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：

#pragma once
#include <vector>
#include "ogrsf_frmts.h"
#include "ogr_core.h"
using namespace std;

#ifndef _POINTD
#define _POINTD
typedef struct tagPOINTD
{
double x;
double y;
}POINTD;
#endif // _POINTD

/* 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
{
long nID;		//空间对象ID号
OGREnvelope envelope;	//空间对象MBR范围坐标
}SHPMBRInfo;

/* 四叉树节点类型结构 */
typedef struct QuadNode
{
OGREnvelope	envelope;		//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,OGRLayer *poLayer,QuadTree* pQuadTree);

//创建各个分支
void CreateQuadBranch(int depth,OGREnvelope &rect,QuadNode** node);

//构建四叉树空间索引
void BuildQuadTree(OGRLayer*poLayer,QuadTree* pQuadTree);

//四叉树索引查询(矩形查询)
void SearchQuadTree(QuadNode* node,OGREnvelope &queryRect,vector<long>& ItemSearched);

//四叉树索引查询(矩形查询)并行查询
void SearchQuadTreePara(vector<QuadNode*> resNodes,OGREnvelope &queryRect,vector<long>& ItemSearched);

//四叉树的查询（点查询）
void PtSearchQTree(QuadNode* node,double cx,double cy,vector<long>& ItemSearched);

//将指定的空间对象插入到四叉树中
void Insert(long key,OGREnvelope &itemRect,QuadNode* pNode);

//将指定的空间对象插入到四叉树中
void InsertQuad(long key,OGREnvelope &itemRect,QuadNode* pNode);

//将指定的空间对象插入到四叉树中
void InsertQuad2(long key,OGREnvelope &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<long>& 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);

void split(OGREnvelope origin,OGREnvelope target[]);

bool IsPointInRect(OGREnvelope envelope,POINTD point);

bool IsPointInRect(OGREnvelope envelope,double cx,double cy);

源文件如下：

<pre name="code" class="cpp">#include "StdAfx.h"
#include <assert.h>
#include <algorithm>
#include <deque>
#include "QuadTree.h"

QuadNode *InitQuadNode()
{
QuadNode *node = new QuadNode;
node->envelope.MaxX = 0;
node->envelope.MaxY = 0;
node->envelope.MinX = 0;
node->envelope.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,OGRLayer *poLayer,QuadTree* pQuadTree)
{
pQuadTree->depth = depth;

OGREnvelope env;	//整个图层的MBR
poLayer->GetExtent(&env);

OGREnvelope 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();
OGRFeature **pFeatureClass = new OGRFeature*[nCount];
for (int i = 0; i < poLayer->GetFeatureCount(); ++i)
{
pFeatureClass[i] = poLayer->GetFeature(i);
}

//插入各个要素
OGREnvelope envObj;	//空间对象的MBR
//#pragma omp parallel for
for (int i = 0; i < nCount; ++i)
{
pFeatureClass[i]->GetGeometryRef()->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,OGREnvelope &rect,QuadNode** node)
{
if (depth != 0)
{
*node = InitQuadNode();	//创建树根
QuadNode *pNode = *node;
pNode->envelope = rect;
pNode->nChildCount = 4;

OGREnvelope boxs[4];
split(pNode->envelope,boxs);
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]->envelope = boxs[i];

CreateQuadBranch(depth-1,boxs[i],&(pNode->children[i]));
}
}
}

void BuildQuadTree(OGRLayer *poLayer,QuadTree* pQuadTree)
{
assert(poLayer);
OGREnvelope env;	//整个图层的MBR
poLayer->GetExtent(&env);
pQuadTree->root = InitQuadNode();

QuadNode* rootNode = pQuadTree->root;

rootNode->envelope.MinX = env.MinX;
rootNode->envelope.MinY = env.MinY;
rootNode->envelope.MaxX = env.MaxX;
rootNode->envelope.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();

OGREnvelope envObj;	//空间对象的MBR
for (int i = 0; i < nCount; ++i)
{
poLayer->GetFeature(i)->GetGeometryRef()->getEnvelope(&envObj);
InsertQuad2(i,envObj,rootNode);
printf("Shape:%d\n",i);
}

