Scipy：Voronoi图单元似乎从无处产生

Question

我正在研究Lloyd iteration，这是一种在空间中分布点的迭代算法。在每次迭代中，劳埃德算法都会在其自己的Voronoi单元格中构建每个输入点的Voronoi映射，然后将每个点置于其Voronoi单元格中。

我在Scipy的Voronoi实现中看到了一些奇怪的行为：似乎某些点在某些迭代中突然出现。下图捕获了此行为。如果仔细观察，将会发现两个新点，并且单元格在地图的中心出现了一些迭代：

以下是用于生成Voronoi分布的代码：

from scipy.spatial import Voronoi, voronoi_plot_2d
import matplotlib.pyplot as plt
import numpy as np
import umap, os

def find_centroid(verts):
  '''Return the centroid of a polygon described by `verts`'''
  area = 0
  x = 0
  y = 0
  for i in range(len(verts)-1):
    step = (verts[i, 0] * verts[i+1, 1]) - (verts[i+1, 0] * verts[i, 1])
    area += step
    x += (verts[i, 0] + verts[i+1, 0]) * step
    y += (verts[i, 1] + verts[i+1, 1]) * step
  if area == 0: area += 0.01
  return np.array([  (1/(3*area))*x,  (1/(3*area))*y  ])

def lloyd_iterate(X):
  voronoi = Voronoi(X, qhull_options='Qbb Qc Qx')
  centroids = []
  for i in voronoi.regions:
    region = voronoi.vertices[i + [i[0]]]
    centroids.append( find_centroid( region ) )
  return np.array(centroids)

def plot(X, name):
  '''Plot the Voronoi map of 2D numpy array X'''
  v = Voronoi(X, qhull_options='Qbb Qc Qx')
  plot = voronoi_plot_2d(v, show_vertices=False, line_colors='y', line_alpha=0.5, point_size=5)
  plot.set_figheight(14)
  plot.set_figwidth(20)
  plt.axis([-10, 10, -10, 10])
  if not os.path.exists('plots'): os.makedirs('plots')
  plot.savefig( 'plots/' + str(name) + '.png' )

# get 1000 observations in two dimensions and plot their Voronoi map
X = np.random.rand(1000, 4)
X = umap.UMAP().fit_transform(X)
plot(X, 0)

# run several iterations, plotting each result
for i in range(20):
  X = lloyd_iterate(X)
  plot(X, i)

我在俯视什么，还是这里发生了一些有趣的事情？其他人可以提供的任何见解将不胜感激。