八叉树 C++ 基础 源码

http://blog.csdn.net/pizi0475/article/details/6269060

四叉树或四元树也被称为Q树（Q-Tree）。四叉树广泛应用于图像处理、空间数据索引、2D中的快速碰撞检测、存储稀疏数据等，而八叉树（Octree）主要应用于3D图形处理。

实际的数据结构，就是一个树根不断地往下扩，每次分成八个枝，直到叶子为止。

叶子节点代表了分辨率最高的情况。例如分辨率设成0.01m，那么每个叶子就是一个1cm见方的小方块

#include <iostream>
using namespace std;

//定义八叉树节点类
template<class T>
struct OctreeNode
{
T data; //节点数据
T xMin, xMax; //节点坐标，即六面体个顶点的坐标
T yMin, yMax;
T zMin, zMax;
OctreeNode <T> *top_left_front, *top_left_back; //该节点的个子结点
OctreeNode <T> *top_right_front, *top_right_back;
OctreeNode <T> *bottom_left_front, *bottom_left_back;
OctreeNode <T> *bottom_right_front, *bottom_right_back;
OctreeNode //节点类
(T nodeValue = T(),
T xminValue = T(), T xmaxValue = T(),
T yminValue = T(), T ymaxValue = T(),
T zminValue = T(), T zmaxValue = T(),
OctreeNode<T>* top_left_front_Node = NULL,
OctreeNode<T>* top_left_back_Node = NULL,
OctreeNode<T>* top_right_front_Node = NULL,
OctreeNode<T>* top_right_back_Node = NULL,
OctreeNode<T>* bottom_left_front_Node = NULL,
OctreeNode<T>* bottom_left_back_Node = NULL,
OctreeNode<T>* bottom_right_front_Node = NULL,
OctreeNode<T>* bottom_right_back_Node = NULL)
: data(nodeValue),
xMin(xminValue), xMax(xmaxValue),
yMin(yminValue), yMax(ymaxValue),
zMin(zminValue), zMax(zmaxValue),
top_left_front(top_left_front_Node),
top_left_back(top_left_back_Node),
top_right_front(top_right_front_Node),
top_right_back(top_right_back_Node),
bottom_left_front(bottom_left_front_Node),
bottom_left_back(bottom_left_back_Node),
bottom_right_front(bottom_right_front_Node),
bottom_right_back(bottom_right_back_Node) {}
};

//创建八叉树
template <class T>
void createOctree(OctreeNode<T> * &root, int maxdepth, double xMin, double xMax, double yMin, double yMax, double zMin, double zMax)
{
cout << "处理中，请稍候……" << endl;
maxdepth = maxdepth - 1; //每递归一次就将最大递归深度-1
if (maxdepth >= 0)
{
root = new OctreeNode<T>();
root->data = 9; //为节点赋值，可以存储节点信息，如物体可见性。由于是简单实现八叉树功能，简单赋值为。
root->xMin = xMin; //为节点坐标赋值
root->xMax = xMax;
root->yMin = yMin;
root->yMax = yMax;
root->zMin = zMin;
root->zMax = zMax;
double xMind = (xMax - xMin) / 2;//计算节点个维度上的半边长
double yMind = (yMax - yMin) / 2;
double zMind = (zMax - zMin) / 2;
//递归创建子树，根据每一个节点所处（是几号节点）的位置决定其子结点的坐标。
createOctree(root->top_left_front, maxdepth, xMin, xMax - xMind, yMax - yMind, yMax, zMax - zMind, zMax);
createOctree(root->top_left_back, maxdepth, xMin, xMax - xMind, yMin, yMax - yMind, zMax - zMind, zMax);
createOctree(root->top_right_front, maxdepth, xMax - xMind, xMax, yMax - yMind, yMax, zMax - zMind, zMax);
createOctree(root->top_right_back, maxdepth, xMax - xMind, xMax, yMin, yMax - yMind, zMax - zMind, zMax);
createOctree(root->bottom_left_front, maxdepth, xMin, xMax - xMind, yMax - yMind, yMax, zMin, zMax - zMind);
createOctree(root->bottom_left_back, maxdepth, xMin, xMax - xMind, yMin, yMax - yMind, zMin, zMax - zMind);
createOctree(root->bottom_right_front, maxdepth, xMax - xMind, xMax, yMax - yMind, yMax, zMin, zMax - zMind);
createOctree(root->bottom_right_back, maxdepth, xMax - xMind, xMax, yMin, yMax - yMind, zMin, zMax - zMind);
}
}

