UVA 190 - Circle Through Three Points

题意：给出三点坐标，求过三点圆的标准方程和一般方程

解法：

已知两点(x1,y1)(x2,y2)求直线中垂线方程ax+by+c=0结论：

a= x2-x1,b=y2-y1,c=(x1*x1-x2*x2+y1*y1-y2*y2)/2

已知两直线方程a1x+b1y+c1=0，a2x+b2y+c2=0求交点结论：

(  (b1*c2-b2*c1)/ (a1*b2-b1*a2)  ,  (c1*a2-c2*a1)/(a1*b2-b1*a2)  )

两条直线中垂线交点坐标即为圆心坐标

代码如下：（这题我就不该用cout，太恶心了=-=）

#include <bits/stdc++.h>

using namespace std;
const double M=1e-10;
double a1,b1,c1,a2,b2,c2,x,y;
void A(double x1,double y1,double x2,double y2,double x3,double y3)
{
    a1=x2-x1;
    b1=y2-y1;
    c1=(x1*x1-x2*x2+y1*y1-y2*y2)/2;
    a2=x3-x1;
    b2=y3-y1;
    c2=(x1*x1-x3*x3+y1*y1-y3*y3)/2;
    x=(b1*c2-b2*c1)/(a1*b2-a2*b1);
    y=(c1*a2-c2*a1)/(a1*b2-a2*b1);
}
int main()
{
    double x1,y1,x2,y2,x3,y3,r;
    while(cin>>x1>>y1>>x2>>y2>>x3>>y3)
    {
        A(x1,y1,x2,y2,x3,y3);
        r=sqrt((x1-x)*(x1-x)+(y1-y)*(y1-y));
        if(x>M)
        {
            if(y>M)
                {cout<<"(x - "<<fixed<<setprecision(3)<<x<<")^2 + (y - "<<fixed<<setprecision(3)<<y<<")^2 = "<<fixed<<setprecision(3)<<r<<"^2"<<endl;
                if((x*x+y*y-r*r)>M)
                    cout<<"x^2 + y^2 - "<<fixed<<setprecision(3)<<2*x<<"x - "<<fixed<<setprecision(3)<<2*y<<"y + "<<fixed<<setprecision(3)<<(x*x+y*y-r*r)<<" = 0"<<endl;
                else
                    cout<<"x^2 + y^2 - "<<fixed<<setprecision(3)<<2*x<<"x - "<<fixed<<setprecision(3)<<2*y<<"y - "<<fixed<<setprecision(3)<<abs(x*x+y*y-r*r)<<" = 0"<<endl;}
            else
                {cout<<"(x - "<<fixed<<setprecision(3)<<x<<")^2 + (y + "<<fixed<<setprecision(3)<<abs(y)<<")^2 = "<<fixed<<setprecision(3)<<r<<"^2"<<endl;
                if((x*x+y*y-r*r)>M)
                    cout<<"x^2 + y^2 - "<<fixed<<setprecision(3)<<2*x<<"x + "<<fixed<<setprecision(3)<<abs(2*y)<<"y + "<<fixed<<setprecision(3)<<(x*x+y*y-r*r)<<" = 0"<<endl;
                else
                    cout<<"x^2 + y^2 - "<<fixed<<setprecision(3)<<2*x<<"x + "<<fixed<<setprecision(3)<<abs(2*y)<<"y - "<<fixed<<setprecision(3)<<abs(x*x+y*y-r*r)<<" = 0"<<endl;}
        }
        else
        {
            if(y>M)
                {cout<<"(x + "<<fixed<<setprecision(3)<<abs(x)<<")^2 + (y - "<<fixed<<setprecision(3)<<y<<")^2 = "<<fixed<<setprecision(3)<<r<<"^2"<<endl;
                if((x*x+y*y-r*r)>M)
                    cout<<"x^2 + y^2 + "<<fixed<<setprecision(3)<<abs(2*x)<<"x - "<<fixed<<setprecision(3)<<2*y<<"y + "<<fixed<<setprecision(3)<<(x*x+y*y-r*r)<<" = 0"<<endl;
                else
                    cout<<"x^2 + y^2 + "<<fixed<<setprecision(3)<<abs(2*x)<<"x - "<<fixed<<setprecision(3)<<2*y<<"y - "<<fixed<<setprecision(3)<<abs(x*x+y*y-r*r)<<" = 0"<<endl;}
            else
                {cout<<"(x + "<<fixed<<setprecision(3)<<abs(x)<<")^2 + (y + "<<fixed<<setprecision(3)<<abs(y)<<")^2 = "<<fixed<<setprecision(3)<<r<<"^2"<<endl;
                if((x*x+y*y-r*r)>M)
                    cout<<"x^2 + y^2 + "<<fixed<<setprecision(3)<<abs(2*x)<<"x + "<<fixed<<setprecision(3)<<abs(2*y)<<"y + "<<fixed<<setprecision(3)<<(x*x+y*y-r*r)<<" = 0"<<endl;
                else
                    cout<<"x^2 + y^2 + "<<fixed<<setprecision(3)<<abs(2*x)<<"x + "<<fixed<<setprecision(3)<<abs(2*y)<<"y - "<<fixed<<setprecision(3)<<abs(x*x+y*y-r*r)<<" = 0"<<endl;}
        }
        cout<<endl;
    }
    return 0;
}