计算几何-UVa10652

This article is made by Jason-Cow.
Welcome to reprint.
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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);

 

  1 #include <algorithm>
  2 #include <iostream>
  3 #include <cstring>
  4 #include <cstdlib>
  5 #include <cstdio>
  6 #include <vector>
  7 #include <cmath>
  8 #include <queue>
  9 #include <map>
 10 #include <set>
 11 using namespace std;
 12 #define sqr(x) ((x)*(x))
 13 #define RG register
 14 #define op operator
 15 #define IL inline
 16 #define db double
 17 #define bl bool
 18 #define vo void
 19 IL vo read(int&x){
 20   x=0;char c=getchar(),f=0;
 21   while(c<'0'||c>'9'){if(c=='-')f=1;c=getchar();}
 22   while(c>='0'&&c<='9')x=x*10+c-'0',c=getchar();
 23   if(f)x=-x;
 24 }
 25 const db pi=acos(-1.0),eps=1e-10;
 26 struct D{
 27   db x,y;
 28   D(db x=0.0,db y=0.0):x(x),y(y){}
 29 };
 30 typedef D V;
 31 bl op<(D A,D B){return A.x<B.x||(A.x==B.x&&A.y<B.y);}
 32 V op+(V A,V B){return V(A.x+B.x,A.y+B.y);}
 33 V op-(V A,V B){return V(A.x-B.x,A.y-B.y);}
 34 V op*(V A,db N){return V(A.x*N,A.y*N);}
 35 V op/(V A,db N){return V(A.x/N,A.y/N);}
 36 
 37 
 38 db Ang(db x){return(x*180.0/pi);}
 39 db Rad(db x){return(x*pi/180.0);}
 40 V Rotate(V A,db a){return V(A.x*cos(a)-A.y*sin(a),A.x*sin(a)+A.y*cos(a));}
 41 db Dis(D A,D B){return sqrt(sqr(A.x-B.x)+sqr(A.y-B.y));}
 42 db Cross(V A,V B){return A.x*B.y-A.y*B.x;}
 43 
 44 db Area(D*R,int n){
 45     db S=0.0;
 46     for(int i=1;i<n;i++)S+=Cross(R[i]-R[1],R[i+1]-R[1]);
 47     return S/2;
 48 }
 49 db Leng(D*R,int n){
 50     db C=0.0;
 51     for(int i=2;i<=n;i++)C+=Dis(R[i],R[i-1]);
 52     return C+Dis(R[n],R[1]);
 53 }
 54 
 55 int Andrew(D*R,int n,D*A){
 56     int m=0;
 57     sort(R+1,R+n+1);
 58     for(int i=1;i<=n;i++){
 59         while(m>=2 && Cross(A[m]-A[m-1],R[i]-A[m-1])<=0)m--;
 60         A[++m]=R[i];
 61     }
 62     int k=m;
 63     for(int i=n-1;i>=1;i--){
 64         while(m>k  && Cross(A[m]-A[m-1],R[i]-A[m-1])<=0)m--;
 65         A[++m]=R[i];
 66     }
 67     return n>1?m-1:m;
 68 }
 69 
 70 D GO;
 71 bl acomp(D A,D B){
 72     db x=Cross(A-GO,B-GO);
 73     if(x>0)return 1;if(x<0)return 0;
 74     return Dis(GO,A)<Dis(GO,B);
 75 }
 76 
 77 int Graham(D*R,int n,D*A){
 78     for(int i=1;i<=n;i++){
 79         if(R[i].y<R[1].y)swap(R[i],R[1]);
 80         else if(R[i].y==R[1].y&&R[i].x<R[1].x)swap(R[i],R[1]);
 81     }
 82     GO=R[1],sort(R+2,R+n+1,acomp);
 83     int m=0;A[++m]=R[1],A[++m]=R[2];
 84     for(int i=3;i<=n;i++)
 85     {
 86         while(m>1 && Cross(A[m-1]-R[i],A[m]-R[i])<=0)m--;
 87         A[++m]=R[i];
 88     }
 89     return m;
 90 }
 91 const int maxn=(600<<2)+10;
 92 D R[maxn],A[maxn];
 93 int main(){
 94     int T;
 95     for(scanf("%d",&T);T--;){
 96         int n,cnt=0;db S1=0.0;
 97         for(scanf("%d",&n);n--;){        
 98             db x,y,w,h,j,a;
 99             scanf("%lf%lf%lf%lf%lf",&x,&y,&w,&h,&j);
100             D O(x,y);a=-Rad(j);
101             R[++cnt]=O+Rotate(V(-w/2,-h/2),a);
102             R[++cnt]=O+Rotate(V( w/2,-h/2),a);
103             R[++cnt]=O+Rotate(V(-w/2, h/2),a);
104             R[++cnt]=O+Rotate(V( w/2, h/2),a);
105             S1+=w*h;
106         }
107         int m=Andrew(R,cnt,A);
108         db S2=Area(A,m);
109         printf("%.1lf %%\n",S1*100.0/S2);
110     }    
111   return 0;
112 }
UVa10652

 

posted @ 2017-03-20 23:40  墨鳌  阅读(268)  评论(0)  编辑  收藏  举报