HDU4273(求三维凸包重心到表面的最短距离)

题目：Rescue

 

题意：求三维凸包重心到表面的最短距离

#include<stdio.h> #include<algorithm> #include<string.h> #include<math.h> #include<stdlib.h> using namespace std; const int MAXN=1050; 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*2double area(Point a,Point b,Point c){return vlen((b-a)*(c-a));}//四面体有向体积*6double 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;//这里注意顺序，要成右手系add.ok=true;g[p][b]=g[a][p]=g[b][a]=num;F[num++]=add;}}}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 &&fabs(volume(a,b,c,P[F[t].b]))<eps &&fabs(volume(a,b,c,P[F[t].c]))<eps;}//构建三维凸包void create(){int i,j,tmp;face add;num=0;if(n<4)return;//**********************************************//此段是为了保证前四个点不共面bool flag=true;for(i=1;i<n;i++){if(vlen(P[0]-P[i])>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;i<n;i++){if(vlen((P[0]-P[1])*(P[1]-P[i]))>eps){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;i<n;i++){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];}//表面积double area(){double res=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(){double res=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);}//表面三角形个数int triangle(){return num;}//表面多边形个数int polygon(){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;}//三维凸包重心Point barycenter(){Point ans(0,0,0),o(0,0,0);double all=0;for(int i=0;i<num;i++){double vol=volume(o,P[F[i].a],P[F[i].b],P[F[i].c]);ans=ans+(o+P[F[i].a]+P[F[i].b]+P[F[i].c])/4.0*vol;all+=vol;}ans=ans/all;return ans;}//点到面的距离double ptoface(Point p,int i){return fabs(volume(P[F[i].a],P[F[i].b],P[F[i].c],p)/vlen((P[F[i].b]-P[F[i].a])*(P[F[i].c]-P[F[i].a])));} };CH3D hull;int main() {while(scanf("%d",&hull.n)==1){for(int i=0;i<hull.n;i++){scanf("%lf%lf%lf",&hull.P[i].x,&hull.P[i].y,&hull.P[i].z);}hull.create();Point p=hull.barycenter();double minn=1e20;for(int i=0;i<hull.num;i++){minn=min(minn,hull.ptoface(p,i));}printf("%.3lf\n",minn);}return 0; }

 

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