四叉树空间索引原理及其实现

转自原文 四叉树空间索引原理及其实现

四叉树索引的基本思想是将地理空间递归划分为不同层次的树结构。它将已知范围的空间等分成四个相等的子空间，如此递归下去，直至树的层次达到一定深度或者满足某种要求后停止分割。四叉树的结构比较简单，并且当空间数据对象分布比较均匀时，具有比较高的空间数据插入和查询效率，因此四叉树是GIS中常用的空间索引之一。常规四叉树的结构如图所示，地理空间对象都存储在叶子节点上，中间节点以及根节点不存储地理空间对象。

 

四叉树示意图

 

四叉树对于区域查询，效率比较高。但如果空间对象分布不均匀，随着地理空间对象的不断插入，四叉树的层次会不断地加深，将形成一棵严重不平衡的四叉树，那么每次查询的深度将大大的增多，从而导致查询效率的急剧下降。

 

本节将介绍一种改进的四叉树索引结构。四叉树结构是自顶向下逐步划分的一种树状的层次结构。传统的四叉树索引存在着以下几个缺点：

(1)空间实体只能存储在叶子节点中，中间节点以及根节点不能存储空间实体信息，随着空间对象的不断插入，最终会导致四叉树树的层次比较深，在进行空间数据窗口查询的时候效率会比较低下。

(2)同一个地理实体在四叉树的分裂过程中极有可能存储在多个节点中，这样就导致了索引存储空间的浪费。

(3)由于地理空间对象可能分布不均衡，这样会导致常规四叉树生成一棵极为不平衡的树，这样也会造成树结构的不平衡以及存储空间的浪费。

相应的改进方法，将地理实体信息存储在完全包含它的最小矩形节点中，不存储在它的父节点中，每个地理实体只在树中存储一次，避免存储空间的浪费。首先生成满四叉树，避免在地理实体插入时需要重新分配内存，加快插入的速度，最后将空的节点所占内存空间释放掉。改进后的四叉树结构如下图所示。四叉树的深度一般取经验值4-7之间为最佳。

 

图改进的四叉树结构

 

为了维护空间索引与对存储在文件或数据库中的空间数据的一致性，作者设计了如下的数据结构支持四叉树的操作。

(1)四分区域标识

分别定义了一个平面区域的四个子区域索引号，右上为第一象限0，左上为第二象限1，左下为第三象限2，右下为第四象限3。

typedef enum

{

      UR = 0,// UR第一象限

      UL = 1, // UL为第二象限

      LL = 2, // LL为第三象限

      LR = 3  // LR为第四象限

}QuadrantEnum;

(2)空间对象数据结构

空间对象数据结构是对地理空间对象的近似，在空间索引中，相当一部分都是采用MBR作为近似。

/*空间对象MBR信息*/

typedef struct SHPMBRInfo

{

      int nID;       //空间对象ID号

      MapRect Box;    //空间对象MBR范围坐标

}SHPMBRInfo;

nID是空间对象的标识号，Box是空间对象的最小外包矩形（MBR）。

(3)四叉树节点数据结构

四叉树节点是四叉树结构的主要组成部分，主要用于存储空间对象的标识号和MBR，也是四叉树算法操作的主要部分。

/*四叉树节点类型结构*/

typedef struct QuadNode

{

      MapRect            Box;                   //节点所代表的矩形区域

      int                nShpCount;        //节点所包含的所有空间对象个数

      SHPMBRInfo* pShapeObj;          //空间对象指针数组

      int         nChildCount;            //子节点个数

      QuadNode *children[4];             //指向节点的四个孩子

}QuadNode;

Box是代表四叉树对应区域的最小外包矩形，上一层的节点的最小外包矩形包含下一层最小外包矩形区域；nShpCount代表本节点包含的空间对象的个数；pShapeObj代表指向空间对象存储地址的首地址，同一个节点的空间对象在内存中连续存储；nChildCount代表节点拥有的子节点的数目；children是指向孩子节点指针的数组。

上述理论部分都都讲的差不多了，下面就贴上我的C语言实现版本代码。

头文件如下：

    #ifndef __QUADTREE_H_59CAE94A_E937_42AD_AA27_794E467715BB__  
    #define __QUADTREE_H_59CAE94A_E937_42AD_AA27_794E467715BB__  
      
