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=1;i<n;i++)S+=Cross(R[i]-R[1],R[i+1]-R[1]);
    return S/2;
}

int n,cnt=0;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/2,-h/2),a);
  R[++cnt]=O+Rotate(V( w/2,-h/2),a);
  R[++cnt]=O+Rotate(V(-w/2, h/2),a);
  R[++cnt]=O+Rotate(V( w/2, h/2),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=0;char c=getchar(),f=0;
  while(c<'0'||c>'9'){if(c=='-')f=1;c=getchar();}
  while(c>='0'&&c<='9')x=x*10+c-'0',c=getchar();
  if(f)x=-x;
}
const db pi=acos(-1.0),eps=1e-10;
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=1;i<n;i++)S+=Cross(R[i]-R[1],R[i+1]-R[1]);
    return S/2;
}
db Leng(D*R,int n){
    db C=0.0;
    for(int i=2;i<=n;i++)C+=Dis(R[i],R[i-1]);
    return C+Dis(R[n],R[1]);
}

int Andrew(D*R,int n,D*A){
    int m=0;
    sort(R+1,R+n+1);
    for(int i=1;i<=n;i++){
        while(m>=2 && Cross(A[m]-A[m-1],R[i]-A[m-1])<=0)m--;
        A[++m]=R[i];
    }
    int k=m;
    for(int i=n-1;i>=1;i--){
        while(m>k  && Cross(A[m]-A[m-1],R[i]-A[m-1])<=0)m--;
        A[++m]=R[i];
    }
    return n>1?m-1:m;
}

D GO;
bl acomp(D A,D B){
    db x=Cross(A-GO,B-GO);
    if(x>0)return 1;if(x<0)return 0;
    return Dis(GO,A)<Dis(GO,B);
}

int Graham(D*R,int n,D*A){
    for(int i=1;i<=n;i++){
        if(R[i].y<R[1].y)swap(R[i],R[1]);
        else if(R[i].y==R[1].y&&R[i].x<R[1].x)swap(R[i],R[1]);
    }
    GO=R[1],sort(R+2,R+n+1,acomp);
    int m=0;A[++m]=R[1],A[++m]=R[2];
    for(int i=3;i<=n;i++)
    {
        while(m>1 && Cross(A[m-1]-R[i],A[m]-R[i])<=0)m--;
        A[++m]=R[i];
    }
    return m;
}
const int maxn=(600<<2)+10;
D R[maxn],A[maxn];
int main(){
    int T;
    for(scanf("%d",&T);T--;){
        int n,cnt=0;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/2,-h/2),a);
            R[++cnt]=O+Rotate(V( w/2,-h/2),a);
            R[++cnt]=O+Rotate(V(-w/2, h/2),a);
            R[++cnt]=O+Rotate(V( w/2, h/2),a);
            S1+=w*h;
        }
        int m=Andrew(R,cnt,A);
        db S2=Area(A,m);
        printf("%.1lf %%\n",S1*100.0/S2);
    }    
  return 0;
}