rtree.h 56.8 KB
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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 Min
  #define Min std::min
#endif    // Min
#ifndef Max
  #define Max std::max
#endif    // Max

//
// RTree.h
//

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#define RTREE_TEMPLATE          template <class DATATYPE, class ELEMTYPE, int NUMDIMS, \
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    class ELEMTYPEREAL, int TMAXNODES, int TMINNODES>
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#define RTREE_SEARCH_TEMPLATE   template <class DATATYPE, class ELEMTYPE, int NUMDIMS, \
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    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_searchResult Search result array.  Caller should set grow size. Function will reset, not append to array.
    /// \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;
1290
    int             best = 0;
1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482
    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]    = Min( a_rectA->m_min[index], a_rectB->m_min[index] );
        newRect.m_max[index]    = Max( 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;
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    int             group, chosen = 0, betterGroup = 0;
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    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 )
{
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    int             seed0 = 0, seed1 = 0;
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    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