store Nodes that are too empty.
+RTREE_TEMPLATE
+typename RTREE_QUAL::ListNode* RTREE_QUAL::AllocListNode()
+{
+#ifdef RTREE_DONT_USE_MEMPOOLS
+    return new ListNode;
+#else       // RTREE_DONT_USE_MEMPOOLS
+    // EXAMPLE
+#endif      // RTREE_DONT_USE_MEMPOOLS
+}
+
+
+RTREE_TEMPLATE
+void RTREE_QUAL::FreeListNode( ListNode* a_listNode )
+{
+#ifdef RTREE_DONT_USE_MEMPOOLS
+    delete a_listNode;
+#else       // RTREE_DONT_USE_MEMPOOLS
+    // EXAMPLE
+#endif      // RTREE_DONT_USE_MEMPOOLS
+}
+
+
+RTREE_TEMPLATE
+void RTREE_QUAL::InitNode( Node* a_node )
+{
+    a_node->m_count = 0;
+    a_node->m_level = -1;
+}
+
+
+RTREE_TEMPLATE
+void RTREE_QUAL::InitRect( Rect* a_rect )
+{
+    for( int index = 0; index < NUMDIMS; ++index )
+    {
+        a_rect->m_min[index]    = (ELEMTYPE) 0;
+        a_rect->m_max[index]    = (ELEMTYPE) 0;
+    }
+}
+
+
+// Inserts a new data rectangle into the index structure.
+// Recursively descends tree, propagates splits back up.
+// Returns 0 if node was not split.  Old node updated.
+// If node was split, returns 1 and sets the pointer pointed to by
+// new_node to point to the new node.  Old node updated to become one of two.
+// The level argument specifies the number of steps up from the leaf
+// level to insert; e.g. a data rectangle goes in at level = 0.
+RTREE_TEMPLATE
+bool RTREE_QUAL::InsertRectRec( Rect*           a_rect,
+                                const DATATYPE& a_id,
+                                Node*           a_node,
+                                Node**          a_newNode,
+                                int             a_level )
+{
+    ASSERT( a_rect && a_node && a_newNode );
+    ASSERT( a_level >= 0 && a_level <= a_node->m_level );
+
+    int     index;
+    Branch  branch;
+    Node*   otherNode;
+
+    // Still above level for insertion, go down tree recursively
+    if( a_node->m_level > a_level )
+    {
+        index = PickBranch( a_rect, a_node );
+
+        if( !InsertRectRec( a_rect, a_id, a_node->m_branch[index].m_child, &otherNode, a_level ) )
+        {
+            // Child was not split
+            a_node->m_branch[index].m_rect =
+                CombineRect( a_rect, &(a_node->m_branch[index].m_rect) );
+            return false;
+        }
+        else // Child was split
+        {
+            a_node->m_branch[index].m_rect = NodeCover( a_node->m_branch[index].m_child );
+            branch.m_child  = otherNode;
+            branch.m_rect   = NodeCover( otherNode );
+            return AddBranch( &branch, a_node, a_newNode );
+        }
+    }
+    else if( a_node->m_level == a_level ) // Have reached level for insertion. Add rect, split if necessary
+    {
+        branch.m_rect   = *a_rect;
+        branch.m_child  = (Node*) a_id;
+        // Child field of leaves contains id of data record
+        return AddBranch( &branch, a_node, a_newNode );
+    }
+    else
+    {
+        // Should never occur
+        ASSERT( 0 );
+        return false;
+    }
+}
+
+
+// Insert a data rectangle into an index structure.
+// InsertRect provides for splitting the root;
+// returns 1 if root was split, 0 if it was not.
+// The level argument specifies the number of steps up from the leaf
+// level to insert; e.g. a data rectangle goes in at level = 0.
+// InsertRect2 does the recursion.
