3D Trilateration in Javascript

Question

I'm trying to do 3D trilateration in Javascript using https://github.com/gheja/trilateration.js and it seems to be working. However, certain simple cases should be yielding solutions but they are not. For example:

var p1 = {x:69, y:0,  r:69, z:0}
var p2 = {x:0,  y:50, r:50, z:0};
var p3 = {x:0,  y:80, r:80, z:0};
trilaterate(p1, p2, p3, false)

This seems like a ridiculously simple example that should yield a solution at x:0,y:0, but instead the function tells me that there is no solution. Am I misunderstanding something about trilateration or is there an error in the function?

Any help would be appreciated.

Answer 1

Yes, it was actually a bug in the library, thanks @logidelic for finding it and @dtudury for tracking it down.

I have fixed it now by zeroing the value if it is near to zero:

b = sqr(p1.r) - sqr(x) - sqr(y);

if (Math.abs(b) < 0.0000000001)
{
    b = 0;
}

z = Math.sqrt(b);

Answer 2

it looks like it's an issue with the repo you found.

specifically if you look at this line https://github.com/gheja/trilateration.js/blob/master/trilateration.js#L111 and log out the values it's using to calculate z = Math.sqrt(sqr(p1.r) - sqr(x) - sqr(y));:

sqr(p1.r): 4761
-sqr(x) - sqr(y): -4761.000000000017
sqr(p1.r) - sqr(x) - sqr(y): -0.000000000017
z: Math.sqrt(-0.000000000017)
therefore: z: NaN

it's just a feature of floats (Is floating point math broken?). If you change the order of your arguments (trilaterate(p1, p3, p2, false)) you get 2 values that are very close to the right answer.

Really your test should be a special case; the intersection of your first 2 spheres is a single point. You might consider forking the repo and testing for just barely touching spheres if this is an expected use case.