在圆上取三个点求圆的位置及圆的半径：

恒二

根据圆的直角坐标方程：
(X-a)*(X-a)+(Z-b)*(Z-b)=R*R
圆心坐标（a,b）
从圆上取三个点求圆心坐标（a,b）和圆半径R
(X1 Z1)(X2 Z2)(X3 Z3)
X1:#511
X2:#512
X3:#513
Z1:#521
Z2:#522
Z3:#523
列方程组：
[#511-a]*[#511-a]+[#521-b]*[#521-b]=R*R
[#512-a]*[#512-a]+[#522-b]*[#522-b]=R*R
[#513-a]*[#513-a]+[#523-b]*[#523-b]=R*R
换算得到以下方程组：
[#511-a]*[#511-a]+[#521-b]*[#521-b]=[#512-a]*[#512-a]+[#522-b]*[#522-b](1)
[#512-a]*[#512-a]+[#522-b]*[#522-b]=[#513-a]*[#513-a]+[#523-b]*[#523-b](2)
化简：
(1):
[#511-a]*[#511-a]+[#521-b]*[#521-b]=[#512-a]*[#512-a]+[#522-b]*[#522-b](1)
#511*#511-2*a*#511+a*a+#521*#521-2*b*#521+b*b=#512*#512-2*a*#512+a*a+#522*#522-2*b*#522+b*b
#511*#511-2*a*#511+#521*#521-2*b*#521=#512*#512-2*a*#512+#522*#522-2*b*#522
#511*#511+#521*#521-2*a*#511-2*b*#521=#512*#512+#522*#522-2*a*#512-2*b*#522
#511*#511+#521*#521-#512*#512-#522*#522=2*a*#511+2*b*#521-2*a*#512-2*b*#522
#511*#511+#521*#521-#512*#512-#522*#522=2*a*#511-2*a*#512+2*b*#521-2*b*#522
#511*#511+#521*#521-#512*#512-#522*#522=2*a*[#511-#512]+2*b*[#521-#522]
#511*#511-#512*#512+#521*#521-#522*#522=2*a*[#511-#512]+2*b*[#521-#522]
[#511*#511-#512*#512+#521*#521-#522*#522]-2*b*[#521-#522]=2*a*[#511-#512]
[[#511*#511-#512*#512+#521*#521-#522*#522]-2*b*[#521-#522]]/[2*[#511-#512]]=a

(2):
[#512-a]*[#512-a]+[#522-b]*[#522-b]=[#513-a]*[#513-a]+[#523-b]*[#523-b](2)
#512*#512-2*a*#512+a*a+#522*#522-2*b*#522+b*b=#513*#513-2*a*#513+a*a+#523*#523-2*b*#523+b*b
#512*#512-2*a*#512+#522*#522-2*b*#522=#513*#513-2*a*#513+#523*#523-2*b*#523
#512*#512+#522*#522-2*a*#512-2*b*#522=#513*#513+#523*#523-2*a*#513-2*b*#523
#512*#512+#522*#522-#513*#513-#523*#523=2*a*#512+2*b*#522-2*a*#513-2*b*#523
#512*#512-#513*#513+#522*#522-#523*#523=2*a*#512+2*b*#522-2*a*#513-2*b*#523
#512*#512-#513*#513+#522*#522-#523*#523=2*a[#512-#513]+2*b[#522-#523]
[#512*#512-#513*#513+#522*#522-#523*#523]-[2*a[#512-#513]]=2*b[#522-#523]
[[#512*#512-#513*#513+#522*#522-#523*#523]-[2*a[#512-#513]]]/[2*[#522-#523]]=b

令：
#531=#511*#511-#512*#512+#521*#521-#522*#522
#532=#512*#512-#513*#513+#522*#522-#523*#523


#533=2*[#522-#523]
#534=2*[#512-#513]/#533
继续化简：
[[#531]-2*b*[#521-#522]]/[2*[#511-#512]]=a
[[#532]-[2*a[#512-#513]]]/[2*[#522-#523]]=b
[[#532]-[a*2*[#512-#513]]]/[2*[#522-#523]]=b

[#532-[2*a[#512-#513]]]/#533=b
[#532-[a*2*[#512-#513]]]/#533=b
#532/#533-a*#534=b

#532/#533-b=[[[#531]-2*b*[#521-#522]]/[2*[#511-#512]]]*#534
#532/#533-b=#534/[2*[#511-#512]]*[[#531]-2*b*[#521-#522]]
#532/#533-#534/[2*[#511-#512]]*[#531]=-2*b*[#521-#522]*#534/[2*[#511-#512]]+b
#532/#533-#534/[2*[#511-#512]]*[#531]=b-2*b*[#521-#522]*#534/[2*[#511-#512]]
b-2*b*[#521-#522]*#534/[2*[#511-#512]]=#532/#533-#534/[2*[#511-#512]]*[#531]
b[1-2*[#521-#522]*#534/[2*[#511-#512]]]=#532/#533-#534/[2*[#511-#512]]*[#531]
b=[#532/#533-#534/[2*[#511-#512]]*[#531]]/[1-2*[#521-#522]*#534/[2*[#511-#512]]]

简化后得到所需要的公式：
b:[#532/#533-#534/[2*[#511-#512]]*[#531]]/[1-2*[#521-#522]*#534/[2*[#511-#512]]](Z 坐标)
a:#536=[#531-2*#535*[#521-#522]]/[#511-#512]/2(X 坐标)
R:#537=SQRT[[#511-#536]*[#511-#536]+[#521-#535]*[#521-#535]](半径)

注意这里的计算不包含刀具球半径，实际应用时要算进去！