      
      
      
    /* 一个矩形区域的象限划分：: 
     
    UL(1)   |    UR(0) 
    ----------|----------- 
    LL(2)   |    LR(3) 
    以下对该象限类型的枚举 
    */  
    typedef enum  
    {  
        UR = 0,  
        UL = 1,  
        LL = 2,  
        LR = 3  
    }QuadrantEnum;  
      
    /*空间对象MBR信息*/  
    typedef struct SHPMBRInfo  
    {  
        int nID;        //空间对象ID号  
        MapRect Box;    //空间对象MBR范围坐标  
    }SHPMBRInfo;  
      
    /* 四叉树节点类型结构 */  
    typedef struct QuadNode  
    {  
        MapRect     Box;            //节点所代表的矩形区域  
        int         nShpCount;      //节点所包含的所有空间对象个数  
        SHPMBRInfo* pShapeObj;      //空间对象指针数组  
        int     nChildCount;        //子节点个数  
        QuadNode  *children[4];     //指向节点的四个孩子   
    }QuadNode;  
      
    /* 四叉树类型结构 */  
    typedef struct quadtree_t  
    {  
        QuadNode  *root;  
        int         depth;           // 四叉树的深度                      
    }QuadTree;  
      
      
        //初始化四叉树节点  
        QuadNode *InitQuadNode();  
      
        //层次创建四叉树方法（满四叉树）  
        void CreateQuadTree(int depth,GeoLayer *poLayer,QuadTree* pQuadTree);  
      
        //创建各个分支  
        void CreateQuadBranch(int depth,MapRect &rect,QuadNode** node);  
      
        //构建四叉树空间索引  
        void BuildQuadTree(GeoLayer*poLayer,QuadTree* pQuadTree);  
      
        //四叉树索引查询(矩形查询)  
        void SearchQuadTree(QuadNode* node,MapRect &queryRect,vector<int>& ItemSearched);  
      
        //四叉树索引查询(矩形查询)并行查询  
        void SearchQuadTreePara(vector<QuadNode*> resNodes,MapRect &queryRect,vector<int>& ItemSearched);  
      
        //四叉树的查询（点查询）  
        void PtSearchQTree(QuadNode* node,double cx,double cy,vector<int>& ItemSearched);  
      
        //将指定的空间对象插入到四叉树中  
        void Insert(long key,MapRect &itemRect,QuadNode* pNode);  
      
        //将指定的空间对象插入到四叉树中  
        void InsertQuad(long key,MapRect &itemRect,QuadNode* pNode);  
      
        //将指定的空间对象插入到四叉树中  
        void InsertQuad2(long key,MapRect &itemRect,QuadNode* pNode);  
      
        //判断一个节点是否是叶子节点  
        bool IsQuadLeaf(QuadNode* node);  
      
        //删除多余的节点  
        bool DelFalseNode(QuadNode* node);  
      
        //四叉树遍历(所有要素)  
        void TraversalQuadTree(QuadNode* quadTree,vector<int>& resVec);  
      
        //四叉树遍历（所有节点）  
        void TraversalQuadTree(QuadNode* quadTree,vector<QuadNode*>& arrNode);  
      
        //释放树的内存空间  
        void ReleaseQuadTree(QuadNode** quadTree);  
      
        //计算四叉树所占的字节的大小  
        long CalByteQuadTree(QuadNode* quadTree,long& nSize);  
      
      
    #endif  

源文件如下：

    #include "QuadTree.h"  
      
      
    QuadNode *InitQuadNode()  
    {  
        QuadNode *node = new QuadNode;  
        node->Box.maxX = 0;  
        node->Box.maxY = 0;  
        node->Box.minX = 0;  
        node->Box.minY = 0;  
      
        for (int i = 0; i < 4; i ++)  
        {  
            node->children[i] = NULL;  
        }  
        node->nChildCount = 0;  
        node->nShpCount = 0;  
        node->pShapeObj = NULL;  
      
        return node;  
    }  
      
    void CreateQuadTree(int depth,GeoLayer *poLayer,QuadTree* pQuadTree)  
    {  
        pQuadTree->depth = depth;  
      
        GeoEnvelope env;    //整个图层的MBR  
        poLayer->GetExtent(&env);  
          