+//
+RTREE_TEMPLATE
+bool RTREE_QUAL::InsertRect( Rect* a_rect, const DATATYPE& a_id, Node** a_root, int a_level )
+{
+    ASSERT( a_rect && a_root );
+    ASSERT( a_level >= 0 && a_level <= (*a_root)->m_level );
+#ifdef _DEBUG
+
+    for( int index = 0; index < NUMDIMS; ++index )
+    {
+        ASSERT( a_rect->m_min[index] <= a_rect->m_max[index] );
+    }
+
+#endif    // _DEBUG
+
+    Node*   newRoot;
+    Node*   newNode;
+    Branch  branch;
+
+    if( InsertRectRec( a_rect, a_id, *a_root, &newNode, a_level ) ) // Root split
+    {
+        newRoot = AllocNode();                                      // Grow tree taller and new root
+        newRoot->m_level    = (*a_root)->m_level + 1;
+        branch.m_rect       = NodeCover( *a_root );
+        branch.m_child      = *a_root;
+        AddBranch( &branch, newRoot, NULL );
+        branch.m_rect   = NodeCover( newNode );
+        branch.m_child  = newNode;
+        AddBranch( &branch, newRoot, NULL );
+        *a_root = newRoot;
+        return true;
+    }
+
+    return false;
+}
+
+
+// Find the smallest rectangle that includes all rectangles in branches of a node.
+RTREE_TEMPLATE
+typename RTREE_QUAL::Rect RTREE_QUAL::NodeCover( Node* a_node )
+{
+    ASSERT( a_node );
+
+    int     firstTime = true;
+    Rect    rect;
+    InitRect( &rect );
+
+    for( int index = 0; index < a_node->m_count; ++index )
+    {
+        if( firstTime )
+        {
+            rect = a_node->m_branch[index].m_rect;
+            firstTime = false;
+        }
+        else
+        {
+            rect = CombineRect( &rect, &(a_node->m_branch[index].m_rect) );
+        }
+    }
+
+    return rect;
+}
+
+
+// Add a branch to a node.  Split the node if necessary.
+// Returns 0 if node not split.  Old node updated.
+// Returns 1 if node split, sets *new_node to address of new node.
+// Old node updated, becomes one of two.
+RTREE_TEMPLATE
+bool RTREE_QUAL::AddBranch( Branch* a_branch, Node* a_node, Node** a_newNode )
+{
+    ASSERT( a_branch );
+    ASSERT( a_node );
+
+    if( a_node->m_count < MAXNODES ) // Split won't be necessary
+    {
+        a_node->m_branch[a_node->m_count] = *a_branch;
+        ++a_node->m_count;
+
+        return false;
+    }
+    else
+    {
+        ASSERT( a_newNode );
+
+        SplitNode( a_node, a_branch, a_newNode );
+        return true;
+    }
+}
+
+
+// Disconnect a dependent node.
+// Caller must return (or stop using iteration index) after this as count has changed
+RTREE_TEMPLATE
+void RTREE_QUAL::DisconnectBranch( Node* a_node, int a_index )
+{
+    ASSERT( a_node && (a_index >= 0) && (a_index < MAXNODES) );
+    ASSERT( a_node->m_count > 0 );
+
+    // Remove element by swapping with the last element to prevent gaps in array
+    a_node->m_branch[a_index] = a_node->m_branch[a_node->m_count - 1];
+
+    --a_node->m_count;
+}
+
+
+// Pick a branch.  Pick the one that will need the smallest increase
+// in area to accomodate the new rectangle.  This will result in the
+// least total area for the covering rectangles in the current node.
+// In case of a tie, pick the one which was smaller before, to get
+// the best resolution when searching.
+RTREE_TEMPLATE
+int RTREE_QUAL::PickBranch( Rect* a_rect, Node* a_node )
+{
+    ASSERT( a_rect && a_node );
+
+    bool            firstTime = true;
+    ELEMTYPEREAL    increase;
+    ELEMTYPEREAL    bestIncr = (ELEMTYPEREAL) -1;
+    ELEMTYPEREAL    area;
+    ELEMTYPEREAL    bestArea = 0;
+    int             best = 0;
+    Rect            tempRect;
+
+    for( int index = 0; index < a_node->m_count; ++index )
+    {
+        Rect* curRect = &a_node->m_branch[index].m_rect;
+        area        = CalcRectVolume( curRect );
+        tempRect    = CombineRect( a_rect, curRect );
+        increase    = CalcRectVolume( &tempRect ) - area;
+
+        if( (increase < bestIncr) || firstTime )
+        {
+            best        = index;
+            bestArea    = area;
+            bestIncr    = increase;
+            firstTime   = false;
+        }
+        else if( (increase == bestIncr) && (area < bestArea) )
+        {
+            best        = index;
+            bestArea    = area;
+            bestIncr    = increase;
+        }
+    }
+
+    return best;
+}
+
+
+// Combine two rectangles into larger one containing both
+RTREE_TEMPLATE
+typename RTREE_QUAL::Rect RTREE_QUAL::CombineRect( Rect* a_rectA, Rect* a_rectB )
+{
+    ASSERT( a_rectA && a_rectB );
+
+    Rect newRect;
+
+    for( int index = 0; index < NUMDIMS; ++index )
+    {
+        newRect.m_min[index]    = rMin( a_rectA->m_min[index], a_rectB->m_min[index] );
+        newRect.m_max[index]    = rMax( a_rectA->m_max[index], a_rectB->m_max[index] );
+    }
+
+    return newRect;
+}
+
+
+// Split a node.
