 | J=Σ_i {(Xi-Xo)^2+(Yi-Yo)^2-r^2}^2
∂J/∂Xo=4Σ_i (Xo-Xi){(Xi-Xo)^2+(Yi-Yo)^2-r^2}=0
∂J/∂Yo=4Σ_i (Yo-Yi){(Xi-Xo)^2+(Yi-Yo)^2-r^2}=0
∂J/∂r=4Σ_i -r{(Xi-Xo)^2+(Yi-Yo)^2-r^2}=0
Σ_i (Xo-Xi){(Xi-Xo)^2+(Yi-Yo)^2-r^2}=0
Σ_i (Yo-Yi){(Xi-Xo)^2+(Yi-Yo)^2-r^2}=0
rΣ_i {(Xi-Xo)^2+(Yi-Yo)^2-r^2}=0 , r≠0
Σ_i {(Xi-Xo)^2+(Yi-Yo)^2-r^2}=0
Σ_i (Xo-Xi){(Xi-Xo)^2+(Yi-Yo)^2-r^2}=XoΣ_i {(Xi-Xo)^2+(Yi-Yo)^2-r^2}-Σ_i Xi{(Xi-Xo)^2+(Yi-Yo)^2-r^2}=0
Σ_i Xi{(Xi-Xo)^2+(Yi-Yo)^2-r^2}=0
同様に
Σ_i Yi{(Xi-Xo)^2+(Yi-Yo)^2-r^2}=0
Σ_i {Xi^2-2XoXi+Xo^2+Yi^2-2YoYi+Yo^2-r^2}
= nXo^2+nYo^2-nr^2-(2Σ_i Xi)Xo-(2Σ_i Yi)Yo+Σ_i {Xi^2+Yi^2}=0
同様に…
A=Σ_i Xi, B=Σ_i Yi, C=Σ_i Xi^2, D=Σ_i Yi^2, E=Σ_i Xi^3, F=Σ_i Yi^3,
G=Σ_i XiYi, H=Σ_i Xi^2Yi, I=Σ_i XiYi^2, Xo=x, Yo=y, r=z
n(x^2+y^2-z^2)-2Ax-2By+(C+D)=0
nA(x^2+y^2-z^2)-2Cx-2Gy+(E+I)=0
nB(x^2+y^2-z^2)-2Gx-2Dy+(H+F)=0
-2(C-A^2)x-2(G-AB)y+(E+I-A(C+D))=0
-2(G-AB)x-2(D-B^2)y+(E+I-B(C+D))=0
2[(C-A^2) (G-AB) : (G-AB) (D-B^2)][x y]'= [(E+I-A(C+D)) : (E+I-B(C+D))]
P=2[(C-A^2) (G-AB) : (G-AB) (D-B^2)], Q=[(E+I-A(C+D)) : (E+I-B(C+D))]
[x y]'=P^-1 Q
z= √ {(x^2+y^2)+(-2Ax-2By+C+D)/n}
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