        MapRect rect;  
        rect.minX = env.MinX;  
        rect.minY = env.MinY;  
        rect.maxX = env.MaxX;  
        rect.maxY = env.MaxY;  
          
        //创建各个分支  
        CreateQuadBranch(depth,rect,&(pQuadTree->root));  
      
        int nCount = poLayer->GetFeatureCount();  
        GeoFeature **pFeatureClass = new GeoFeature*[nCount];  
        for (int i = 0; i < poLayer->GetFeatureCount(); i ++)  
        {  
            pFeatureClass[i] = poLayer->GetFeature(i);   
        }  
      
        //插入各个要素  
        GeoEnvelope envObj; //空间对象的MBR  
        //#pragma omp parallel for  
        for (int i = 0; i < nCount; i ++)  
        {  
            pFeatureClass[i]->GetGeometry()->getEnvelope(&envObj);  
            rect.minX = envObj.MinX;  
            rect.minY = envObj.MinY;  
            rect.maxX = envObj.MaxX;  
            rect.maxY = envObj.MaxY;  
            InsertQuad(i,rect,pQuadTree->root);  
        }  
      
        //DelFalseNode(pQuadTree->root);  
    }  
      
    void CreateQuadBranch(int depth,MapRect &rect,QuadNode** node)  
    {  
        if (depth != 0)  
        {  
            *node = InitQuadNode(); //创建树根  
            QuadNode *pNode = *node;  
            pNode->Box = rect;  
            pNode->nChildCount = 4;  
      
            MapRect boxs[4];  
            pNode->Box.Split(boxs,boxs+1,boxs+2,boxs+3);  
            for (int i = 0; i < 4; i ++)  
            {  
                //创建四个节点并插入相应的MBR  
                pNode->children[i] = InitQuadNode();  
                pNode->children[i]->Box = boxs[i];  
      
                CreateQuadBranch(depth-1,boxs[i],&(pNode->children[i]));  
            }  
        }  
    }  
      
    void BuildQuadTree(GeoLayer *poLayer,QuadTree* pQuadTree)  
    {  
        assert(poLayer);  
        GeoEnvelope env;    //整个图层的MBR  
        poLayer->GetExtent(&env);  
        pQuadTree->root = InitQuadNode();  
      
        QuadNode* rootNode = pQuadTree->root;  
      
        rootNode->Box.minX = env.MinX;  
        rootNode->Box.minY = env.MinY;  
        rootNode->Box.maxX = env.MaxX;  
        rootNode->Box.maxY = env.MaxY;  
      
        //设置树的深度(   根据等比数列的求和公式)  
        //pQuadTree->depth = log(poLayer->GetFeatureCount()*3/8.0+1)/log(4.0);  
        int nCount = poLayer->GetFeatureCount();  
      
        MapRect rect;  
        GeoEnvelope envObj; //空间对象的MBR  
        for (int i = 0; i < nCount; i ++)  
        {  
            poLayer->GetFeature(i)->GetGeometry()->getEnvelope(&envObj);  
            rect.minX = envObj.MinX;  
            rect.minY = envObj.MinY;  
            rect.maxX = envObj.MaxX;  
            rect.maxY = envObj.MaxY;  
            InsertQuad2(i,rect,rootNode);  
        }  
      
        DelFalseNode(pQuadTree->root);  
    }  
      
    void SearchQuadTree(QuadNode* node,MapRect &queryRect,vector<int>& ItemSearched)  
    {  
        assert(node);  
      
        //int coreNum = omp_get_num_procs();  
        //vector<int> * pResArr = new vector<int>[coreNum];  
      
        if (NULL != node)  
        {  
            for (int i = 0; i < node->nShpCount; i ++)  
            {  
                if (queryRect.Contains(node->pShapeObj[i].Box)  
                    || queryRect.Intersects(node->pShapeObj[i].Box))  
                {  
                    ItemSearched.push_back(node->pShapeObj[i].nID);  
                }  
            }  
      
            //并行搜索四个孩子节点  
            /*#pragma omp parallel sections 
            { 
                #pragma omp section 
                if ((node->children[0] != NULL) &&  
                    (node->children[0]->Box.Contains(queryRect) 
                    || node->children[0]->Box.Intersects(queryRect))) 
                { 
                    int tid = omp_get_thread_num(); 
                    SearchQuadTree(node->children[0],queryRect,pResArr[tid]); 
                } 
     
