Trilaterate algorithm in Python3 with NumPy

trilaterate.py

import numpy as np

def trilaterate(points, distances):
    # ported from https://github.com/gheja/trilateration.js
    # points -> list of np arrays in the form of [[x, y, z], [x, y, z]
    # distances -> np array [r1, r2, r3]
    p1,p2,p3 = points
    r1,r2,r3 = distances
    def norm(v):
        return np.sqrt(np.sum(v**2))
    def dot(v1,v2):
        return np.dot(v1,v2)
    def cross(v1,v2):
        return np.cross(v1,v2)

    ex = (p2-p1) / norm(p2-p1)
    i = dot(ex, p3-p1)
    a = (p3-p1) - ex*i
    ey = a / norm(a)
    ez = cross(ex, ey)
    d = norm(p2-p1)
    j = dot(ey, p3-p1)
    x = (r1**2 - r2**2 + d**2) / (2*d)
    y = (r1**2 - r3**2 + i**2 + j**2) / (2*j) - (i/j) * x
    b = r1**2 - x**2 - y**2

    # floating point math flaw in IEEE 754 standard
    # see https://github.com/gheja/trilateration.js/issues/2
    if (np.abs(b) < 0.0000000001):
        b = 0

    z = np.sqrt(b)
    if np.isnan(z):
        raise Exception('NaN met, cannot solve for z')

    a = p1 + ex*x + ey*y
    p4a = a + ez*z
    p4b = a - ez*z

    return p4a, p4b