计算几何-UVa10652

This article is made by Jason-Cow.
Welcome to reprint.
But please post the article's address.

题意见白书，P272~273

把之前的板子拼起来就可以了

ans=(S(木板)*100/S(凸包))%

板子太长，先贴关键

求面积

db Area(D*R,int n){
    db S=0.0;
    for(int i=;i<n;i++)S+=Cross(R[i]-R[],R[i+]-R[]);
    return S/;
}

int n,cnt=;db S1=0.0;
for(scanf("%d",&n);n--;){
  db x,y,w,h,j,a;
  scanf("%lf%lf%lf%lf%lf",&x,&y,&w,&h,&j);
  D O(x,y);a=-Rad(j);
  R[++cnt]=O+Rotate(V(-w/,-h/),a);
  R[++cnt]=O+Rotate(V( w/,-h/),a);
  R[++cnt]=O+Rotate(V(-w/, h/),a);
  R[++cnt]=O+Rotate(V( w/, h/),a);
  S1+=w*h;
}
int m=Andrew(R,cnt,A);
db S2=Area(A,m);
printf("%.1lf %%\n",S1*100.0/S2);

 #include <algorithm>
 #include <iostream>
 #include <cstring>
 #include <cstdlib>
 #include <cstdio>
 #include <vector>
 #include <cmath>
 #include <queue>
 #include <map>
 #include <set>
 using namespace std;
 #define sqr(x) ((x)*(x))
 #define RG register
 #define op operator
 #define IL inline
 #define db double
 #define bl bool
 #define vo void
 IL vo read(int&x){
   x=;char c=getchar(),f=;
   while(c<''||c>''){if(c=='-')f=;c=getchar();}
   while(c>=''&&c<='')x=x*+c-'',c=getchar();
   if(f)x=-x;
 }
 const db pi=acos(-1.0),eps=1e-;
 struct D{
   db x,y;
   D(db x=0.0,db y=0.0):x(x),y(y){}
 };
 typedef D V;
 bl op<(D A,D B){return A.x<B.x||(A.x==B.x&&A.y<B.y);}
 V op+(V A,V B){return V(A.x+B.x,A.y+B.y);}
 V op-(V A,V B){return V(A.x-B.x,A.y-B.y);}
 V op*(V A,db N){return V(A.x*N,A.y*N);}
 V op/(V A,db N){return V(A.x/N,A.y/N);}

 db Ang(db x){return(x*180.0/pi);}
 db Rad(db x){return(x*pi/180.0);}
 V Rotate(V A,db a){return V(A.x*cos(a)-A.y*sin(a),A.x*sin(a)+A.y*cos(a));}
 db Dis(D A,D B){return sqrt(sqr(A.x-B.x)+sqr(A.y-B.y));}
 db Cross(V A,V B){return A.x*B.y-A.y*B.x;}

 db Area(D*R,int n){
     db S=0.0;
     for(int i=;i<n;i++)S+=Cross(R[i]-R[],R[i+]-R[]);
     return S/;
 }
 db Leng(D*R,int n){
     db C=0.0;
     for(int i=;i<=n;i++)C+=Dis(R[i],R[i-]);
     return C+Dis(R[n],R[]);
 }

 int Andrew(D*R,int n,D*A){
     int m=;
     sort(R+,R+n+);
     for(int i=;i<=n;i++){
         while(m>= && Cross(A[m]-A[m-],R[i]-A[m-])<=)m--;
         A[++m]=R[i];
     }
     int k=m;
     for(int i=n-;i>=;i--){
         while(m>k  && Cross(A[m]-A[m-],R[i]-A[m-])<=)m--;
         A[++m]=R[i];
     }
     return n>?m-:m;
 }

 D GO;
 bl acomp(D A,D B){
     db x=Cross(A-GO,B-GO);
     if(x>)return ;if(x<)return ;
     return Dis(GO,A)<Dis(GO,B);
 }

 int Graham(D*R,int n,D*A){
     for(int i=;i<=n;i++){
         if(R[i].y<R[].y)swap(R[i],R[]);
         else if(R[i].y==R[].y&&R[i].x<R[].x)swap(R[i],R[]);
     }
     GO=R[],sort(R+,R+n+,acomp);
     int m=;A[++m]=R[],A[++m]=R[];
     for(int i=;i<=n;i++)
     {
         while(m> && Cross(A[m-]-R[i],A[m]-R[i])<=)m--;
         A[++m]=R[i];
     }
     return m;
 }
 const int maxn=(<<)+;
 D R[maxn],A[maxn];
 int main(){
     int T;
     for(scanf("%d",&T);T--;){
         int n,cnt=;db S1=0.0;
         for(scanf("%d",&n);n--;){
             db x,y,w,h,j,a;
             scanf("%lf%lf%lf%lf%lf",&x,&y,&w,&h,&j);
             D O(x,y);a=-Rad(j);
             R[++cnt]=O+Rotate(V(-w/,-h/),a);
             R[++cnt]=O+Rotate(V( w/,-h/),a);
             R[++cnt]=O+Rotate(V(-w/, h/),a);
             R[++cnt]=O+Rotate(V( w/, h/),a);
             S1+=w*h;
         }
         int m=Andrew(R,cnt,A);
         db S2=Area(A,m);
         printf("%.1lf %%\n",S1*100.0/S2);
     }
   return ;
 }

UVa10652