coord_system_from_line.py

import numpy as np


def get_coord_bazises(point_1, point_2):
    """"Function defines coordinate system basizes: Oz as vector parrallel to line point_1, point_2
    Ox as random orthogonal vector to Oz, and Oy as vector orthogonal to Oz and Ox.
    """
    vec_z = point_2 - point_1
    vec_z = vec_z / np.linalg.norm(vec_z)

    # non-random value is used to make tests repeatable
    random_point = [10, 10, 10]
    vec_t = random_point - point_1
    vec_x = np.cross(vec_z, vec_t)

    # check that vec_t is not parralel with vec_z
    axis_idx = 0
    while vec_x[0] == 0.0 and vec_x[1] == 0.0 and vec_x[2] == 0.0:
        random_point[axis_idx % 3] += 1
        axis_idx += 1
        vec_t = random_point - point_1
        vec_x = np.cross(vec_z, vec_t)

    vec_x = vec_x / np.linalg.norm(vec_x)

    vec_y = np.cross(vec_z, vec_x)

    return vec_x, vec_y, vec_z