空间四点确定球心坐标(克莱姆法则)

void get_xyz(double x1,double y1,double z1,
             double x2,double y2,double z2,
             double x3,double y3,double z3,
             double x4,double y4,double z4,
             double &x,double &y,double &z)//空间四点确定球心坐标(克莱姆法则)
{
    double a11,a12,a13,a21,a22,a23,a31,a32,a33,b1,b2,b3,d,d1,d2,d3;
    a11=2*(x2-x1); a12=2*(y2-y1); a13=2*(z2-z1);
    a21=2*(x3-x2); a22=2*(y3-y2); a23=2*(z3-z2);
    a31=2*(x4-x3); a32=2*(y4-y3); a33=2*(z4-z3);
    b1=x2*x2-x1*x1+y2*y2-y1*y1+z2*z2-z1*z1;
    b2=x3*x3-x2*x2+y3*y3-y2*y2+z3*z3-z2*z2;
    b3=x4*x4-x3*x3+y4*y4-y3*y3+z4*z4-z3*z3;
    d=a11*a22*a33+a12*a23*a31+a13*a21*a32-a11*a23*a32-a12*a21*a33-a13*a22*a31;
    d1=b1*a22*a33+a12*a23*b3+a13*b2*a32-b1*a23*a32-a12*b2*a33-a13*a22*b3;
    d2=a11*b2*a33+b1*a23*a31+a13*a21*b3-a11*a23*b3-b1*a21*a33-a13*b2*a31;
    d3=a11*a22*b3+a12*b2*a31+b1*a21*a32-a11*b2*a32-a12*a21*b3-b1*a22*a31;
    x=d1/d;
    y=d2/d;
    z=d3/d;
}