+// Divides the nodes branches and the extra one between two nodes.
+// Old node is one of the new ones, and one really new one is created.
+// Tries more than one method for choosing a partition, uses best result.
+RTREE_TEMPLATE
+void RTREE_QUAL::SplitNode( Node* a_node, Branch* a_branch, Node** a_newNode )
+{
+    ASSERT( a_node );
+    ASSERT( a_branch );
+
+    // Could just use local here, but member or external is faster since it is reused
+    PartitionVars   localVars;
+    PartitionVars*  parVars = &localVars;
+    int             level;
+
+    // Load all the branches into a buffer, initialize old node
+    level = a_node->m_level;
+    GetBranches( a_node, a_branch, parVars );
+
+    // Find partition
+    ChoosePartition( parVars, MINNODES );
+
+    // Put branches from buffer into 2 nodes according to chosen partition
+    *a_newNode = AllocNode();
+    (*a_newNode)->m_level = a_node->m_level = level;
+    LoadNodes( a_node, *a_newNode, parVars );
+
+    ASSERT( (a_node->m_count + (*a_newNode)->m_count) == parVars->m_total );
+}
+
+
+// Calculate the n-dimensional volume of a rectangle
+RTREE_TEMPLATE
+ELEMTYPEREAL RTREE_QUAL::RectVolume( Rect* a_rect )
+{
+    ASSERT( a_rect );
+
+    ELEMTYPEREAL volume = (ELEMTYPEREAL) 1;
+
+    for( int index = 0; index<NUMDIMS; ++index )
+    {
+        volume *= a_rect->m_max[index] - a_rect->m_min[index];
+    }
+
+    ASSERT( volume >= (ELEMTYPEREAL) 0 );
+
+    return volume;
+}
+
+
+// The exact volume of the bounding sphere for the given Rect
+RTREE_TEMPLATE
+ELEMTYPEREAL RTREE_QUAL::RectSphericalVolume( Rect* a_rect )
+{
+    ASSERT( a_rect );
+
+    ELEMTYPEREAL    sumOfSquares = (ELEMTYPEREAL) 0;
+    ELEMTYPEREAL    radius;
+
+    for( int index = 0; index < NUMDIMS; ++index )
+    {
+        ELEMTYPEREAL halfExtent =
+            ( (ELEMTYPEREAL) a_rect->m_max[index] - (ELEMTYPEREAL) a_rect->m_min[index] ) * 0.5f;
+        sumOfSquares += halfExtent * halfExtent;
+    }
+
+    radius = (ELEMTYPEREAL) sqrt( sumOfSquares );
+
+    // Pow maybe slow, so test for common dims like 2,3 and just use x*x, x*x*x.
+    if( NUMDIMS == 3 )
+    {
+        return radius * radius * radius * m_unitSphereVolume;
+    }
+    else if( NUMDIMS == 2 )
+    {
+        return radius * radius * m_unitSphereVolume;
+    }
+    else
+    {
+        return (ELEMTYPEREAL) (pow( radius, NUMDIMS ) * m_unitSphereVolume);
+    }
+}
+
+
+// Use one of the methods to calculate retangle volume
+RTREE_TEMPLATE
+ELEMTYPEREAL RTREE_QUAL::CalcRectVolume( Rect* a_rect )
+{
+#ifdef RTREE_USE_SPHERICAL_VOLUME
+    return RectSphericalVolume( a_rect );   // Slower but helps certain merge cases
+#else                                       // RTREE_USE_SPHERICAL_VOLUME
+    return RectVolume( a_rect );            // Faster but can cause poor merges
+#endif                                      // RTREE_USE_SPHERICAL_VOLUME
+}
+
+
+// Load branch buffer with branches from full node plus the extra branch.