int i = 1;
//先序遍历八叉树
template <class T>
void preOrder(OctreeNode<T> * & p)
{
if (p)
{
cout << i << ".当前节点的值为：" << p->data << "\n坐标为：";
cout << " xMin: " << p->xMin << " xMax: " << p->xMax;
cout << " yMin: " << p->yMin << " yMax: " << p->yMax;
cout << " zMin: " << p->zMin << " zMax: " << p->zMax;
i += 1;
cout << endl;
preOrder(p->top_left_front);
preOrder(p->top_left_back);
preOrder(p->top_right_front);
preOrder(p->top_right_back);
preOrder(p->bottom_left_front);
preOrder(p->bottom_left_back);
preOrder(p->bottom_right_front);
preOrder(p->bottom_right_back);
cout << endl;
}
}

//求八叉树的深度
template<class T>
int depth(OctreeNode<T> *& p)
{
if (p == NULL)
return -1;
int h = depth(p->top_left_front);
return h + 1;
}

//计算单位长度，为查找点做准备
int cal(int num)
{
int result = 1;
if (1 == num)
result = 1;
else
{
for (int i = 1; i < num; i++)
result = 2 * result;
}
return result;
}

//查找点
int maxdepth = 0;
int times = 0;
static double xMin = 0, xMax = 0, yMin = 0, yMax = 0, zMin = 0, zMax = 0;
int tmaxdepth = 0;
double txm = 1, tym = 1, tzm = 1;

template<class T>
void find(OctreeNode<T> *& p, double x, double y, double z)
{
double xMind = (p->xMax - p->xMin) / 2;
double yMind = (p->yMax - p->yMin) / 2;
double zMind = (p->yMax - p->yMin) / 2;
times++;
if (x > xMax || x<xMin || y>yMax || y<yMin || z>zMax || z < zMin)
{
cout << "该点不在场景中！" << endl;
return;
}
if (x <= p->xMin + txm && x >= p->xMax - txm && y <= p->yMin + tym &&
y >= p->yMax - tym && z <= p->zMin + tzm && z >= p->zMax - tzm)
{
cout << endl << "找到该点！" << "该点位于" << endl;
cout << " xMin: " << p->xMin << " xMax: " << p->xMax;
cout << " yMin: " << p->yMin << " yMax: " << p->yMax;
cout << " zMin: " << p->zMin << " zMax: " << p->zMax;
cout << "节点内！" << endl;
cout << "共经过" << times << "次递归！" << endl;
}
else if (x < (p->xMax - xMind) && y < (p->yMax - yMind) && z < (p->zMax - zMind))
{
cout << "当前经过节点坐标：" << endl;
cout << " xMin: " << p->xMin << " xMax: " << p->xMax;
cout << " yMin: " << p->yMin << " yMax: " << p->yMax;
cout << " zMin: " << p->zMin << " zMax: " << p->zMax;
cout << endl;
find(p->bottom_left_back, x, y, z);
}
else if (x < (p->xMax - xMind) && y<(p->yMax - yMind) && z>(p->zMax - zMind))
{
cout << "当前经过节点坐标：" << endl;
cout << " xMin: " << p->xMin << " xMax: " << p->xMax;
cout << " yMin: " << p->yMin << " yMax: " << p->yMax;
cout << " zMin: " << p->zMin << " zMax: " << p->zMax;
cout << endl;
find(p->top_left_back, x, y, z);
}
else if (x > (p->xMax - xMind) && y < (p->yMax - yMind) && z < (p->zMax - zMind))
{
cout << "当前经过节点坐标：" << endl;
cout << " xMin: " << p->xMin << " xMax: " << p->xMax;
cout << " yMin: " << p->yMin << " yMax: " << p->yMax;
cout << " zMin: " << p->zMin << " zMax: " << p->zMax;
cout << endl;
find(p->bottom_right_back, x, y, z);
}
else if (x > (p->xMax - xMind) && y<(p->yMax - yMind) && z>(p->zMax - zMind))
{
cout << "当前经过节点坐标：" << endl;
cout << " xMin: " << p->xMin << " xMax: " << p->xMax;
cout << " yMin: " << p->yMin << " yMax: " << p->yMax;
cout << " zMin: " << p->zMin << " zMax: " << p->zMax;
cout << endl;
find(p->top_right_back, x, y, z);
}
else if (x<(p->xMax - xMind) && y>(p->yMax - yMind) && z < (p->zMax - zMind))
{
cout << "当前经过节点坐标：" << endl;
cout << " xMin: " << p->xMin << " xMax: " << p->xMax;
cout << " yMin: " << p->yMin << " yMax: " << p->yMax;
cout << " zMin: " << p->zMin << " zMax: " << p->zMax;
cout << endl;
find(p->bottom_left_front, x, y, z);
}
else if (x<(p->xMax - xMind) && y>(p->yMax - yMind) && z > (p->zMax - zMind))
{
cout << "当前经过节点坐标：" << endl;
cout << " xMin: " << p->xMin << " xMax: " << p->xMax;
cout << " yMin: " << p->yMin << " yMax: " << p->yMax;
cout << " zMin: " << p->zMin << " zMax: " << p->zMax;
cout << endl;
find(p->top_left_front, x, y, z);
}
else if (x > (p->xMax - xMind) && y > (p->yMax - yMind) && z < (p->zMax - zMind))
{
cout << "当前经过节点坐标：" << endl;
cout << " xMin: " << p->xMin << " xMax: " << p->xMax;
cout << " yMin: " << p->yMin << " yMax: " << p->yMax;
cout << " zMin: " << p->zMin << " zMax: " << p->zMax;
cout << endl;
find(p->bottom_right_front, x, y, z);
}
else if (x > (p->xMax - xMind) && y > (p->yMax - yMind) && z > (p->zMax - zMind))
{
cout << "当前经过节点坐标：" << endl;
cout << " xMin: " << p->xMin << " xMax: " << p->xMax;
cout << " yMin: " << p->yMin << " yMax: " << p->yMax;
cout << " zMin: " << p->zMin << " zMax: " << p->zMax;
cout << endl;
find(p->top_right_front, x, y, z);
}
}

