Reverse GPS API

-- Copied from comptuercraft gps api
function trilaterate( A, B, C )
    local a2b = B.vPosition - A.vPosition
    local a2c = C.vPosition - A.vPosition

    if math.abs( a2b:normalize():dot( a2c:normalize() ) ) > 0.999 then
        return nil
    end

    local d = a2b:length()
    local ex = a2b:normalize( )
    local i = ex:dot( a2c )
    local ey = (a2c - (ex * i)):normalize()
    local j = ey:dot( a2c )
    local ez = ex:cross( ey )

    local r1 = A.nDistance
    local r2 = B.nDistance
    local r3 = C.nDistance

    local x = (r1*r1 - r2*r2 + d*d) / (2*d)
    local y = (r1*r1 - r3*r3 - x*x + (x-i)*(x-i) + j*j) / (2*j)

    local result = A.vPosition + (ex * x) + (ey * y)

    local zSquared = r1*r1 - x*x - y*y
    if zSquared > 0 then
        local z = math.sqrt( zSquared )
        local result1 = result + (ez * z)
        local result2 = result - (ez * z)

        local rounded1, rounded2 = result1:round( 0.01 ), result2:round( 0.01 )
        if rounded1.x ~= rounded2.x or rounded1.y ~= rounded2.y or rounded1.z ~= rounded2.z then
            return rounded1, rounded2
        else
            return rounded1
        end
    end
    return result:round( 0.01 )

end

function narrow( p1, p2, fix )
    local dist1 = math.abs( (p1 - fix.vPosition):length() - fix.nDistance )
    local dist2 = math.abs( (p2 - fix.vPosition):length() - fix.nDistance )

    if math.abs(dist1 - dist2) < 0.01 then
        return p1, p2
    elseif dist1 < dist2 then
        return p1:round( 0.01 )
    else
        return p2:round( 0.01 )
    end
end