上海到南通自驾要多久:在三维坐标系中,已知在同心圆上的三个点的坐标X、Y、Z,求圆心的坐标X0、Y0、Z0

来源:百度文库 编辑:中科新闻网 时间:2024/05/13 20:01:31
请高手们指教,最好是把公式写出来,谢谢!

这要解方程组:
√[(X1-X0)^2+(Y1-Y0)^2+(Z1-Z0)^2]=√[(X2-X0)^2+(Y2-Y0)^2+(Z2-Z0)^2]

√[(X1-X0)^2+(Y1-Y0)^2+(Z1-Z0)^2]=√[(X3-X0)^2+(Y3-Y0)^2+(Z3-Z0)^2]

p12:=p2.trans-p1.trans;
p13:=p3.trans-p1.trans;
p23:=p3.trans-p2.trans;
a:=Sqrt(p12.x*p12.x+p12.y*p12.y+p12.z*p12.z);
b:=Sqrt(p13.x*p13.x+p13.y*p13.y+p13.z*p13.z);
c:=Sqrt(p23.x*p23.x+p23.y*p23.y+p23.z*p23.z);
s:=(a+b+c)/2;
ai:=1/a;
bi:=1/b;
Radius:=0.25*a*b*c/Sqrt(s*(s-a)*(s-b)*(s-c));
IF a>b THEN
p23:=p13;
p13:=p12;
p12:=p23;
a:=b;
ENDIF
pn12:=p12*ai;
pn13:=p13*bi;
k2:=pn12*pn13*pn12;
kl:=1/Sqrt(k2.x*k2.x+k2.y*k2.y+k2.z*k2.z);
k2:=kl*k2;
d:=Sqrt(Radius*Radius-a*a/4);
p0:=p1;
p0.trans:=p1.trans+0.5*p12+d*k2;
RETURN p0;