Quadlateration Trilateration formula

[insolace]

I've been running some numbers based on a formula I found here:

http://en.wikipedia.org/wiki/Trilateration

This formula allows you to solve for the X, Y, and Z coordinates of an object in 3d space given the distances to that object from three different known points (spheres). However it occasionally gives an inconclusive answer (or even an imaginary number).

Is there a way to derive the X,Y, and Z coordinates using 4 points that will give a conclusive answer each time? I'm using this in a simple program I am writting and what I really need is a formula that I can plug the numbers into.

 

[dmoravec]

I'm sure there are formulas, but what about when all 4 points are in a plane... then any distances you give would yield 2 points. Is that the type of inclousiveness you are talking about?