hdu3662 +3D Convex Hull+三维凸包的表面多边形个数
2016-08-22 09:38:10

Description
There are N points in 3D-space which make up a 3D-Convex hull*. How many faces does the 3D-convexhull have? It is guaranteed that all the points are not in the same plane.

In case you don’t know the definition of convex hull, here we give you a clarification from Wikipedia:
*Convex hull: In mathematics, the convex hull, for a set of points X in a real vector space V, is the minimal convex set containing X.

Input
There are several test cases. In each case the first line contains an integer N indicates the number of 3D-points (3< N <= 300), and then N lines follow, each line contains three numbers x, y, z (between -10000 and 10000) indicate the 3d-position of a point.

Output
Output the number of faces of the 3D-Convex hull.

Sample Input

7
1 1 0
1 -1 0
-1 1 0
-1 -1 0
0 0 1
0 0 0
0 0 -0.1
7
1 1 0
1 -1 0
-1 1 0
-1 -1 0
0 0 1
0 0 0
0 0 0.1

Sample Output

8
5

```#include
#include
#include
#include
#include
using namespace std;

const int MAXN=550;
const double eps=1e-8;

struct Point {
double x,y,z;
Point() {}

Point(double xx,double yy,double zz):x(xx),y(yy),z(zz) {}
//两向量之差
Point operator -(const Point p1) {
return Point(x-p1.x,y-p1.y,z-p1.z);
}
//两向量之和
Point operator +(const Point p1) {
return Point(x+p1.x,y+p1.y,z+p1.z);
}
//叉乘
Point operator *(const Point p) {
return Point(y*p.z-z*p.y,z*p.x-x*p.z,x*p.y-y*p.x);
}
Point operator *(double d) {
return Point(x*d,y*d,z*d);
}
Point operator / (double d) {
return Point(x/d,y/d,z/d);
}
//点乘
double  operator ^(Point p) {
return (x*p.x+y*p.y+z*p.z);
}
};

struct CH3D {
struct face {
//表示凸包一个面上的三个点的编号
int a,b,c;
//表示该面是否属于最终凸包上的面
bool ok;
};
//初始顶点数
int n;
//初始顶点
Point P[MAXN];
//凸包表面的三角形数
int num;
//凸包表面的三角形
face F[8*MAXN];
//凸包表面的三角形
int g[MAXN][MAXN];

//向量长度
double vlen(Point a) {
return sqrt(a.x*a.x+a.y*a.y+a.z*a.z);
}
//叉乘
Point cross(const Point &a,const Point &b,const Point &c) {
return Point((b.y-a.y)*(c.z-a.z)-(b.z-a.z)*(c.y-a.y),
(b.z-a.z)*(c.x-a.x)-(b.x-a.x)*(c.z-a.z),
(b.x-a.x)*(c.y-a.y)-(b.y-a.y)*(c.x-a.x)
);
}
//三角形面积*2
double area(Point a,Point b,Point c) {
return vlen((b-a)*(c-a));
}
//四面体有向体积*6
double volume(Point a,Point b,Point c,Point d) {
return (b-a)*(c-a)^(d-a);
}
//正：点在面同向
double dblcmp(Point &p,face &f) {
Point m=P[f.b]-P[f.a];
Point n=P[f.c]-P[f.a];
Point t=p-P[f.a];
return (m*n)^t;
}
void deal(int p,int a,int b) {
int f=g[a][b];//搜索与该边相邻的另一个平面
if(F[f].ok) {
if(dblcmp(P[p],F[f])>eps)
dfs(p,f);
else {
g[p][b]=g[a][p]=g[b][a]=num;
}
}
}
void dfs(int p,int now) { //递归搜索所有应该从凸包内删除的面
F[now].ok=0;
deal(p,F[now].b,F[now].a);
deal(p,F[now].c,F[now].b);
deal(p,F[now].a,F[now].c);
}
bool same(int s,int t) {
Point &a=P[F[s].a];
Point &b=P[F[s].b];
Point &c=P[F[s].c];
return fabs(volume(a,b,c,P[F[t].a]))eps) {
swap(P[1],P[i]);
flag=false;
break;
}
}
if(flag)return;
flag=true;
//使前三个点不共线
for(i=2; ieps) {
swap(P[2],P[i]);
flag=false;
break;
}
}
if(flag)return;
flag=true;
//使前四个点不共面
for(int i=3; ieps) {
swap(P[3],P[i]);
flag=false;
break;
}
}
if(flag)return;
//*****************************************
for(i=0; i<4; i++) {
}
for(i=4; ieps) {
dfs(i,j);
break;
}
}
}
tmp=num;
for(i=num=0; ```