+RTREE_TEMPLATE
+void RTREE_QUAL::GetBranches( Node* a_node, Branch* a_branch, PartitionVars* a_parVars )
+{
+    ASSERT( a_node );
+    ASSERT( a_branch );
+
+    ASSERT( a_node->m_count == MAXNODES );
+
+    // Load the branch buffer
+    for( int index = 0; index < MAXNODES; ++index )
+    {
+        a_parVars->m_branchBuf[index] = a_node->m_branch[index];
+    }
+
+    a_parVars->m_branchBuf[MAXNODES] = *a_branch;
+    a_parVars->m_branchCount = MAXNODES + 1;
+
+    // Calculate rect containing all in the set
+    a_parVars->m_coverSplit = a_parVars->m_branchBuf[0].m_rect;
+
+    for( int index = 1; index < MAXNODES + 1; ++index )
+    {
+        a_parVars->m_coverSplit =
+            CombineRect( &a_parVars->m_coverSplit, &a_parVars->m_branchBuf[index].m_rect );
+    }
+
+    a_parVars->m_coverSplitArea = CalcRectVolume( &a_parVars->m_coverSplit );
+
+    InitNode( a_node );
+}
+
+
+// Method #0 for choosing a partition:
+// As the seeds for the two groups, pick the two rects that would waste the
+// most area if covered by a single rectangle, i.e. evidently the worst pair
+// to have in the same group.
+// Of the remaining, one at a time is chosen to be put in one of the two groups.
+// The one chosen is the one with the greatest difference in area expansion
+// depending on which group - the rect most strongly attracted to one group
+// and repelled from the other.
+// If one group gets too full (more would force other group to violate min
+// fill requirement) then other group gets the rest.
+// These last are the ones that can go in either group most easily.
+RTREE_TEMPLATE
+void RTREE_QUAL::ChoosePartition( PartitionVars* a_parVars, int a_minFill )
+{
+    ASSERT( a_parVars );
+
+    ELEMTYPEREAL    biggestDiff;
+    int             group, chosen = 0, betterGroup = 0;
+
+    InitParVars( a_parVars, a_parVars->m_branchCount, a_minFill );
+    PickSeeds( a_parVars );
+
+    while( ( (a_parVars->m_count[0] + a_parVars->m_count[1]) < a_parVars->m_total )
+           && ( a_parVars->m_count[0] < (a_parVars->m_total - a_parVars->m_minFill) )
+           && ( a_parVars->m_count[1] < (a_parVars->m_total - a_parVars->m_minFill) ) )
+    {
+        biggestDiff = (ELEMTYPEREAL) -1;
+
+        for( int index = 0; index<a_parVars->m_total; ++index )
+        {
+            if( !a_parVars->m_taken[index] )
+            {
+                Rect*           curRect = &a_parVars->m_branchBuf[index].m_rect;
+                Rect            rect0   = CombineRect( curRect, &a_parVars->m_cover[0] );
+                Rect            rect1   = CombineRect( curRect, &a_parVars->m_cover[1] );
+                ELEMTYPEREAL    growth0 = CalcRectVolume( &rect0 ) - a_parVars->m_area[0];
+                ELEMTYPEREAL    growth1 = CalcRectVolume( &rect1 ) - a_parVars->m_area[1];
+                ELEMTYPEREAL    diff    = growth1 - growth0;
+
+                if( diff >= 0 )
+                {
+                    group = 0;
+                }
+                else
+                {
+                    group   = 1;
+                    diff    = -diff;
+                }
+
+                if( diff > biggestDiff )
+                {
+                    biggestDiff = diff;
+                    chosen = index;
+                    betterGroup = group;
+                }
+                else if( (diff == biggestDiff)
+                         && (a_parVars->m_count[group] < a_parVars->m_count[betterGroup]) )
+                {
+                    chosen = index;
+                    betterGroup = group;
+                }
+            }
+        }
+
+        Classify( chosen, betterGroup, a_parVars );
+    }
+
+    // If one group too full, put remaining rects in the other
+    if( (a_parVars->m_count[0] + a_parVars->m_count[1]) < a_parVars->m_total )
+    {
+        if( a_parVars->m_count[0] >= a_parVars->m_total - a_parVars->m_minFill )
+        {
+            group = 1;
+        }
+        else
+        {
+            group = 0;
+        }
+
+        for( int index = 0; index<a_parVars->m_total; ++index )
+        {
+            if( !a_parVars->m_taken[index] )
+            {
+                Classify( index, group, a_parVars );
+            }
+        }
+    }
+
+    ASSERT( (a_parVars->m_count[0] + a_parVars->m_count[1]) == a_parVars->m_total );
+    ASSERT( (a_parVars->m_count[0] >= a_parVars->m_minFill)
+            && (a_parVars->m_count[1] >= a_parVars->m_minFill) );
+}
+
+
+// Copy branches from the buffer into two nodes according to the partition.
