Just wanted to know what is the best algorithm (in terms of speed and accuracy) to determine the intersection of N spheres (in 3D). With intersection I mean the following; in 2D and in the case of two overlapping circles of finite radius R1 and R2, they will have two points P1 and P2 in common in the case that distance between centers C1 and C2 is smaller than R1+R2, so that if we trace lines starting from one of the centers to this two points, we get an isosceles triangle. If we add a new circle at C3 with radius R3, so that d31 (distance between sphere 3 and 1) is smaller thant R1+R3 and d32 smaller than R2 and R3, we will have 2 new points of the same "kind", let's call them P3 and P4. Now if we assume that P1 lies somewhere inside the three circles, the other points P2, P3 and P4 lie "outside". Using C1, C2 and C3, and P2, P3, and P4 we could easily calculate the surrounding line from the intersection between the three spheres. These "outside" points P2, P3 and P4 I call them vertices.
Now let's say we have N spheres and we move in the 3D world, how to fastly calculate these vertices?