四叉树空间索引原理及其实现

淡淡的烟草味﹌ 2022-10-07 10:46 209阅读 0赞

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。

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzIyNjQyMjM5_size_16_color_FFFFFF_t_70][]

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。

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzIyNjQyMjM5_size_16_color_FFFFFF_t_70 1][]

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;
    }

代码有点长，有需要的朋友可以借鉴并自己优化。  
————————————————  
版权声明：本文为CSDN博主「周旭光」的原创文章，遵循CC 4.0 BY-SA版权协议，转载请附上原文出处链接及本声明。  
原文链接：https://blog.csdn.net/zhouxuguang236/article/details/12312099

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