+RTREE_TEMPLATE
+void RTREE_QUAL::LoadNodes( Node* a_nodeA, Node* a_nodeB, PartitionVars* a_parVars )
+{
+    ASSERT( a_nodeA );
+    ASSERT( a_nodeB );
+    ASSERT( a_parVars );
+
+    for( int index = 0; index < a_parVars->m_total; ++index )
+    {
+        ASSERT( a_parVars->m_partition[index] == 0 || a_parVars->m_partition[index] == 1 );
+
+        if( a_parVars->m_partition[index] == 0 )
+        {
+            AddBranch( &a_parVars->m_branchBuf[index], a_nodeA, NULL );
+        }
+        else if( a_parVars->m_partition[index] == 1 )
+        {
+            AddBranch( &a_parVars->m_branchBuf[index], a_nodeB, NULL );
+        }
+    }
+}
+
+
+// Initialize a PartitionVars structure.
+RTREE_TEMPLATE
+void RTREE_QUAL::InitParVars( PartitionVars* a_parVars, int a_maxRects, int a_minFill )
+{
+    ASSERT( a_parVars );
+
+    a_parVars->m_count[0]   = a_parVars->m_count[1] = 0;
+    a_parVars->m_area[0]    = a_parVars->m_area[1] = (ELEMTYPEREAL) 0;
+    a_parVars->m_total      = a_maxRects;
+    a_parVars->m_minFill    = a_minFill;
+
+    for( int index = 0; index < a_maxRects; ++index )
+    {
+        a_parVars->m_taken[index]       = false;
+        a_parVars->m_partition[index]   = -1;
+    }
+}
+
+
+RTREE_TEMPLATE
+void RTREE_QUAL::PickSeeds( PartitionVars* a_parVars )
+{
+    int             seed0 = 0, seed1 = 0;
+    ELEMTYPEREAL    worst, waste;
+    ELEMTYPEREAL    area[MAXNODES + 1];
+
+    for( int index = 0; index<a_parVars->m_total; ++index )
+    {
+        area[index] = CalcRectVolume( &a_parVars->m_branchBuf[index].m_rect );
+    }
+
+    worst = -a_parVars->m_coverSplitArea - 1;
+
+    for( int indexA = 0; indexA < a_parVars->m_total - 1; ++indexA )
+    {
+        for( int indexB = indexA + 1; indexB < a_parVars->m_total; ++indexB )
+        {
+            Rect oneRect = CombineRect( &a_parVars->m_branchBuf[indexA].m_rect,
+                                        &a_parVars->m_branchBuf[indexB].m_rect );
+            waste = CalcRectVolume( &oneRect ) - area[indexA] - area[indexB];
+
+            if( waste >= worst )
+            {
+                worst   = waste;
+                seed0   = indexA;
+                seed1   = indexB;
+            }
+        }
+    }
+
+    Classify( seed0, 0, a_parVars );
+    Classify( seed1, 1, a_parVars );
+}
+
+
+// Put a branch in one of the groups.