                #pragma omp section 
                if ((node->children[1] != NULL) &&  
                    (node->children[1]->Box.Contains(queryRect) 
                    || node->children[1]->Box.Intersects(queryRect))) 
                { 
                    int tid = omp_get_thread_num(); 
                    SearchQuadTree(node->children[1],queryRect,pResArr[tid]); 
                } 
     
                #pragma omp section 
                if ((node->children[2] != NULL) &&  
                    (node->children[2]->Box.Contains(queryRect) 
                    || node->children[2]->Box.Intersects(queryRect))) 
                { 
                    int tid = omp_get_thread_num(); 
                    SearchQuadTree(node->children[2],queryRect,pResArr[tid]); 
                } 
     
                #pragma omp section 
                if ((node->children[3] != NULL) &&  
                    (node->children[3]->Box.Contains(queryRect) 
                    || node->children[3]->Box.Intersects(queryRect))) 
                { 
                    int tid = omp_get_thread_num(); 
                    SearchQuadTree(node->children[3],queryRect,pResArr[tid]); 
                } 
            }*/  
            for (int i = 0; i < 4; i ++)  
            {  
                if ((node->children[i] != NULL) &&   
                    (node->children[i]->Box.Contains(queryRect)  
                    || node->children[i]->Box.Intersects(queryRect)))  
                {  
                    SearchQuadTree(node->children[i],queryRect,ItemSearched);  
                    //node = node->children[i];  //非递归  
                }  
            }  
        }  
      
        /*for (int i = 0 ; i < coreNum; i ++) 
        { 
            ItemSearched.insert(ItemSearched.end(),pResArr[i].begin(),pResArr[i].end()); 
        }*/  
      
    }  
      
    void SearchQuadTreePara(vector<QuadNode*> resNodes,MapRect &queryRect,vector<int>& ItemSearched)  
    {  
        int coreNum = omp_get_num_procs();  
        omp_set_num_threads(coreNum);  
        vector<int>* searchArrs = new vector<int>[coreNum];  
        for (int i = 0; i < coreNum; i ++)  
        {  
            searchArrs[i].clear();  
        }  
      
        #pragma omp parallel for  
        for (int i = 0; i < resNodes.size(); i ++)  
        {  
            int tid = omp_get_thread_num();  
            for (int j = 0; j < resNodes[i]->nShpCount; j ++)  
            {  
                if (queryRect.Contains(resNodes[i]->pShapeObj[j].Box)  
                    || queryRect.Intersects(resNodes[i]->pShapeObj[j].Box))  
                {  
                    searchArrs[tid].push_back(resNodes[i]->pShapeObj[j].nID);  
                }  
            }  
        }  
      
        for (int i = 0; i < coreNum; i ++)  
        {  
            ItemSearched.insert(ItemSearched.end(),  
                searchArrs[i].begin(),searchArrs[i].end());  
        }  
      
        delete [] searchArrs;  
        searchArrs = NULL;  
    }  
      
    void PtSearchQTree(QuadNode* node,double cx,double cy,vector<int>& ItemSearched)  
    {  
        assert(node);  
        if (node->nShpCount >0)       //节点            
        {  
            for (int i = 0; i < node->nShpCount; i ++)  
            {  
                if (node->pShapeObj[i].Box.IsPointInRect(cx,cy))  
                {  
                    ItemSearched.push_back(node->pShapeObj[i].nID);  
                }  
            }  
        }  
      
        else if (node->nChildCount >0)                //节点  
        {  
            for (int i = 0; i < 4; i ++)  
            {  
                if (node->children[i]->Box.IsPointInRect(cx,cy))  
                {  
                    PtSearchQTree(node->children[i],cx,cy,ItemSearched);  
                }  
            }  
        }  
      
        //找出重复元素的位置  
        sort(ItemSearched.begin(),ItemSearched.end());  //先排序,默认升序  
        vector<int>::iterator unique_iter =   
            unique(ItemSearched.begin(),ItemSearched.end());  
        ItemSearched.erase(unique_iter,ItemSearched.end());  
    }  
      
    void Insert(long key, MapRect &itemRect,QuadNode* pNode)  
    {  
        QuadNode *node = pNode;     //保留根节点副本  
        SHPMBRInfo pShpInfo;  
          