DelFalseNode(pQuadTree->root);
}

void SearchQuadTree(QuadNode* node,OGREnvelope &queryRect,vector<long>& 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].envelope)
|| queryRect.Intersects(node->pShapeObj[i].envelope))
{
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]->envelope.Contains(queryRect)
|| node->children[i]->envelope.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,OGREnvelope &queryRect,vector<long>& 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 < (int)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].envelope)
// 				|| queryRect.Intersects(resNodes[i]->pShapeObj[j].envelope))
// 			{
// 				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;
vector<long> searchArrs;

for (int i = 0; i < (int)resNodes.size(); ++i)
{
for (int j = 0; j < resNodes[i]->nShpCount; ++j)
{
if (queryRect.Contains(resNodes[i]->pShapeObj[j].envelope)
|| queryRect.Intersects(resNodes[i]->pShapeObj[j].envelope))
{
searchArrs.push_back(resNodes[i]->pShapeObj[j].nID);
}
}
}

ItemSearched.insert(ItemSearched.end(),	searchArrs.begin(),searchArrs.end());
}

void PtSearchQTree(QuadNode* node,double cx,double cy,vector<long>& ItemSearched)
{
assert(node);
if (node->nShpCount >0)		//节点
{
for (int i = 0; i < node->nShpCount; ++i)
{
if (IsPointInRect(node->pShapeObj[i].envelope,cx,cy))
{
ItemSearched.push_back(node->pShapeObj[i].nID);
}
}
}
else if (node->nChildCount >0)				//子节点
{
for (int i = 0; i < 4; ++i)
{
if (IsPointInRect(node->children[i]->envelope,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<long>::iterator unique_iter =
unique(ItemSearched.begin(),ItemSearched.end());
ItemSearched.erase(unique_iter,ItemSearched.end());
}

void Insert(long key, OGREnvelope &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]->envelope.Contains(itemRect)
|| node->children[i]->envelope.Intersects(itemRect))
{
//node = node->children[i];
Insert(key,itemRect,node->children[i]);
}
}
}
else if (1 == node->nShpCount)//如果当前节点存在一个子节点时
{
OGREnvelope boxs[4];
split(node->envelope,boxs);

//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]->envelope = boxs[0];
node->children[UL]->envelope = boxs[1];
node->children[LL]->envelope = boxs[2];
node->children[LR]->envelope = 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]->envelope.Contains(node->pShapeObj[j].envelope)
|| node->children[i]->envelope.Intersects(node->pShapeObj[j].envelope))
{
++node->children[i]->nShpCount;
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]->envelope.Contains(itemRect)
|| node->children[i]->envelope.Intersects(itemRect))
{
pShpInfo.envelope = itemRect;
pShpInfo.nID = key;
if (node->children[i]->nShpCount == 0)	 //如果之前没有节点
{
++node->children[i]->nShpCount;
node->children[i]->pShapeObj =
(SHPMBRInfo*)malloc(sizeof(SHPMBRInfo)*node->children[i]->nShpCount);
}
else if	(node->children[i]->nShpCount > 0)
{
++node->children[i]->nShpCount;
node->children[i]->pShapeObj =
(SHPMBRInfo *)realloc(node->children[i]->pShapeObj,
sizeof(SHPMBRInfo)*node->children[i]->nShpCount);
}
memcpy(node->children[i]->pShapeObj,&pShpInfo,sizeof(SHPMBRInfo));
}
}
}
else if (0 == node->nShpCount)//当前节点没有空间对象
{
++node->nShpCount;
node->pShapeObj =
(SHPMBRInfo*)malloc(sizeof(SHPMBRInfo)*node->nShpCount);

pShpInfo.envelope = itemRect;
pShpInfo.nID = key;
memcpy(node->pShapeObj,&pShpInfo,sizeof(SHPMBRInfo));
}
}

void InsertQuad(long key,OGREnvelope &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]->envelope.Contains(itemRect)
&& pNode->envelope.Contains(itemRect))
{
++nCorver;
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;
pNode->pShapeObj =
(SHPMBRInfo*)malloc(sizeof(SHPMBRInfo)*pNode->nShpCount);
}
else
{
++pNode->nShpCount;
pNode->pShapeObj =
(SHPMBRInfo *)realloc(pNode->pShapeObj,sizeof(SHPMBRInfo)*pNode->nShpCount);
}

