如何为 Voronoi 镶嵌设置固定的外边界？

Question

我画了一个 Voronoi 镶嵌（采矿业的爆炸模式）。我必须绘制 Voronoi 镶嵌的外边界，但我不想要盒子的边界；我想设置固定的外部单元格边界。

• 我得到这个结果：
• 我想要的结果是：

代码：

import xlrd
import operator
import matplotlib.pyplot as plt
from scipy.spatial import Voronoi, voronoi_plot_2d

wb = xlrd.open_workbook('C:/Users/s.gaur/desktop/Collar Coordinates 2620 S3C 5007 P2.xls')
sh1 = wb.sheet_by_name(u'2620-s3c-5007')

x = sh1.col_values(0)
y = sh1.col_values(1)

L = sorted(zip(x,y), key = operator.itemgetter(0))

Point = (L)

vor = Voronoi(Point)

voronoi_plot_2d(vor)
plt.show()

如何将外部边缘边界固定到外部 Voronoi 多边形的边界？

Answer 1

def voronoi_finite_polygons_2d(vor, radius=None):
    """
    Reconstruct infinite voronoi regions in a 2D diagram to finite
    regions.
    Parameters
    ----------
    vor : Voronoi
        Input diagram
    radius : float, optional
        Distance to 'points at infinity'.
    Returns
    -------
    regions : list of tuples
        Indices of vertices in each revised Voronoi regions.
    vertices : list of tuples
        Coordinates for revised Voronoi vertices. Same as coordinates
        of input vertices, with 'points at infinity' appended to the
        end.
    """

    if vor.points.shape[1] != 2:
        raise ValueError("Requires 2D input")

    new_regions = []
    new_vertices = vor.vertices.tolist()

    center = vor.points.mean(axis=0)
    if radius is None:
        radius = vor.points.ptp().max()*2

    # Construct a map containing all ridges for a given point
    all_ridges = {}
    for (p1, p2), (v1, v2) in zip(vor.ridge_points, vor.ridge_vertices):
        all_ridges.setdefault(p1, []).append((p2, v1, v2))
        all_ridges.setdefault(p2, []).append((p1, v1, v2))

    # Reconstruct infinite regions
    for p1, region in enumerate(vor.point_region):
        vertices = vor.regions[region]

        if all(v >= 0 for v in vertices):
            # finite region
            new_regions.append(vertices)
            continue

        # reconstruct a non-finite region
        ridges = all_ridges[p1]
        new_region = [v for v in vertices if v >= 0]

        for p2, v1, v2 in ridges:
            if v2 < 0:
                v1, v2 = v2, v1
            if v1 >= 0:
                # finite ridge: already in the region
                continue

            # Compute the missing endpoint of an infinite ridge

            t = vor.points[p2] - vor.points[p1] # tangent
            t /= np.linalg.norm(t)
            n = np.array([-t[1], t[0]])  # normal

            midpoint = vor.points[[p1, p2]].mean(axis=0)
            direction = np.sign(np.dot(midpoint - center, n)) * n
            far_point = vor.vertices[v2] + direction * radius

            new_region.append(len(new_vertices))
            new_vertices.append(far_point.tolist())

        # sort region counterclockwise
        vs = np.asarray([new_vertices[v] for v in new_region])
        c = vs.mean(axis=0)
        angles = np.arctan2(vs[:,1] - c[1], vs[:,0] - c[0])
        new_region = np.array(new_region)[np.argsort(angles)]

        # finish
        new_regions.append(new_region.tolist())

    return new_regions, np.asarray(new_vertices)


# compute Voronoi tesselation
vor = Voronoi(points)

regions, vertices = voronoi_finite_polygons_2d(vor)

pts = MultiPoint([Point(i) for i in points])
mask = pts.convex_hull
new_vertices = []
for region in regions:
    polygon = vertices[region]
    shape = list(polygon.shape)
    shape[0] += 1
    p = Polygon(np.append(polygon, polygon[0]).reshape(*shape)).intersection(mask)
    poly = np.array(list(zip(p.boundary.coords.xy[0][:-1], p.boundary.coords.xy[1][:-1])))
    new_vertices.append(poly)
    plt.fill(*zip(*poly),"brown", alpha = 0.4, edgecolor = 'black')


plt.plot(x, y, 'ko')
plt.plot(Dx,Dy, 'ko',markerfacecolor = 'red', markersize = 10)
plt.title("Blast 2620 S3C 5009 P1")
plt.show()