UVA10652 Board Wrapping-凸包入门

原题链接：UVA10652 Board Wrapping

题意：有n块矩形木板，你要用一个尽量小的凸多边形把它们包起来，求出木板面积占凸多边形的总面积的百分比

分析：显然是求凸包，如图，我们可以把n个矩形的四个点都加入到待求凸包数组里。。。

向量OA我们按照题意旋转得到，A点坐标等于向量O1O+向量OA，同样B,C,D我们也可以求出，然后就是套凸包的板子。。。

#include <bits/stdc++.h>
using namespace std;
double eps=1e-10;
double pi=acos(-1);
struct Point{
    double x,y;
    Point(double x=0,double y=0):x(x),y(y){}
};
typedef Point Vector;
Vector operator + (Vector A,Vector B){return Vector(A.x+B.x,A.y+B.y);}
Vector operator - (Vector A,Vector B){return Vector(A.x-B.x,A.y-B.y);}
Vector operator * (Vector A,double B){return Vector(A.x*B,A.y*B);}
Vector operator / (Vector A,double B){return Vector(A.x/B,A.y/B);}
int dcmp(double x){
    if(fabs(x)<eps)return 0;
    else return x<0?-1:1;
}
bool operator < (const Point &a,const Point &b){
    return dcmp(a.x-b.x)<0||(dcmp(a.x-b.x)==0&&dcmp(a.y-b.y)<0);
}
bool operator == (const Point &a,const Point &b){
    return dcmp(a.x-b.x)==0&&dcmp(a.y-b.y)==0;
}
double Cross(Vector A,Vector B){
    return A.x*B.y-A.y*B.x;
}
Vector Rotate(Vector A,double rad){
    return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));
}
int tubao(Point *p,int n,Point *ch){
    sort(p,p+n);
    n=unique(p,p+n)-p;
    int m=0;
    for(int i=0;i<n;i++){
        while(m>1&&Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0)m--;
        ch[m++]=p[i];
    }
    int k=m;
    for(int i=n-2;i>=0;i--){
        while(m>k&&Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0)m--;
        ch[m++]=p[i];
    }
    if(n>1)m--;
    return m;
}
double tubaos(Point *p,int n){
    double area=0;
    for(int i=1;i<n-1;i++){
        area+=Cross(p[i]-p[0],p[i+1]-p[0]);
    }
    return area/2;
}
double torad(double x){
    return x*pi/180;
}
int T,n,cnt;
double x,y,w,h,seta,area1,area2;
Point p[3000],ch[3000];
int main(){
    scanf("%d",&T);
    while(T--){
        scanf("%d",&n);
        area1=area2=0;
        cnt=0;
        while(n--){
            scanf("%lf%lf%lf%lf%lf",&x,&y,&w,&h,&seta);
            Point o(x,y);
            seta=-torad(seta);
            p[cnt++]=o+Rotate(Vector(-w/2,-h/2),seta);
            p[cnt++]=o+Rotate(Vector(w/2,-h/2),seta);
            p[cnt++]=o+Rotate(Vector(-w/2,h/2),seta);
            p[cnt++]=o+Rotate(Vector(w/2,h/2),seta);
            area1+=w*h;
        }
        int m=tubao(p,cnt,ch);
        double area2=tubaos(ch,m);
        printf("%.1lf %%\n",area1*100/area2);
    }
}