systems of equations solving

hi everyone. im trying to use the arduino to preform a trilateration function by basically finding the intersection of 3 spheres in space. the only way i know how to do this is by using a systems of equations. the problem is i have absolutely no idea how to translate this non-linear math into a code the arduino can preform repetitively with different information each time.

the equation of a sphere is: (x - h)^2 + (y - j)^2 + (z - k)^2 = r^2 so what i need to solve is the systems of: (x - h1)^2 + (y - j1)^2 + (z - k1)^2 = r1^2 (x - h2)^2 + (y - j2)^2 + (z - k2)^2 = r2^2 (x - h2)^2 + (y - j3)^2 + (z - k3)^2 = r3^2

thanks for the help

Hey there,

This is a problem that many academics have tried to address in the past. There is heaps out there on how to do this, so if I where you, I'd read up on how a few different people have tried to do this and try a few of them yourself.

Here is a good start:


Look for "geometric locating process".