+RTREE_TEMPLATE
+void RTREE_QUAL::Classify( int a_index, int a_group, PartitionVars* a_parVars )
+{
+    ASSERT( a_parVars );
+    ASSERT( !a_parVars->m_taken[a_index] );
+
+    a_parVars->m_partition[a_index] = a_group;
+    a_parVars->m_taken[a_index]     = true;
+
+    if( a_parVars->m_count[a_group] == 0 )
+    {
+        a_parVars->m_cover[a_group] = a_parVars->m_branchBuf[a_index].m_rect;
+    }
+    else
+    {
+        a_parVars->m_cover[a_group] = CombineRect( &a_parVars->m_branchBuf[a_index].m_rect,
+                                                   &a_parVars->m_cover[a_group] );
+    }
+
+    a_parVars->m_area[a_group] = CalcRectVolume( &a_parVars->m_cover[a_group] );
+    ++a_parVars->m_count[a_group];
+}
+
+
+// Delete a data rectangle from an index structure.
+// Pass in a pointer to a Rect, the tid of the record, ptr to ptr to root node.
+// Returns 1 if record not found, 0 if success.
+// RemoveRect provides for eliminating the root.
+RTREE_TEMPLATE
+bool RTREE_QUAL::RemoveRect( Rect* a_rect, const DATATYPE& a_id, Node** a_root )
+{
+    ASSERT( a_rect && a_root );
+    ASSERT( *a_root );
+
+    Node*       tempNode;
+    ListNode*   reInsertList = NULL;
+
+    if( !RemoveRectRec( a_rect, a_id, *a_root, &reInsertList ) )
+    {
+        // Found and deleted a data item
+        // Reinsert any branches from eliminated nodes
+        while( reInsertList )
+        {
+            tempNode = reInsertList->m_node;
+
+            for( int index = 0; index < tempNode->m_count; ++index )
+            {
+                InsertRect( &(tempNode->m_branch[index].m_rect),
+                            tempNode->m_branch[index].m_data,
+                            a_root,
+                            tempNode->m_level );
+            }
+
+            ListNode* remLNode = reInsertList;
+            reInsertList = reInsertList->m_next;
+
+            FreeNode( remLNode->m_node );
+            FreeListNode( remLNode );
+        }
+
+        // Check for redundant root (not leaf, 1 child) and eliminate
+        if( (*a_root)->m_count == 1 && (*a_root)->IsInternalNode() )
+        {
+            tempNode = (*a_root)->m_branch[0].m_child;
+
+            ASSERT( tempNode );
+            FreeNode( *a_root );
+            *a_root = tempNode;
+        }
+
+        return false;
+    }
+    else
+    {
+        return true;
+    }
+}
+
+
+// Delete a rectangle from non-root part of an index structure.
+// Called by RemoveRect.  Descends tree recursively,
+// merges branches on the way back up.
+// Returns 1 if record not found, 0 if success.
+RTREE_TEMPLATE
+bool RTREE_QUAL::RemoveRectRec( Rect*           a_rect,
+                                const DATATYPE& a_id,
+                                Node*           a_node,
+                                ListNode**      a_listNode )
+{
+    ASSERT( a_rect && a_node && a_listNode );
+    ASSERT( a_node->m_level >= 0 );
+
+    if( a_node->IsInternalNode() ) // not a leaf node
+    {
+        for( int index = 0; index < a_node->m_count; ++index )
+        {
+            if( Overlap( a_rect, &(a_node->m_branch[index].m_rect) ) )
+            {
+                if( !RemoveRectRec( a_rect, a_id, a_node->m_branch[index].m_child, a_listNode ) )
+                {
+                    if( a_node->m_branch[index].m_child->m_count >= MINNODES )
+                    {
+                        // child removed, just resize parent rect
+                        a_node->m_branch[index].m_rect =
+                            NodeCover( a_node->m_branch[index].m_child );
+                    }
+                    else
+                    {
+                        // child removed, not enough entries in node, eliminate node
+                        ReInsert( a_node->m_branch[index].m_child, a_listNode );
+                        DisconnectBranch( a_node, index ); // Must return after this call as count has changed
+                    }
+
+                    return false;
+                }
+            }
+        }
+
+        return true;
+    }
+    else // A leaf node
+    {
+        for( int index = 0; index < a_node->m_count; ++index )
+        {
+            if( a_node->m_branch[index].m_child == (Node*) a_id )
+            {
+                DisconnectBranch( a_node, index ); // Must return after this call as count has changed
+                return false;
+            }
+        }
+
+        return true;
+    }
+}
+
+
+// Decide whether two rectangles overlap.