//main函数
int main()
{
OctreeNode<double> * rootNode = NULL;
int choiced = 0;
while (true)
{
system("cls");
cout << "请选择操作：\n";
cout << "1.创建八叉树 2.先序遍历八叉树\n";
cout << "3.查看树深度 4.查找节点   \n";
cout << "0.退出\n\n";
cin >> choiced;
if (choiced == 0)
{
return 0;
}
else if (choiced == 1)
{
system("cls");
cout << "请输入最大递归深度：" << endl;
cin >> maxdepth;
cout << "请输入外包盒坐标，顺序如下：xMin,xMax,yMin,yMax,zMin,zMax" << endl;
cin >> xMin >> xMax >> yMin >> yMax >> zMin >> zMax;
if (maxdepth >= 0 || xMax > xMin || yMax > yMin || zMax > zMin || xMin > 0 || yMin > 0 || zMin > 0)
{
tmaxdepth = cal(maxdepth);
txm = (xMax - xMin) / tmaxdepth;
tym = (yMax - yMin) / tmaxdepth;
tzm = (zMax - zMin) / tmaxdepth;
createOctree(rootNode, maxdepth, xMin, xMax, yMin, yMax, zMin, zMax);
}
else
{
cout << "输入错误！";
return 0;
}
}
else if (choiced == 2)
{
system("cls");
cout << "先序遍历八叉树结果：\n";
i = 1;
preOrder(rootNode);
cout << endl;
system("pause");
}
else if (choiced == 3)
{
system("cls");
int dep = depth(rootNode);
cout << "此八叉树的深度为" << dep + 1 << endl;
system("pause");
}
else if (choiced == 4)
{
system("cls");
cout << "请输入您希望查找的点的坐标，顺序如下：x,y,z\n";
double x, y, z;
cin >> x >> y >> z;
times = 0;
cout << endl << "开始搜寻该点……" << endl;
find(rootNode, x, y, z);
system("pause");
}
else
{
system("cls");
cout << "\n\n错误选择！\n";
system("pause");
}
}
}