        //节点有孩子  
        if (0 < node->nChildCount)  
        {  
            for (int i = 0; i < 4; i ++)  
            {    
                //如果包含或相交，则将节点插入到此节点  
                if (node->children[i]->Box.Contains(itemRect)  
                    || node->children[i]->Box.Intersects(itemRect))  
                {  
                    //node = node->children[i];  
                    Insert(key,itemRect,node->children[i]);  
                }  
            }  
        }  
      
        //如果当前节点存在一个子节点时  
        else if (1 == node->nShpCount)  
        {  
            MapRect boxs[4];  
            node->Box.Split(boxs,boxs+1,boxs+2,boxs+3);  
      
            //创建四个节点并插入相应的MBR  
            node->children[UR] = InitQuadNode();  
            node->children[UL] = InitQuadNode();  
            node->children[LL] = InitQuadNode();  
            node->children[LR] = InitQuadNode();  
      
            node->children[UR]->Box = boxs[0];  
            node->children[UL]->Box = boxs[1];  
            node->children[LL]->Box = boxs[2];  
            node->children[LR]->Box = boxs[3];  
            node->nChildCount = 4;  
      
            for (int i = 0; i < 4; i ++)  
            {    
                //将当前节点中的要素移动到相应的子节点中  
                for (int j = 0; j < node->nShpCount; j ++)  
                {  
                    if (node->children[i]->Box.Contains(node->pShapeObj[j].Box)  
                        || node->children[i]->Box.Intersects(node->pShapeObj[j].Box))  
                    {  
                        node->children[i]->nShpCount += 1;  
                        node->children[i]->pShapeObj =   
                            (SHPMBRInfo*)malloc(node->children[i]->nShpCount*sizeof(SHPMBRInfo));  
                          
                        memcpy(node->children[i]->pShapeObj,&(node->pShapeObj[j]),sizeof(SHPMBRInfo));  
      
                        free(node->pShapeObj);  
                        node->pShapeObj = NULL;  
                        node->nShpCount = 0;  
                    }  
                }  
            }  
      
            for (int i = 0; i < 4; i ++)  
            {    
                //如果包含或相交，则将节点插入到此节点  
                if (node->children[i]->Box.Contains(itemRect)  
                    || node->children[i]->Box.Intersects(itemRect))  
                {  
                    if (node->children[i]->nShpCount == 0)     //如果之前没有节点  
                    {  
                        node->children[i]->nShpCount += 1;  
                        node->pShapeObj =   
                            (SHPMBRInfo*)malloc(sizeof(SHPMBRInfo)*node->children[i]->nShpCount);  
                    }  
                    else if (node->children[i]->nShpCount > 0)  
                    {  
                        node->children[i]->nShpCount += 1;  
                        node->children[i]->pShapeObj =   
                            (SHPMBRInfo *)realloc(node->children[i]->pShapeObj,  
                            sizeof(SHPMBRInfo)*node->children[i]->nShpCount);  
                    }  
      
                    pShpInfo.Box = itemRect;  
                    pShpInfo.nID = key;  
                    memcpy(node->children[i]->pShapeObj,  
                        &pShpInfo,sizeof(SHPMBRInfo));  
                }  
            }  
        }  
      
        //当前节点没有空间对象  
        else if (0 == node->nShpCount)  
        {  
            node->nShpCount += 1;  
            node->pShapeObj =   
                (SHPMBRInfo*)malloc(sizeof(SHPMBRInfo)*node->nShpCount);  
      
            pShpInfo.Box = itemRect;  
            pShpInfo.nID = key;  
            memcpy(node->pShapeObj,&pShpInfo,sizeof(SHPMBRInfo));  
        }  
    }  
      
    void InsertQuad(long key,MapRect &itemRect,QuadNode* pNode)  
    {  
        assert(pNode != NULL);  
      
        if (!IsQuadLeaf(pNode))    //非叶子节点  
        {  
            int nCorver = 0;        //跨越的子节点个数  
            int iIndex = -1;        //被哪个子节点完全包含的索引号  
            for (int i = 0; i < 4; i ++)  
            {  
                if (pNode->children[i]->Box.Contains(itemRect)  
                    && pNode->Box.Contains(itemRect))  
                {  
                    nCorver += 1;  
                    iIndex = i;  
                }  
            }  
      
