解析 c语言编写的根据三点得出圆心和半径的数学含义

Question

能否把每一行的数学中的几何意义说明一下，感谢各位前辈，(倒数第二行是求半径，已知数学意义)

Answer 1

/***************
* 已知三点求圆的 get_circle() 函数
* x1, y1为第一个点的坐标，以此类推
* r为求出的半径，x0, y0为圆心坐标
* 调用函数之前应先检查三点是否共线 否则会弹出被零除的错误
***************/
# include <math.h>
void get_circle(double x1, double y1, double x2, double y2, double x3, double y3, double* r, double* x0, double* y0)
{
double m1, n1, m2, n2, a1, b1, a2, b2;
m1 = (x1 + x3) / 2;
n1 = (y1 + y3) / 2;
m2 = (x2 + x3) / 2;
n2 = (y2 + y3) / 2;
a1 = (y3 - y1) / (x3 - x1);
b1 = n1 - a1*m1;
a2 = (y3 - y2) / (x3 - x2);
b2 = n2 - a2*m2;
*x0 = (b2 - b1) / (a1 - a2);
*y0 = a1 * *x0 + b1;
*r = sqrt((x1-x0)*(x1-x0) + (y1-y0)*(y1-y0));
return;
}

希望对你有帮助！

Answer 2

已验证楼上的程序有些小错误，导致无法输出或者结果错误，正确程序是
void get_circle(double x1, double y1, double x2, double y2, double x3, double y3)
{
double m1, n1, m2, n2, a1, b1, a2, b2,x0, y0, r;
m1 = (x1 + x2) / 2;
n1 = (y1 + y2) / 2;
printf("\n\t第一条垂直平分线必过点为(%f,%f)", m1, n1);
m2 = (x2 + x3) / 2;
n2 = (y2 + y3) / 2;
printf("\n\t第二条垂直平分线必过点为(%f,%f)", m2, n2);
a1 = -(x2 - x1) / (y2 - y1);
b1 = n1 - a1 * m1;
printf("\n\t第一条垂直平分线为y=%fx+%f", a1, b1);
a2 = -(x3 - x2) / (y3 - y2);
b2 = n2 - a2 * m2;
printf("\n\t第二条垂直平分线为y=%fx+%f", a2, b2);
x0 = (b2 - b1) / (a1 - a2);
y0 = a1 * x0 + b1;
r = sqrt((x1 - x0) * (x1 - x0) + (y1 - y0) * (y1 - y0));
printf("\n\t%lf %lf %lf", x0, y0, r);
return;
}