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“图”，如以下内容：

区域的颜色并不重要，我要实现的目标是沿Voronoi地区边缘的可变“厚度”（特别是它们看起来像它们看起来像一个更大的圆形斑点在拐角处相遇，在他们的中间更薄）。

我尝试了每个像素的“手动绘画”基于到每个质心的最小距离（每种与颜色相关联）：

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')

或通过scipy.spatial.voronoi我的顶点点，尽管我仍然看不到如何用所需的可变厚度通过它们绘制一条线。

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：

我设法通过侵蚀 +转角平滑（通过评论中建议的中间过滤器）在每个区域上获得了一个令人满意的结果，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)

但是，如您所见，沿该区域的边界/边缘的“拉伸”线不完全存在。还有其他建议吗？

Answer 1

这就是@Johanc的建议。 IMO，它看起来比我在Bezziele曲线的尝试要好得多。 但是，圆形Polygon类似乎存在一个小问题，因为有时在拐角处存在很小的缺陷（例如，下图中的蓝色和紫色之间的缺陷）。

编辑。 ：我修复了圆形的polygon类。

#!/usr/bin/env python
# coding: utf-8
"""
https://stackoverflow.com/questions/72061965/create-voronoi-art-with-rounded-region-edges
"""

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):
    # https://stackoverflow.com/a/66279687/2912349
    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()

Answer 2

诸如bezier多边形“近似”之类的东西可以帮助我吗？

尝试使用bezier曲线：

#!/usr/bin/env python
# coding: utf-8
"""
https://stackoverflow.com/questions/72061965/create-voronoi-art-with-rounded-region-edges
"""

import numpy as np
import matplotlib.pyplot as plt

from scipy.spatial import Voronoi, voronoi_plot_2d
from bezier.curve import Curve # https://bezier.readthedocs.io/en/stable/python/index.html


def get_bezier(polygon, n=10):
    closed_polygon = np.concatenate([polygon, [polygon[0]]])
    # Insert additional points lying along the edges of the polygon;
    # this allows us to use higher order bezier curves.
    augmented_polygon = np.array(augment(closed_polygon, n))
    # The bezier package does not seem to support closed bezier curves;
    # to simulate a closed bezier curve, we triplicate the polygon,
    # and only evaluate the curve on the inner third.
    triplicated_polygon = np.vstack([augmented_polygon, augmented_polygon, augmented_polygon])
    bezier_curve = Curve(triplicated_polygon.T, degree=len(triplicated_polygon)-1)
    return bezier_curve.evaluate_multi(np.linspace(1./3, 2./3, 100)).T


def augment(polygon, n=10):
    new_points = []
    for ii, (x0, y0) in enumerate(polygon[:-1]):
        x1, y1 = polygon[ii+1]
        x = np.linspace(x0, x1, n)
        y = np.linspace(y0, y1, n)
        new_points.extend(list(zip(x[:-1], y[:-1])))
    new_points.append((x1, y1))
    return new_points


if __name__ == '__main__':

    # make up data points
    points = np.random.randint(0, 11, size=(50, 2))

    # 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)
    # voronoi_plot_2d(vor)

    fig, ax = plt.subplots()
    for region in vor.regions:
        if region and (not -1 in region):
            polygon = np.array([vor.vertices[i] for i in region])
            bezier_curve_points = get_bezier(polygon, 40)
            ax.fill(*zip(*bezier_curve_points))

    ax.axis([1, 9, 1, 9])
    ax.axis('off')
    plt.show()