Quadlateration Trilateration formula

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SUMMARY

The discussion focuses on the application of trilateration for determining the X, Y, and Z coordinates of an object in 3D space using distances from three known points. The user seeks a more reliable method, specifically a quadlateration formula, to consistently derive coordinates from four points, addressing the limitations of trilateration when points are coplanar. The inquiry highlights the potential for inconclusive results or imaginary numbers when using traditional trilateration methods.

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  • Understanding of trilateration principles
  • Familiarity with 3D coordinate systems
  • Basic knowledge of geometry and spatial reasoning
  • Experience with mathematical programming or algorithms
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insolace
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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.
 
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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?
 

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