SHPMBRInfo pShpInfo;
pShpInfo.envelope = itemRect;
pShpInfo.nID = key;
memcpy(pNode->pShapeObj+pNode->nShpCount-1,&pShpInfo,sizeof(SHPMBRInfo));
}
}
else if (IsQuadLeaf(pNode))//如果是叶子节点，直接放进去
{
if (pNode->nShpCount == 0)	 //如果之前没有节点
{
++pNode->nShpCount;
pNode->pShapeObj =
(SHPMBRInfo*)malloc(sizeof(SHPMBRInfo)*pNode->nShpCount);
}
else
{
++pNode->nShpCount;
pNode->pShapeObj =
(SHPMBRInfo *)realloc(pNode->pShapeObj,sizeof(SHPMBRInfo)*pNode->nShpCount);
}

SHPMBRInfo pShpInfo;
pShpInfo.envelope = itemRect;
pShpInfo.nID = key;
memcpy(pNode->pShapeObj+pNode->nShpCount-1,&pShpInfo,sizeof(SHPMBRInfo));
}
}

void InsertQuad2(long key,OGREnvelope &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]->envelope.Contains(itemRect)
|| node->children[i]->envelope.Intersects(itemRect))
{
//node = node->children[i];
Insert(key,itemRect,node->children[i]);
}
}
}
else if (0 == node->nChildCount)//如果当前节点存在一个子节点时
{
OGREnvelope boxs[4];
split(node->envelope,boxs);

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;
break;
}
}

//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]->envelope = boxs[i];
}
node->nChildCount = 4;
InsertQuad2(key,itemRect,node->children[cnt]);	//递归
}
else if (cnt == -1)//如果都不包含，则直接将对象插入此节点
{
if (node->nShpCount == 0)	 //如果之前没有节点
{
++node->nShpCount;
node->pShapeObj = (SHPMBRInfo*)malloc(sizeof(SHPMBRInfo)*node->nShpCount);
}
else if	(node->nShpCount > 0)
{
++node->nShpCount;
node->pShapeObj =
(SHPMBRInfo *)realloc(node->pShapeObj,sizeof(SHPMBRInfo)*node->nShpCount);
}

pShpInfo.envelope = 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 true;
}

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);
}
else if (node->nChildCount > 0)//如果有子节点
{
for (int i = 0; i < 4; ++i)
{
DelFalseNode(node->children[i]);
}
}

return true;
}

void TraversalQuadTree(QuadNode* quadTree,vector<long>& 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;
}

void split( OGREnvelope origin,OGREnvelope target[] )
{
double width = origin.MaxX-origin.MinX;
double height = origin.MaxY-origin.MinY;

target[0].MinX = target[1].MaxX = target[2].MaxX = target[3].MinX = origin.MinX+width/2;
target[0].MaxX = target[3].MaxX = origin.MaxX;
target[1].MinX = target[2].MinX = origin.MinX;

target[0].MaxY = target[1].MaxY = target[2].MinY = target[3].MinY = origin.MinY+height/2;
target[0].MinY = target[1].MinY = origin.MinY;
target[2].MaxY = target[3].MaxY = origin.MaxY;
}

bool IsPointInRect( OGREnvelope envelope,POINTD point )
{
if (envelope.MinX > point.x || envelope.MaxX < point.x || envelope.MinY > point.y || envelope.MaxY < point.y)
{
return false;
}
return true;
}

bool IsPointInRect( OGREnvelope envelope,double cx,double cy )
{
if (envelope.MinX > cx || envelope.MaxX < cx || envelope.MinY > cy || envelope.MaxY < cy)
{
return false;
}
return true;
}

代码有点长，有需要的朋友可以借鉴并自己优化。