本文主要是介绍HDU 4266 The Worm in the Apple（三维凸包内点到表面距离），希望对大家解决编程问题提供一定的参考价值，需要的开发者们随着小编来一起学习吧！
题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=4266
这个题目还是三维凸包模板题，现场如果遇到这个模板要敲好长时间啊！
#include<iostream>
#include<cmath>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include <stdio.h>
using namespace std;const int MAXN=1001;
const int N = 500;
const double EPS=1e-8;int g[MAXN][MAXN];struct Point{double x,y,z;Point(){}Point(double xx,double yy,double zz):x(xx),y(yy),z(zz){}Point operator -(const Point p1){//两向量之差return Point(x-p1.x,y-p1.y,z-p1.z);}Point operator *(Point p){//叉乘return Point(y*p.z-z*p.y,z*p.x-x*p.z,x*p.y-y*p.x);}double operator ^(Point p){//点乘return (x*p.x+y*p.y+z*p.z);}
};struct CH3D{struct face{int a,b,c;//表示凸包一个面上三个点的编号bool ok;//表示该面是否属于最终凸包中的面};int n;//初始顶点数Point P[MAXN];//初始顶点int num; //凸包表面的三角形数face F[8*MAXN];//int g[MAXN][MAXN];//凸包表面的三角形double vlen(Point a){//向量长度return sqrt(a.x*a.x+a.y*a.y+a.z*a.z);}Point cross(const Point &a, const Point &b, const Point &c){//叉乘return Point((b.y-a.y)*(c.z-a.z)-(b.z-a.z)*(c.y-a.y),-((b.x-a.x)*(c.z-a.z)-(b.z-a.z)*(c.x-a.x)),(b.x-a.x)*(c.y-a.y)-(b.y-a.y)*(c.x-a.x));}double area(Point a,Point b,Point c){//三角形面积*2return vlen((b-a)*(c-a));}double volume(Point a,Point b,Point c,Point d){//四面体有向体积*6return (b-a)*(c-a)^(d-a);}double dblcmp(Point &p,face &f){//正:点在面同向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];face add;if(F[f].ok){if(dblcmp(P[p],F[f])>EPS){dfs(p,f);}else {add.a=b;add.b=a;add.c=p;add.ok=1;g[p][b]=g[a][p]=g[b][a]=num;F[num++]=add;}}}void dfs(int p,int now){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 && fabs(volume(a,b,c,P[F[t].b]))<EPS&& fabs(volume(a,b,c,P[F[t].c]))<EPS;}void pretreat(){//构建三维凸包int i,j,tmp;face add;bool flag;num=0;if(n<4) return;flag=true;for(i=1;i<n;i++){//此段是为了保证前四个点不共面,若以保证,则可去掉if(vlen(P[0]-P[i])>EPS){swap(P[1],P[i]);flag=false; break;}}if(flag) return;flag=true;for(i=2;i<n;i++){//使前三点不共线if(vlen((P[0]-P[1])*(P[1]-P[i]))>EPS){swap(P[2],P[i]);flag=false; break;}}if(flag) return;flag=true;for(i=3;i<n;i++){//使前四点不共面if(fabs((P[0]-P[1])*(P[1]-P[2])^(P[0]-P[i]))>EPS){swap(P[3],P[i]);flag=false;break;}}if(flag) return;for(i=0;i<4;i++){add.a=(i+1)%4;add.b=(i+2)%4;add.c=(i+3)%4;add.ok=true;if(dblcmp(P[i],add)>0)swap(add.b,add.c);g[add.a][add.b]=g[add.b][add.c]=g[add.c][add.a]=num;F[num++]=add;}for(i=4;i<n;i++){for(j=0;j<num;j++){if(F[j].ok && dblcmp(P[i],F[j])>EPS){dfs(i,j);break;}}}tmp=num;for(i=num=0;i<tmp;i++){if(F[i].ok) F[num++]=F[i];}}double area(){//表面积double res=0.0;if(n==3){Point p=cross(P[0],P[1],P[2]);res=vlen(p)/2.0;return res;}for(int i=0;i<num;i++)res+=area(P[F[i].a],P[F[i].b],P[F[i].c]);return res/2.0;}double volume(){//体积double res=0.0;Point tmp(0,0,0);for(int i=0;i<num;i++)res+=volume(tmp,P[F[i].a],P[F[i].b],P[F[i].c]);return fabs(res/6.0);}int triangle(){//表面三角形个数return num;}int polygon_bug(){//表面多边形个数int i,j,res,flag;for(i=res=0;i<num;i++){flag=1;for(j=0;j<i;j++){if(same(i,j)){flag=0; break;}res+=flag;}}return res;}
int polygon(){//表面多边形个数int i,j,res,flag;for(i=res=0;i<num;i++){flag=1;for(j=0;j<i;j++)if(same(i,j)){flag=0; break;}res+=flag;}return res;}Point getcent(){//求凸包质心Point ans(0,0,0),temp=P[F[0].a];double v = 0.0,t2;for(int i=0;i<num;i++){if(F[i].ok == true){Point p1=P[F[i].a],p2=P[F[i].b],p3=P[F[i].c];t2 = volume(temp,p1,p2,p3)/6.0;//体积大于0，也就是说，点 temp 不在这个面上if(t2>0){ans.x += (p1.x+p2.x+p3.x+temp.x)*t2;ans.y += (p1.y+p2.y+p3.y+temp.y)*t2;ans.z += (p1.z+p2.z+p3.z+temp.z)*t2;v += t2;}}}ans.x /= (4*v); ans.y /= (4*v); ans.z /= (4*v);return ans;}double function(Point fuck){//点到凸包上的最近距离（枚举每个面到这个点的距离）double min=99999999;for(int i=0;i<num;i++){if(F[i].ok==true){Point p1=P[F[i].a] , p2=P[F[i].b] , p3=P[F[i].c];double a = ( (p2.y-p1.y)*(p3.z-p1.z)-(p2.z-p1.z)*(p3.y-p1.y) );double b = ( (p2.z-p1.z)*(p3.x-p1.x)-(p2.x-p1.x)*(p3.z-p1.z) );double c = ( (p2.x-p1.x)*(p3.y-p1.y)-(p2.y-p1.y)*(p3.x-p1.x) );double d = ( 0-(a*p1.x+b*p1.y+c*p1.z) );double temp = fabs(a*fuck.x+b*fuck.y+c*fuck.z+d)/sqrt(a*a+b*b+c*c);if(temp<min)min = temp;}}return min;}};
int main()
{int i,n,m;while(scanf("%d",&n),n){CH3D hull;memset(g,0,sizeof(g));memset(hull.P,0,sizeof(hull.P));hull.n = n;for(i=0;i<hull.n;i++){scanf("%lf%lf%lf",&hull.P[i].x,&hull.P[i].y,&hull.P[i].z);}hull.pretreat();scanf("%d",&m);Point temp;for(i=0;i<m;i++){scanf("%lf%lf%lf",&temp.x,&temp.y,&temp.z);printf("%.4lf\n",hull.function(temp));}}return 0;
}
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