Python中从3d点到凸包的距离答案

【问题标题】：Distance to convex hull from point in 3d in PythonPython中从3d点到凸包的距离
【发布时间】：2019-08-22 21:58:06
【问题描述】：

我正在寻找 Python 中 3D 中点到 ConvexHull 对象的距离。

我找到了解决 2D 问题的问题： Distance to convexHull 和 Computing the distance to a convex hull

但那些不包含 3D 的解决方案。

import numpy as np
from scipy.spatial import ConvexHull

mat = np.random.rand(100,3)
hull = ConvexHull(mat)
points = np.random.rand(10,3)

有功能就好了

dist(hull,points)

返回从点到凸包的距离列表，对于凸包内部和外部的点具有不同的符号。

【问题讨论】：

Distance to convexHull的可能重复
@meowgoesthedog 我引用了另一个问题并澄清：我需要一个 3d 解决方案，而那个解决方案只提供 2d。

标签： python 3d distance convex-hull

【解决方案1】：

我们可以为此使用PyGEL 3d python 库。

首先，用pip install PyGEL3D安装它

二、代码：

import numpy as np
from scipy.spatial import ConvexHull
from PyGEL3D import gel

mat = np.random.rand(100, 3)
hull = ConvexHull(mat)
points = np.random.rand(10, 3)

def dist(hull, points):
    # Construct PyGEL Manifold from the convex hull
    m = gel.Manifold()
    for s in hull.simplices:
        m.add_face(hull.points[s])

    dist = gel.MeshDistance(m)
    res = []
    for p in points:
        # Get the distance to the point
        # But don't trust its sign, because of possible
        # wrong orientation of mesh face
        d = dist.signed_distance(p)

        # Correct the sign with ray inside test
        if dist.ray_inside_test(p):
            if d > 0:
                d *= -1
        else:
            if d < 0:
                d *= -1
        res.append(d)
    return np.array(res)

print(dist(hull, points))

【讨论】：

【解决方案2】：

from scipy.spatial import distance_matrix, distance
import numpy as np
#point from which distance is to be calculated
reference_point = np.array([1.28442705, 6.75384521e-01, 9.99999997e-07]).reshape(1,3)

#any point/points from convexhull
p = np.array([[1.2844270500,6.75384521e01,9.9999999707], 
[1.2743135700,7.84526169e01,9.9999999707],[1.2844270500,6.7538452101,8.7603122001]]) 

distance_matrix = distance.cdist(reference_point, p, 'euclidean')

【讨论】：

这不是距离度量，其符号取决于参考点是在凸包内部还是外部。此外，“点到凸包的距离”意味着一个数字：最短距离。