python - python中用点均匀随机填充磁盘的方法

Question

我有一个应用程序需要一个以准随机方式填充“n”个点的磁盘。我希望这些点有点随机，但在磁盘上仍具有或多或少的规则密度。

我目前的方法是放置一个点，检查它是否在圆盘内，然后检查它是否也离所有其他已保存的点足够远。我的代码如下:

import os
import random
import math

# ------------------------------------------------ #
# geometric constants
center_x = -1188.2
center_y = -576.9
center_z = -3638.3

disk_distance = 2.0*5465.6
disk_diam = 5465.6

# ------------------------------------------------ #

pts_per_disk = 256
closeness_criteria = 200.0
min_closeness_criteria = disk_diam/closeness_criteria

disk_center = [(center_x-disk_distance),center_y,center_z]
pts_in_disk = []
while len(pts_in_disk) < (pts_per_disk):
    potential_pt_x = disk_center[0]
    potential_pt_dy = random.uniform(-disk_diam/2.0, disk_diam/2.0)
    potential_pt_y = disk_center[1]+potential_pt_dy
    potential_pt_dz = random.uniform(-disk_diam/2.0, disk_diam/2.0)
    potential_pt_z = disk_center[2]+potential_pt_dz
    potential_pt_rad = math.sqrt((potential_pt_dy)**2+(potential_pt_dz)**2)

    if potential_pt_rad < (disk_diam/2.0):
        far_enough_away = True
        for pt in pts_in_disk:
            if math.sqrt((potential_pt_x - pt[0])**2+(potential_pt_y - pt[1])**2+(potential_pt_z - pt[2])**2) > min_closeness_criteria:
                pass
            else:
                far_enough_away = False
                break
        if far_enough_away:
            pts_in_disk.append([potential_pt_x,potential_pt_y,potential_pt_z])

outfile_name = "pt_locs_x_lo_"+str(pts_per_disk)+"_pts.txt"
outfile = open(outfile_name,'w')
for pt in pts_in_disk:
    outfile.write(" ".join([("%.5f" % (pt[0]/1000.0)),("%.5f" % (pt[1]/1000.0)),("%.5f" % (pt[2]/1000.0))])+'\n')
outfile.close()

为了获得最均匀的点密度，我所做的基本上是使用另一个脚本迭代运行此脚本，每次连续迭代都会降低“接近度”标准。在某些时候，脚本无法完成，我只是使用上次成功迭代的点数。

所以我的问题相当广泛:有没有更好的方法来做到这一点？我的方法目前还可以，但我的直觉告诉我有更好的方法来生成这样的点域。

输出的图示如下图所示，一个具有高接近度标准，另一个具有“最低发现”接近度标准(我想要的)。

Answer 1

基于 Disk Point Picking from MathWorld 的简单解决方案:

import numpy as np
import matplotlib.pyplot as plt

n = 1000
r = np.random.uniform(low=0, high=1, size=n)  # radius
theta = np.random.uniform(low=0, high=2*np.pi, size=n)  # angle

x = np.sqrt(r) * np.cos(theta)
y = np.sqrt(r) * np.sin(theta)

# for plotting circle line:
a = np.linspace(0, 2*np.pi, 500)
cx,cy = np.cos(a), np.sin(a)

fg, ax = plt.subplots(1, 1)
ax.plot(cx, cy,'-', alpha=.5) # draw unit circle line
ax.plot(x, y, '.') # plot random points
ax.axis('equal')
ax.grid(True)
fg.canvas.draw()
plt.show()

它给出 .

或者，您也可以创建一个规则网格并随机扭曲它:

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.tri as tri


n = 20
tt = np.linspace(-1, 1, n)
xx, yy = np.meshgrid(tt, tt)  # create unit square grid
s_x, s_y  = xx.ravel(), yy.ravel()
ii = np.argwhere(s_x**2 + s_y**2 <= 1).ravel() # mask off unwanted points
x, y = s_x[ii], s_y[ii]
triang = tri.Triangulation(x, y) # create triangluar grid


# distort the grid
g = .5 # distortion factor
rx = x + np.random.uniform(low=-g/n, high=g/n, size=x.shape)
ry = y + np.random.uniform(low=-g/n, high=g/n, size=y.shape)

rtri = tri.Triangulation(rx, ry, triang.triangles)  # distorted grid

# for circle:
a = np.linspace(0, 2*np.pi, 500)
cx,cy = np.cos(a), np.sin(a)


fg, ax = plt.subplots(1, 1)
ax.plot(cx, cy,'k-', alpha=.2) # circle line
ax.triplot(triang, "g-", alpha=.4)
ax.triplot(rtri, 'b-', alpha=.5)
ax.axis('equal')
ax.grid(True)
fg.canvas.draw()
plt.show()

它给出

三角形只是为了可视化。明显的缺点是，根据您选择的网格，无论是在中间还是在边界(如此处所示)，由于网格离散化，或多或少都会有大“孔”。