            //如果被某一个子节点包含，则进入该子节点  
            if (/*pNode->Box.Contains(itemRect) ||  
                pNode->Box.Intersects(itemRect)*/1 <= nCorver)  
            {   
                InsertQuad(key,itemRect,pNode->children[iIndex]);  
            }  
      
            //如果跨越了多个子节点，直接放在这个节点中  
            else if (nCorver == 0)  
            {  
                if (pNode->nShpCount == 0)    //如果之前没有节点  
                {  
                    pNode->nShpCount += 1;  
                    pNode->pShapeObj =   
                        (SHPMBRInfo*)malloc(sizeof(SHPMBRInfo)*pNode->nShpCount);  
                }  
                else  
                {  
                    pNode->nShpCount += 1;  
                    pNode->pShapeObj =   
                        (SHPMBRInfo *)realloc(pNode->pShapeObj,sizeof(SHPMBRInfo)*pNode->nShpCount);  
                }  
      
                SHPMBRInfo pShpInfo;  
                pShpInfo.Box = itemRect;  
                pShpInfo.nID = key;  
                memcpy(pNode->pShapeObj+pNode->nShpCount-1,&pShpInfo,sizeof(SHPMBRInfo));  
            }  
        }  
      
        //如果是叶子节点，直接放进去  
        else if (IsQuadLeaf(pNode))  
        {  
            if (pNode->nShpCount == 0)    //如果之前没有节点  
            {  
                pNode->nShpCount += 1;  
                pNode->pShapeObj =   
                    (SHPMBRInfo*)malloc(sizeof(SHPMBRInfo)*pNode->nShpCount);  
            }  
            else  
            {  
                pNode->nShpCount += 1;  
                pNode->pShapeObj =   
                    (SHPMBRInfo *)realloc(pNode->pShapeObj,sizeof(SHPMBRInfo)*pNode->nShpCount);  
            }  
      
            SHPMBRInfo pShpInfo;  
            pShpInfo.Box = itemRect;  
            pShpInfo.nID = key;  
            memcpy(pNode->pShapeObj+pNode->nShpCount-1,&pShpInfo,sizeof(SHPMBRInfo));  
        }  
    }  
      
    void InsertQuad2(long key,MapRect &itemRect,QuadNode* pNode)  
    {  
        QuadNode *node = pNode;     //保留根节点副本  
        SHPMBRInfo pShpInfo;  
      
        //节点有孩子  
        if (0 < node->nChildCount)  
        {  
            for (int i = 0; i < 4; i ++)  
            {    
                //如果包含或相交，则将节点插入到此节点  
                if (node->children[i]->Box.Contains(itemRect)  
                    || node->children[i]->Box.Intersects(itemRect))  
                {  
                    //node = node->children[i];  
                    Insert(key,itemRect,node->children[i]);  
                }  
            }  
        }  
      
        //如果当前节点存在一个子节点时  
        else if (0 == node->nChildCount)  
        {  
            MapRect boxs[4];  
            node->Box.Split(boxs,boxs+1,boxs+2,boxs+3);  
      
            int cnt = -1;  
            for (int i = 0; i < 4; i ++)  
            {    
                //如果包含或相交，则将节点插入到此节点  
                if (boxs[i].Contains(itemRect))  
                {  
                    cnt = i;  
                }  
            }  
      
            //如果有一个矩形包含此对象，则创建四个孩子节点  
            if (cnt > -1)  
            {  
                for (int i = 0; i < 4; i ++)  
                {  
                    //创建四个节点并插入相应的MBR  
                    node->children[i] = InitQuadNode();  
                    node->children[i]->Box = boxs[i];  
                }  
                node->nChildCount = 4;  
                InsertQuad2(key,itemRect,node->children[cnt]);   //递归  
            }  
      
