获取与 Voronoi 区域相关的点 (scipy.spatial.Voronoi)

问题描述

我正在使用 scipy.spatial.Voronoi 函数.我使用点的随机二维分布(参见下面的 MCVE).

I'm generating a simple 2D Voronoi tessellation, using the scipy.spatial.Voronoi function. I use a random 2D distribution of points (see MCVE below).

我需要一种方法来遍历每个定义的区域(由 scipy.spatial.Voronoi 定义)并获得与其关联的点的坐标(即:所述区域包围的点).

I need a way to go through each defined region (defined by scipy.spatial.Voronoi) and get the coordinates of the point associated to it (ie: the point that said region encloses).

问题是为 N 点定义了 N+1 个区域(多边形)，我不确定这意味着什么.

The issue is that there are N+1 regions (polygons) defined for the N points, and I'm not sure what this means.

这是一个 MCVE，当它到达最后一个区域时会失败:

Here's a MCVE that will fail when it gets to the last region:

from scipy.spatial import Voronoi
import numpy as np

# Generate random data.
N = 10
x = [np.random.random() for i in xrange(N)]
y = [np.random.random() for i in xrange(N)]
points = zip(x, y)

# Obtain Voronoi regions.
vor = Voronoi(points)

# Loop through each defined region/polygon
for i, reg in enumerate(vor.regions):

    print 'Region:', i
    print 'Indices of vertices of Voronoi region:', reg
    print 'Associated point:', points[i], '\n'

我不明白的另一件事是为什么存储了空的 vor.regions ?根据文档:

Another thing I don't understand is why are there empty vor.regions stored? According to the docs:

regions:形成每个 Voronoi 区域的 Voronoi 顶点的索引.-1 表示在 Voronoi 图之外的顶点.

空白区域是什么意思?

添加

我尝试了 point_region 属性，但显然我不明白它是如何工作的.它返回 points 列表范围之外的索引.例如:在上面的 MCVE 中，对于 10 个点的列表，它总是会显示一个索引 10，这显然超出了范围.

I tried the point_region attribute but apparently I don't understand how it works. It returns indexes outside of the range of the points list. For example: in the MCVE above it will always show an index 10 for a list of 10 points, which is clearly out of range.

推荐答案

对于您的第一个问题:

问题是为 N 个点定义了 N+1 个区域(多边形)，我不确定这意味着什么.

这是因为您的 vor.regions 将始终有一个空数组.类似的东西

This is because your vor.regions will always have an empty array. Something like

    [[],[0, 0],[0, 1],[1, 1]]

这与你的第二个问题有关:

This is related to your second question:

我不明白的另一件事是为什么存储了空的 vor.regions?根据文档:区域:形成每个 Voronoi 区域的 Voronoi 顶点的索引.-1 表示 Voronoi 图之外的顶点.空白区域是什么意思?

默认情况下，Voronoi() 使用 QHull 并启用选项 'Qbb Qc Qz Qx' (qhull.org/html/qvoronoi.htm).这会插入一个无穷大点"，用于提高循环输入的精度.因此，作为假"点，它没有区域.如果您想摆脱这种情况，请尝试删除 Qz 选项:

By default Voronoi() uses QHull with options 'Qbb Qc Qz Qx' enabled (qhull.org/html/qvoronoi.htm). This inserts a "point-at-infinity" which is used to improve precision on circular inputs. Therefore, being a "fake" point, it has no region. If you want to get rid of this, try removing the Qz option:

vor = Voronoi(points, qhull_options='Qbb Qc Qx')

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