计算几何（凸包）：SHTSC 2012 信用卡凸包

　　这道题是水题，发现平移某些边，答案就是圆心的凸包+一个圆的周长。

　　不要忽视精度误差！

 #include <algorithm>
 #include <iostream>
 #include <cstring>
 #include <cstdio>
 #include <cmath>
 using namespace std;
 const int N=;
 const double eps=1e-;
 const double Pi=acos(-1.0);
 int sgn(double x){
     if(x>eps)return ;
     if(x<-eps)return -;
     return ;
 }
 struct Point{
     double x,y;
     Point(double _=,double __=){x=_;y=__;}
     friend Point operator+(Point a,Point b){
         return Point(a.x+b.x,a.y+b.y);
     }
     friend Point operator-(Point a,Point b){
         return Point(a.x-b.x,a.y-b.y);
     }
     friend bool operator<(Point a,Point b){
         return sgn(a.y-b.y)?sgn(b.y-a.y)>:sgn(b.x-a.x)>;
     }
 }st[*N],p[*N];
 double Cross(Point a,Point b){
     return a.x*b.y-a.y*b.x;
 }

 Point Rotate(Point a,double th){
     double s=sin(th),c=cos(th);
     return Point(a.x*c-a.y*s,a.x*s+a.y*c);
 }

 double sqr(double x){return x*x;}
 double Dis(Point a,Point b){
     return sqrt(sqr(a.x-b.x)+sqr(a.y-b.y));
 }

 bool cmp(Point a,Point b){
     double c=Cross(a-p[],b-p[]);
     if(sgn(c)>)return true;
     if(sgn(c)<)return false;
     return sgn(Dis(p[],b)-Dis(p[],a))>;
 }

 double a,b,r;
 double x,y,th;
 int n,pos,top,tot;
 int main(){
     freopen("card.in","r",stdin);
     freopen("card.out","w",stdout);
     scanf("%d",&n);
     scanf("%lf%lf%lf",&b,&a,&r);
     a=a/2.0;a=a-r;b=b/2.0;b=b-r;
     for(int i=;i<=n;i++){
         scanf("%lf%lf%lf",&x,&y,&th);
         Point O(x,y);
         p[i*-]=Rotate(Point(x+a,y+b)-O,th)+O;
         p[i*-]=Rotate(Point(x+a,y-b)-O,th)+O;
         p[i*-]=Rotate(Point(x-a,y+b)-O,th)+O;
         p[i*-]=Rotate(Point(x-a,y-b)-O,th)+O;
     }
     sort(p,p+*n);
     for(int i=;i<*n;i++){
         if(i==)p[tot++]=p[i];
         else if(sgn(p[i].x-p[i-].x)||sgn(p[i].y-p[i-].y))
             p[tot++]=p[i];
     }
     sort(p+,p+tot,cmp);p[tot]=p[];
     st[]=p[];st[]=p[];top=;
     for(int i=;i<=tot;i++){
         while(top>=&&sgn(Cross(st[top]-p[i],st[top-]-p[i]))>=)top--;
         st[++top]=p[i];
     }
     double ans=2.0*Pi*r;
     for(int i=;i<=top;i++)
         ans+=Dis(st[i],st[i-]);
     printf("%.2f\n",ans);
     return ;
 }