            //如果都不包含，则直接将对象插入此节点  
            if (cnt == -1)  
            {  
                if (node->nShpCount == 0)     //如果之前没有节点  
                {  
                    node->nShpCount += 1;  
                    node->pShapeObj =   
                        (SHPMBRInfo*)malloc(sizeof(SHPMBRInfo)*node->nShpCount);  
                }  
                else if (node->nShpCount > 0)  
                {  
                    node->nShpCount += 1;  
                    node->pShapeObj =   
                        (SHPMBRInfo *)realloc(node->pShapeObj,  
                        sizeof(SHPMBRInfo)*node->nShpCount);  
                }  
      
                pShpInfo.Box = itemRect;  
                pShpInfo.nID = key;  
                memcpy(node->pShapeObj,  
                    &pShpInfo,sizeof(SHPMBRInfo));  
            }  
        }  
      
        //当前节点没有空间对象  
        /*else if (0 == node->nShpCount) 
        { 
            node->nShpCount += 1; 
            node->pShapeObj =  
                (SHPMBRInfo*)malloc(sizeof(SHPMBRInfo)*node->nShpCount); 
     
            pShpInfo.Box = itemRect; 
            pShpInfo.nID = key; 
            memcpy(node->pShapeObj,&pShpInfo,sizeof(SHPMBRInfo)); 
        }*/  
    }  
      
    bool IsQuadLeaf(QuadNode* node)  
    {  
        if (NULL == node)  
        {  
            return 1;  
        }  
        for (int i = 0; i < 4; i ++)  
        {  
            if (node->children[i] != NULL)  
            {  
                return 0;  
            }  
        }  
      
        return 1;  
    }  
      
    bool DelFalseNode(QuadNode* node)  
    {  
        //如果没有子节点且没有要素  
        if (node->nChildCount ==0 && node->nShpCount == 0)  
        {  
            ReleaseQuadTree(&node);  
        }  
      
        //如果有子节点  
        else if (node->nChildCount > 0)  
        {  
            for (int i = 0; i < 4; i ++)  
            {  
                DelFalseNode(node->children[i]);  
            }  
        }  
      
        return 1;  
    }  
      
    void TraversalQuadTree(QuadNode* quadTree,vector<int>& resVec)  
    {  
        QuadNode *node = quadTree;  
        int i = 0;   
        if (NULL != node)  
        {  
            //将本节点中的空间对象存储数组中  
            for (i = 0; i < node->nShpCount; i ++)  
            {  
                resVec.push_back((node->pShapeObj+i)->nID);  
            }  
      
            //遍历孩子节点  
            for (i = 0; i < node->nChildCount; i ++)  
            {  
                if (node->children[i] != NULL)  
                {  
                    TraversalQuadTree(node->children[i],resVec);  
                }  
            }  
        }  
      
    }  
      
    void TraversalQuadTree(QuadNode* quadTree,vector<QuadNode*>& arrNode)  
    {  
        deque<QuadNode*> nodeQueue;  
        if (quadTree != NULL)  
        {  
            nodeQueue.push_back(quadTree);  
            while (!nodeQueue.empty())  
            {  
                QuadNode* queueHead = nodeQueue.at(0);  //取队列头结点  
                arrNode.push_back(queueHead);  
                nodeQueue.pop_front();  
                for (int i = 0; i < 4; i ++)  
                {  
                    if (queueHead->children[i] != NULL)  
                    {  
                        nodeQueue.push_back(queueHead->children[i]);  
                    }  
                }  
            }  
        }  
    }  
      
    void ReleaseQuadTree(QuadNode** quadTree)  
    {  
        int i = 0;  
        QuadNode* node = *quadTree;  
        if (NULL == node)  
        {  
            return;  
        }  
      
        else  
        {  
            for (i = 0; i < 4; i ++)  
            {   
                ReleaseQuadTree(&node->children[i]);  
            }  
            free(node);  
            node = NULL;  
        }  
      
        node = NULL;  
    }  
      
    long CalByteQuadTree(QuadNode* quadTree,long& nSize)  
    {  
        if (quadTree != NULL)  
        {  
            nSize += sizeof(QuadNode)+quadTree->nChildCount*sizeof(SHPMBRInfo);  
            for (int i = 0; i < 4; i ++)  
            {  
                if (quadTree->children[i] != NULL)  
                {  
                    nSize += CalByteQuadTree(quadTree->children[i],nSize);  
                }  
            }  
        }  
      
        return 1;  
    }