math - Sphere center point and radius from 3 points on the surface -

Can it find the center of the surface and its radius by 3 digits on the surface?

I am creating a model for the fragmented brain structure, within three point structure; Head, Tail and Medium

Thank you,

Express center center is the equivalent of three points and with them Craniumy (believe that the three given points are on a great circle).

  (x - xa) ² + (y - or) ² + (z - za) ² = r square (x - xb) ² + (y - yb) ² + (z - jb ) ² = R² (x - xc) ² + (y - yse) ² + (z - zc) ² = r² | XYZ 1 | | Yes yes za 1 | XB Yb JB1 | = 0 | Axc UC Jesse 1 |  

By reducing the equation before the second and the third, you get rid of quadratic

  (2x - Xb - Xa) + (2Y - Yb - Ya) + (2Z - Zb - Za) = 0 (2x - Xc - Xa (+ - 2y - Yc - Ya) + (2Z - Zc - Za) = 0  

You now have 3 There is an easy linear system of 3 equations in the unknown.

Xa = Ya = Za = 0 , and simplify equations

  | XYZ | | XB Yb JB | = 0 | Xc Yc Zc | (2x - Xb) XB + (2Y - Yb) Yb + (2Z - Zb) Zb = 0 (2x - Xc) Xc + (2Y - Yc) Yc + (2Z - Zc) Zc = 0  < / Pre> 
 or 
 
  (Yb Zc - Yc Zb) X + (ZB Xc - Zc Xb) Y + (XB Yc - Xc Yb) Z = 0 2 Xb X + 2 Yb Y + 2 Zb Z = Xb² + Yb² + Zb²2 Xc X + 2 Yc Y + 2 Zc Z = Xc² + Yc² + Zc²  
 
 Again,  R² = X² + Y² + Z² , and do not forget to translate back.