hdu5120 Intersection(平面几何+圆相交面积)

hdu512

题目

求两个给定圆环相交部分的面积

思路

最终面积就是大圆相交部分+小圆相交部分-2*大小圆相交的部分，然后就是模版了

代码

#include <iostream>
#include <algorithm>
#include <cmath>
#include <vector>
#include <string>
#include <cstring>
#include <cstdio>

using namespace std;

const double pi = acos(-1.0);

struct point
{
    double x,y,r;
};

double S(point a)
{
    return pi*a.r*a.r;
}

double dis(point a,point b)
{
    return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
}

double calu(point a,point b)
{
    point tmpa=a,tmpb=b;
    if(tmpa.r<tmpb.r) swap(tmpa,tmpb);
    double area = 0;
    double dd = dis(tmpa,tmpb);
    if(dd>tmpa.r-tmpb.r&&dd<tmpa.r+tmpb.r)
    {
        double cos1 = (tmpa.r*tmpa.r+dd*dd-tmpb.r*tmpb.r)/(2*tmpa.r*dd);
        double cos2 = (tmpb.r*tmpb.r+dd*dd-tmpa.r*tmpa.r)/(2*tmpb.r*dd);
        double th1 = 2*acos(cos1);
        double th2 = 2*acos(cos2);
        double s1 = 0.5*tmpa.r*tmpa.r*sin(th1);
        double s2 = 0.5*tmpb.r*tmpb.r*sin(th2);
        double s3 = (th1/2)*tmpa.r*tmpa.r;
        double s4 = (th2/2)*tmpb.r*tmpb.r;
        area = s3+s4-s1-s2;
    }
    else if(dd<=tmpa.r-tmpb.r)
        area = S(tmpb);
    return area;
}

int main()
{
    int T;
    int kase=1;
    scanf("%d",&T);
    double r,R,x1,x2,y1,y2;
    point p[4];
    while(T--)
    {
        scanf("%lf%lf",&r,&R);
        scanf("%lf%lf%lf%lf",&x1,&y1,&x2,&y2);
        p[0].x=x1,p[0].y=y1,p[0].r=r;
        p[1].x=x1,p[1].y=y1,p[1].r=R;
        p[2].x=x2,p[2].y=y2,p[2].r=r;
        p[3].x=x2,p[3].y=y2,p[3].r=R;
        double s1=calu(p[3],p[1]);
        double s2=calu(p[0],p[3]);
        double s3=calu(p[1],p[2]);
        double s4=calu(p[0],p[2]);
        printf("Case #%d: %.6lf\n",kase++,s1+s4-s2-s3);
    }

    return 0;
}