Python+Scipyでランダムに作成した点から凸包を描く

久しぶりに小ネタ。

やること

• 適当に2次元に点群を取得する
• 点群から凸包を計算する
• 点群と凸包をmatplotlibで描画する

ソース

# -*- coding: utf-8 -*-

import numpy as np
import matplotlib.pyplot as plt
import scipy.spatial as ssp


def point_in_hull(point, hull, tolerance=1e-6):
  return all(
    (np.dot(eq[:-1], point) + eq[-1] <= tolerance)
    for eq in hull.equations)


def main():
  N = 100
  points = np.random.rand(N, 2)
  idx_bases = np.random.choice(range(N), 5, replace=False)
  bases = points[idx_bases, :]

  # hull
  hull = ssp.ConvexHull(bases)
  idx = [i for i in range(N) if point_in_hull(points[i, :], hull)]

  # vis
  fig = plt.figure(figsize=(5, 5))
  ax = fig.gca()
  ax.scatter(points[:, 0], points[:, 1], c='r', marker='o')
  ax.scatter(bases[:, 0], bases[:, 1], c='b', marker='o')

  # in hull vertex and borders
  pidx = points[idx, :]
  ax.scatter(pidx[:, 0], pidx[:, 1], c='c', marker='x')
  for simplex in hull.simplices:
    plt.plot(bases[simplex, 0], bases[simplex, 1], "k--")

  ax.axis("off")
  ax.margins(x=0.015, y=0.015)
  ax.set_position([0.05, 0.05, 0.9, 0.9])
  plt.show()
  plt.close()


if __name__ == '__main__':
  main()

実行例