fast_line_math.py

# -*- coding: utf-8 -*-
"""
Created on Thu May 24 17:00:23 2018

@author: sakurai
"""

import numpy as np
import sympy.geometry as sg

# Copied from https://github.com/is0280fp/Side-by-Side-Walking-Model/blob/009779de45ca13efa3ff9fff836ad7aa685d344f/line_math.py#L22
#  点p1と点p2を結ぶ直線上のp1=(x1, y1)から同じ直線上で距離r離れた点を求める
def other_p_1(p1, p2, r):
    center = sg.Point(p1[0], p1[1])
    radius = r

    circle = sg.Circle(center, radius)
    line = sg.Line(sg.Point(p1[0], p1[1]), sg.Point(p2[0], p2[1]))
    return np.array(sg.intersection(circle, line), np.float)


# Numpy implementation
#  点p1と点p2を結ぶ直線上のp1=(x1, y1)から同じ直線上で距離r離れた点を求める
def other_p_2(p1, p2, r):
    v12 = p2 - p1
    distance = np.linalg.norm(v12)
    unit_vector = v12 / distance
    return np.array([p1 - r * unit_vector, p1 + r * unit_vector])


if __name__ == '__main__':
    p1 = np.array([0, 0], np.float64)
    p2 = np.array([2, 2], np.float64)
    r = 1

    center_p_1 = other_p_1(p1, p2, r)
    center_p_2 = other_p_2(p1, p2, r)

    np.testing.assert_allclose(center_p_1, center_p_2)

    # IPython コンソール上で
    # ```
    # timeit other_p_1(p1, p2, r)
    # ```
    # を実行すると `other_p_1(p1, p2, r)` の平均実行時間が計測できます．
    # ↓は2つの実装の実行時間を比較してみた結果です（numpyのほうが4000倍速い）
    # timeit other_p_1(p1, p2, r)
    # 45 ms ± 467 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)
    # timeit other_p_2(p1, p2, r)
    # 7.48 µs ± 123 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)