Theory of calculating sphere centres from surface co-ordinates

[broouk]

I have 35 x, y, z co-ordinates on a sphere surface and I need to calculate the sphere centre point. I am currently using sets of 4 points and determinant equations as shown at http://local.wasp.uwa.edu.au/pbourke~/geometry/spherefrom4/
This method works fine but I want to know the theory behind how the calculation works and also if this is the best method to use. Any help/recommended textbooks/websites would be much appreciated.

[torquil]

Your link didn't work. Here is the correct one:

http://local.wasp.uwa.edu.au/~pbourke/geometry/spherefrom4/

[Tinyboss]

I like how the author of that page requires that no three points be colinear, and that all four not be coplanar.