检查点是否位于凸包内

Question

我正在使用 scipy.spatial 包制作一个凸包 http://docs.scipy.org/doc/scipy/reference/generated/scipy.spatial.ConvexHull.html#scipy.spatial.ConvexHull

我试过搜索，但还不知道是否有一种简单的方法可以找到凸包内是否有任何点 (latitude/longitude)。有什么建议吗？

Answer 1

我之前用的方法是用Pathclassmatplotlib。这有一个 contains_point 方法可以做到这一点。还有一个 contains_points 允许您查询点数组。

要使用这个你会做

from scipy.spatial import ConvexHull
from matplotlib.path import Path

hull = ConvexHull( points )

hull_path = Path( points[hull.vertices] )

print hull_path.contains_point((1,2)) # Is (1,2) in the convex hull?

Answer 2

matplotlib Path 方法有效，但仅适用于二维数据。适用于任意维度的通用方法是对船体的小平面使用半空间方程。

import numpy as np
from scipy.spatial import ConvexHull

# Assume points are shape (n, d), and that hull has f facets.
hull = ConvexHull(points)

# A is shape (f, d) and b is shape (f, 1).
A, b = hull.equations[:, :-1], hull.equations[:, -1:]

eps = np.finfo(np.float32).eps

def contained(x):
  # The hull is defined as all points x for which Ax + b <= 0.
  # We compare to a small positive value to account for floating
  # point issues.
  #
  # Assuming x is shape (m, d), output is boolean shape (m,).
  return np.all(np.asarray(x) @ A.T + b.T < eps, axis=1)

# To test one point:
print('Point (2,1) is in the hull?', contained([[2, 1]]))

检查点是否位于凸包内

Check if points lies inside a convex hull

python

scipy

spatial

convex-hull