创建具有圆形区域边缘的 Voronoi 艺术

Question

我正在尝试创建一些艺术“情节”，如下所示：

区域的颜色并不重要，我想要实现的是沿着 Voronoi 区域的边缘的可变“厚度”（特别是，它们看起来像一个更大的圆形斑点，在拐角处相交，在拐角处相交处更薄）他们的中间点）。

我尝试根据到每个质心的最小距离“手动绘制”每个像素（每个像素与一种颜色相关联）：

n_centroids = 10
centroids = [(random.randint(0, h), random.randint(0, w)) for _ in range(n_centroids)]
colors = np.array([np.random.choice(range(256), size=3) for _ in range(n_centroids)]) / 255

for x, y in it.product(range(h), range(w)):
    distances = np.sqrt([(x - c[0])**2 + (y - c[1])**2 for c in centroids])
    centroid_i = np.argmin(distances)
    img[x, y] = colors[centroid_i]
    
plt.imshow(img, cmap='gray')

或者通过scipy.spatial.Voronoi，这也给了我顶点，尽管我仍然不知道如何以所需的可变厚度通过它们画一条线。

from scipy.spatial import Voronoi, voronoi_plot_2d

# make up data points
points = [(random.randint(0, 10), random.randint(0, 10)) for _ in range(10)]

# add 4 distant dummy points
points = np.append(points, [[999,999], [-999,999], [999,-999], [-999,-999]], axis = 0)

# compute Voronoi tesselation
vor = Voronoi(points)

# plot
voronoi_plot_2d(vor)

# colorize
for region in vor.regions:
    if not -1 in region:
        polygon = [vor.vertices[i] for i in region]
        plt.fill(*zip(*polygon))

# fix the range of axes
plt.xlim([-2,12]), plt.ylim([-2,12])
plt.show()

编辑：

我成功地通过对每个单独区域的侵蚀+角平滑（通过评论中建议的中值滤波器）获得了一些令人满意的结果，然后将其绘制到黑色背景中。

res = np.zeros((h,w,3))
for color in colors:
    region = (img == color)[:,:,0]
    region = region.astype(np.uint8) * 255
    region = sg.medfilt2d(region, 15) # smooth corners
    # make edges from eroding regions
    region = cv2.erode(region, np.ones((3, 3), np.uint8))
    region = region.astype(bool)
    res[region] = color
    
plt.imshow(res)

但正如您所看到的，沿着区域边界/边缘的“拉伸”线并不完全存在。还有其他建议吗？

Answer 1

这就是@JohanC 建议的样子。IMO，它看起来比我尝试使用贝塞尔曲线要好得多。不过，似乎有一个小问题RoundedPolygon，因为有时在角落处存在小缺陷（例如下图中的蓝色和紫色之间）。

编辑：我修复了 RoundedPolygon 类。

#!/usr/bin/env python
# coding: utf-8
"""
/sf/ask/5044337581/
"""

import numpy as np
import matplotlib.pyplot as plt

from matplotlib import patches, path
from scipy.spatial import Voronoi, voronoi_plot_2d


def shrink(polygon, pad):
    center = np.mean(polygon, axis=0)
    resized = np.zeros_like(polygon)
    for ii, point in enumerate(polygon):
        vector = point - center
        unit_vector = vector / np.linalg.norm(vector)
        resized[ii] = point - pad * unit_vector
    return resized


class RoundedPolygon(patches.PathPatch):
    # /sf/answers/4639578121/
    def __init__(self, xy, pad, **kwargs):
        p = path.Path(*self.__round(xy=xy, pad=pad))
        super().__init__(path=p, **kwargs)

    def __round(self, xy, pad):
        n = len(xy)

        for i in range(0, n):

            x0, x1, x2 = np.atleast_1d(xy[i - 1], xy[i], xy[(i + 1) % n])

            d01, d12 = x1 - x0, x2 - x1
            l01, l12 = np.linalg.norm(d01), np.linalg.norm(d12)
            u01, u12 = d01 / l01, d12 / l12

            x00 = x0 + min(pad, 0.5 * l01) * u01
            x01 = x1 - min(pad, 0.5 * l01) * u01
            x10 = x1 + min(pad, 0.5 * l12) * u12
            x11 = x2 - min(pad, 0.5 * l12) * u12

            if i == 0:
                verts = [x00, x01, x1, x10]
            else:
                verts += [x01, x1, x10]

        codes = [path.Path.MOVETO] + n*[path.Path.LINETO, path.Path.CURVE3, path.Path.CURVE3]

        verts[0] = verts[-1]

        return np.atleast_1d(verts, codes)


if __name__ == '__main__':

    # make up data points
    n = 100
    max_x = 20
    max_y = 10
    points = np.c_[np.random.uniform(0, max_x, size=n),
                   np.random.uniform(0, max_y, size=n)]

    # add 4 distant dummy points
    points = np.append(points, [[2 * max_x, 2 * max_y],
                                [   -max_x, 2 * max_y],
                                [2 * max_x,    -max_y],
                                [   -max_x,    -max_y]], axis = 0)

    # compute Voronoi tesselation
    vor = Voronoi(points)

    fig, ax = plt.subplots(figsize=(max_x, max_y))
    for region in vor.regions:
        if region and (not -1 in region):
            polygon = np.array([vor.vertices[i] for i in region])
            resized = shrink(polygon, 0.15)
            ax.add_patch(RoundedPolygon(resized, 0.2, color=plt.cm.Reds(0.5 + 0.5*np.random.rand())))

    ax.axis([0, max_x, 0, max_y])
    ax.axis('off')
    ax.set_facecolor('black')
    ax.add_artist(ax.patch)
    ax.patch.set_zorder(-1)
    plt.show()