●POJ 1329 Circle Through Three Points

题链：

http://poj.org/problem?id=1329

题解：

计算几何，求过不共线的三点的圆

就是用向量暴力算出来的东西。。。

（设出外心M的坐标，由于$|\vec{MA}|=|\vec{MB}|=|\vec{MC}|$，可以解出M点坐标。）

代码：

#include<cmath>
#include<cstdio>
#include<cstring>
#include<iostream>
using namespace std;
const double eps=1e-8;
int sign(double x){
	if(fabs(x)<=eps) return 0;
	return x<0?-1:1;
}
void Pout(double x){//Print_Out
	if(sign(x)<0) printf(" - ");
	else printf(" + ");
	printf("%.3lf",fabs(x));
}
struct Point{
	double x,y;
	Point(double _x=0,double _y=0):x(_x),y(_y){}
	int Read(){return scanf("%lf%lf",&x,&y);}
};
typedef Point Vector;
Vector operator + (Vector A,Vector B){return Vector(A.x+B.x,A.y+B.y);}
Vector operator - (Point A,Point B){return Vector(A.x-B.x,A.y-B.y);}
double operator ^ (Vector A,Vector B){return A.x*B.y-A.y*B.x;}
double operator * (Vector A,Vector B){return A.x*B.x+A.y*B.y;}
struct Circle{
	Point o; double r;
	Circle(Point _o=Point(),double _r=0):o(_o),r(_r){}
	void PrintSE(){//Print_Standard_Equation
		printf("(x");Pout(-o.x);printf(")^2"); printf(" + ");
		printf("(y");Pout(-o.y);printf(")^2"); printf(" = ");
		printf("%.3lf^2\n",r);
	}
	void PrintNE(){//Print_Normal_Equation
		printf("x^2 + y^2");
		Pout(-2*o.x);printf("x");
		Pout(-2*o.y);printf("y");
		Pout(o.x*o.x+o.y*o.y-r*r);
		printf(" = 0\n\n");
	}
};
double GL(Vector A){//Get_Length
	return sqrt(A*A);
}
Circle GC(Point P1,Point P2,Point P3){//Get_Circle
	Vector B=P2-P1,C=P3-P1; Point P0;
	P0.x=((B*B)*C.y-(C*C)*B.y)/(2*(B^C))+P1.x;
	P0.y=((B*B)*C.x-(C*C)*B.x)/(2*(C^B))+P1.y;
	return Circle(P0,GL(P0-P1));
}
int main(){
	Point A,B,C;
	while(~A.Read()&&~B.Read()&&~C.Read()){
		GC(A,B,C).PrintSE();
		GC(A,B,C).PrintNE();
	}
	return 0;
}