已知两圆圆心坐标和半径,求相交部分面积:
#include <iostream> using namespace std; #include<cmath> #include<stdio.h> #define PI 3.141593 struct point//点 { double x,y; }; struct circle//圆 { point center; double r; }; float dist(point a,point b)//求圆心距 { return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y)); } int main() { circle a,b; while(cin>>a.center.x>>a.center.y>>a.r>>b.center.x>>b.center.y>>b.r) { if((dist(a.center,b.center)+min(a.r,b.r))<=max(a.r,b.r))//两圆内交或包含 { if(a.r<b.r) printf("%.3lf\n",PI*a.r*a.r); else printf("%.3lf\n",PI*b.r*b.r); } else if(dist(a.center,b.center)>=(a.r+b.r))//两圆外交或相离 cout<<"0.000"<<endl; else { double length=dist(a.center,b.center); double d1=2*acos((a.r*a.r+length*length-b.r*b.r)/(2*a.r*length)); //求两扇形圆心角 double d2=2*acos((b.r*b.r+length*length-a.r*a.r)/(2*b.r*length)); double area1=a.r*a.r*d1/2-a.r*a.r*sin(d1)/2; //根据圆心角求扇形面积,减去三角形面积,得到相交部分面积 //扇形面积:S=PI*r*r*θ/(2*PI) 三角形面积:S=1/2*a*c*sin(B) double area2=b.r*b.r*d2/2-b.r*b.r*sin(d2)/2; double area=area1+area2; printf("%.3lf\n",area); } } return 0; }
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