Funny this conversation was from 10 years ago.... hahaha.
you only need 2 points if you already know it's a sphere.
All axes that are perpendicular to the surface of a sphere will go through the center of that sphere.
Since all axes go through the center, then any 2 will intersect at the center.
Therefore, you only need 2 such points to define 2 such axes to find the center.
Then you can measure from that intersecting point to either of the 2 points on the surface, and you will have your radius.
However in order to define a sphere from points, you'd need 4 points.
Of course, not just any 4 points, you'd need 4 points that are not all coplanar, or colinear, or coincident.
It won't work if any 3 points lie on a line, or if all 4 are co-planar, or if any of the points are coincident.
2 points define a line
or a point if they are coincident.
3 points define a plane unless they all lie on the same line
or a line if they are all colinear
4 points define a sphere
or a plane if they are all coplanar
of a line if they are all colinear
