Simple trilateration algorithm implementation in JavaScript.

trilateration.js

function getTrilateration(position1, position2, position3) {
    var xa = position1.x;
    var ya = position1.y;
    var xb = position2.x;
    var yb = position2.y;
    var xc = position3.x;
    var yc = position3.y;
    var ra = position1.distance;
    var rb = position2.distance;
    var rc = position3.distance;

    var S = (Math.pow(xc, 2.) - Math.pow(xb, 2.) + Math.pow(yc, 2.) - Math.pow(yb, 2.) + Math.pow(rb, 2.) - Math.pow(rc, 2.)) / 2.0;
    var T = (Math.pow(xa, 2.) - Math.pow(xb, 2.) + Math.pow(ya, 2.) - Math.pow(yb, 2.) + Math.pow(rb, 2.) - Math.pow(ra, 2.)) / 2.0;
    var y = ((T * (xb - xc)) - (S * (xb - xa))) / (((ya - yb) * (xb - xc)) - ((yc - yb) * (xb - xa)));
    var x = ((y * (ya - yb)) - T) / (xb - xa);

    return {
        x: x,
        y: y
    };
}

What style of trilateration is this?

It seems to be suited for non earth based coordinates in perhaps virtual environments?

This is not working. I tested with point (0,0) (0,100) and (100, 0) and the answer it gave (NaN, 99.99645) for distances 107.70, 40.0 and 116.619 where as the point should be (40,100)

The issue is that the code assumes that the 'a' and 'b' points don't have the same 'x' co-ordinate. It's the var x = line ending in '/ (xb - xa)'. They need to be different to avoid a divide by zero. Swap your 2nd and 3rd points and it'll work.

Here is a link back to the author's youtube video with the use case: https://www.youtube.com/watch?v=dMWEl6GBGqk

Just posted another trilateration, based on the Wikipedia derivation. I believe it is easier to follow it, also it is working in 3D space and returns [ 39.996, 99.996, +/-0.53 ] for your example input, @ravisharma1987 (can be configured to return the middle, then it returns [ 39.996, 99.996, 0 ]).
https://github.com/gheja/trilateration.js

Hey guys!

I did an example using p5js.org

Thanks @kdzwinel for the help with the math!