🚀 go-pugleaf

In article <4dgoj8$gli@ionews.io.org>, david hoare <techie@io.org> wrote:
>OK...Here's what should be an easy one - - well not for me...
>
>I am looking for the trigonometric / algebreic  formulae one would use
>to triangulate an unknown position, knowing 3 fixed points and the
>respective distances to the unknown point. (make sence?)
>Oh - in 3 dimensional space. 

As phrased, this is not the standard triangulation problem.  The
standard problem would be "given three points and the relative angles
to an unknown point, find the point."  I'll try to address the problem
as you stated it.

Let:
   X  be the unknown point
   A  be a known point
   B  be a known point
   C  be a known point

given that:
    DA = | X - A |
    DB = | X - B |
    DC = | X - C |

are known, what is X?

Is this the problem?

If so, the first condition restricts the solutions to be on a sphere
with a radius of DA centered at A.  The second condition restricts the
solutions to also be on a sphere of radius DB centered at B so the
intersection of the two spheres is a circle in space.  The angles
between A, B, and the points on the circle can be found by the Cosine
Law.  The last condition restricts the solutions to be on a sphere
with radius DC centered at C.  The intersection of a sphere with a
circle is two points, so there are two possible solutions.

Alternatively, you can transform the program into a set of three
simultaneous quadratic equations and fine a simultaneous quadratic
equation solver.  Try looking at:
    http://www.mcs.net/~jlueders/HP_Web/hp48_math.html

Sorry that I don't have a complete solution for you.

>known central point, AND 3 other fixed points, how to find the lengths
>of the lines required to meet at that first point, in 3D.

Can't you just use the Pythagorean theorem three times to find the
distances?
    DA = sqrt((X-A).(X-A))
    DB = sqrt((X-B).(X-B))
    DC = sqrt((X-C).(X-C))

>It's for a program I'm writing, and it's been a while since I've done
>this sort of thing - - my math has left me!
>Any Help would be GREATLY appreciated!!
>
>Thanks,
>David.
>techie@io.org
>
>