"Luc H." <nomail@nomail> wrote:
> Hello
>
> I have 3 points in space, and I'd like to get the coordinates of a 4th point.
>
> The known data are
> P1 : <P1.x, P1.y, P1.z>
> P2 : <P2.x, P1.2, P2.z>
> P3 : <P3.x, P1.3, P3.z>
>
> Distance from point 1 to point 4 : D1
> Distance from point 2 to point 4 : D2
> Distance from point 3 to point 4 : D3
>
>
> I tried with some formula (google : "trilateration" and "triangle resolution")
>
> I could easily do this with 2 known points and 2 distances (on a fixed z plan)
> but no way to get something working in 3D ^^
>
> Any advice ?
>
> Regards,
>  Luc.

In 2D, clearly the condition to find (2) points is that D1+D2 >= D12

In 3D, the condition for (again 2, as remarked) points to exist will be more
complicated, involving the angles of the triangle and all three distances.

I'll think about the POV-Ray macro over the weekend. There should be a
non-iterative solution, when one exists.

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