+RTREE_TEMPLATE
+bool RTREE_QUAL::Overlap( Rect* a_rectA, Rect* a_rectB )
+{
+    ASSERT( a_rectA && a_rectB );
+
+    for( int index = 0; index < NUMDIMS; ++index )
+    {
+        if( a_rectA->m_min[index] > a_rectB->m_max[index]
+            || a_rectB->m_min[index] > a_rectA->m_max[index] )
+        {
+            return false;
+        }
+    }
+
+    return true;
+}
+
+
+// Add a node to the reinsertion list.  All its branches will later
+// be reinserted into the index structure.
+RTREE_TEMPLATE
+void RTREE_QUAL::ReInsert( Node* a_node, ListNode** a_listNode )
+{
+    ListNode* newListNode;
+
+    newListNode = AllocListNode();
+    newListNode->m_node = a_node;
+    newListNode->m_next = *a_listNode;
+    *a_listNode = newListNode;
+}
+
+
+// Search in an index tree or subtree for all data retangles that overlap the argument rectangle.
+RTREE_TEMPLATE
+bool RTREE_QUAL::Search( Node* a_node, Rect* a_rect, int& a_foundCount, bool a_resultCallback(
+                             DATATYPE   a_data,
+                             void*      a_context ), void* a_context )
+{
+    ASSERT( a_node );
+    ASSERT( a_node->m_level >= 0 );
+    ASSERT( a_rect );
+
+    if( a_node->IsInternalNode() ) // This is an internal node in the tree
+    {
+        for( int index = 0; index < a_node->m_count; ++index )
+        {
+            if( Overlap( a_rect, &a_node->m_branch[index].m_rect ) )
+            {
+                if( !Search( a_node->m_branch[index].m_child, a_rect, a_foundCount,
+                             a_resultCallback, a_context ) )
+                {
+                    return false; // Don't continue searching
+                }
+            }
+        }
+    }
+    else // This is a leaf node
+    {
+        for( int index = 0; index < a_node->m_count; ++index )
+        {
+            if( Overlap( a_rect, &a_node->m_branch[index].m_rect ) )
+            {
+                DATATYPE& id = a_node->m_branch[index].m_data;
+
+                // NOTE: There are different ways to return results.  Here's where to modify
+                if( &a_resultCallback )
+                {
+                    ++a_foundCount;
+
+                    if( !a_resultCallback( id, a_context ) )
+                    {
+                        return false; // Don't continue searching
+                    }
+                }
+            }
+        }
+    }
+
+    return true; // Continue searching
+}
+
+
+//calculate the minimum distance between a point and a rectangle as defined by Manolopoulos et al.
+//it uses the square distance to avoid the use of ELEMTYPEREAL values, which are slower.
+RTREE_TEMPLATE
+ELEMTYPE RTREE_QUAL::MinDist( const ELEMTYPE a_point[NUMDIMS], Rect* a_rect )
+{
+    ELEMTYPE *q, *s, *t;
+    q = (ELEMTYPE*) a_point;
+    s = a_rect->m_min;
+    t = a_rect->m_max;
+    int minDist = 0;
+    for( int index = 0; index < NUMDIMS; index++ )
+    {
+        int r = q[index];
+        if( q[index] < s[index] )
+        {
+            r = s[index];
+        }
+        else if( q[index] >t[index] )
+        {
+            r = t[index];
+        }
+        int addend = q[index] - r;
+        minDist += addend * addend;
+    }
+    return minDist;
+}
+
+
+//insert a NNNode in a list sorted by its minDist (desc.)
+RTREE_TEMPLATE
+void RTREE_QUAL::InsertNNListSorted( std::vector<NNNode*>* nodeList, NNNode* newNode )
+{
+    typedef typename std::vector<NNNode*>::iterator iterator;
+    iterator iter = nodeList->begin();
+    while( iter != nodeList->end() && (*iter)->minDist > newNode->minDist )
+    {
+        ++iter;
+    }
+    nodeList->insert(iter, newNode);
+}
+
+
+#undef RTREE_TEMPLATE
+#undef RTREE_QUAL
+#undef RTREE_SEARCH_TEMPLATE
+#undef RTREE_SEARCH_QUAL
+
+#endif    // RTREE_H