Finding intersection points between 3 spheres

Question

I\'m looking for an algorithm to find the common intersection points between 3 spheres.

Baring a complete algorithm, a thorough/detailed description of the math woul

Answer 1

Basically you need to do this in 3 steps. Let's say you've got three spheres, S1, S2, and S3.

1. C12 is the circle created by the intersection of S1 and S2.
2. C23 is the circle created by the intersection of S2 and S3.
3. P1, P2, are the intersection points of C12 and C13.

The only really hard part in here is the sphere intersection, and thankfully Mathworld has that solved pretty well. In fact, Mathworld also has the solution to the circle intersections.

From this information you should be able to create an algorithm.