3D closed-form triangulation solution

[Lagomorph]

Hi,
I have 3 points in 3D space whose positions are known to me and a third target point, whose position I am trying to find. I can obtain the distance between each of the 3 points and the target point. I can easily get 3 equations to obtain the 3 coordinate variables, but these equations are nonlinear.

Do you guys know how I could get a simple, closed-form solution for each of the coordinate variables defining the target point? I figured that this would be a fairly standard problem, but I'm having finding anything written about it.

Thanks in advance.

 

[D H]

This isn't triangulation. Triangulation involves angles. You want something involving distance ... trilateration. See this wiki article on http://en.wikipedia.org/wiki/Trilateration" .

 

[ravenprp]

Hi there,

It sounds like you are trying to solve the problem of 3D triangulation, which is a common problem in geometry and computer graphics. In order to find a closed-form solution, you will need to use a mathematical method known as the "law of cosines." This law allows you to calculate the angles of a triangle using the lengths of its sides.

To apply this to your problem, you will need to set up a system of equations using the known distances between the three points and the target point. From there, you can use the law of cosines to solve for the angles of the triangle formed by these points. Once you have the angles, you can use basic trigonometry to find the coordinates of the target point.

There are also various software and online tools available to help with 3D triangulation, so you may want to consider using one of those as well. I hope this helps and good luck with your problem!