着色Voronoi图 [英] Colorize Voronoi Diagram

问题描述

我正在尝试为使用

I'm trying to colorize a Voronoi Diagram created using scipy.spatial.Voronoi. Here's my code:

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

# make up data points
points = np.random.rand(15,2)

# 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))

plt.show()

结果图像:

如您所见，图像边框处的某些Voronoi区域未着色.这是因为针对这些区域的Voronoi顶点的某些索引被设置为-1，即，对于Voronoi图之外的那些顶点.根据文档:

As you can see some of the Voronoi regions at the border of the image are not colored. That is because some indices to the Voronoi vertices for these regions are set to -1, i.e., for those vertices outside the Voronoi diagram. According to the docs:

区域:(整数列表列表，形状(nregions，*))形成每个Voronoi区域的Voronoi顶点的索引. -1表示Voronoi图之外的顶点.

regions: (list of list of ints, shape (nregions, *)) Indices of the Voronoi vertices forming each Voronoi region. -1 indicates vertex outside the Voronoi diagram.

为了给这些区域着色，我尝试从多边形中删除这些外部"顶点，但这没有用.我认为，我需要在图像区域的边界处填充一些点，但似乎无法弄清楚如何合理地实现这一点.

In order to colorize these regions as well, I've tried to just remove these "outside" vertices from the polygon, but that didn't work. I think, I need to fill in some points at the border of the image region, but I can't seem to figure out how to achieve this reasonably.

任何人都可以帮忙吗?

推荐答案

Voronoi数据结构包含所有必要的信息，以构造无穷远点"的位置. Qhull还将它们简单地报告为-1索引，因此Scipy不会为您计算它们.

The Voronoi data structure contains all the necessary information to construct positions for the "points at infinity". Qhull also reports them simply as -1 indices, so Scipy doesn't compute them for you.

https://gist.github.com/pv/8036995

http://nbviewer.ipython.org/gist/pv/8037100

import numpy as np
import matplotlib.pyplot as plt
from scipy.spatial import Voronoi

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()

    # 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)

# make up data points
np.random.seed(1234)
points = np.random.rand(15, 2)

# compute Voronoi tesselation
vor = Voronoi(points)

# plot
regions, vertices = voronoi_finite_polygons_2d(vor)
print "--"
print regions
print "--"
print vertices

# colorize
for region in regions:
    polygon = vertices[region]
    plt.fill(*zip(*polygon), alpha=0.4)

plt.plot(points[:,0], points[:,1], 'ko')
plt.xlim(vor.min_bound[0] - 0.1, vor.max_bound[0] + 0.1)
plt.ylim(vor.min_bound[1] - 0.1, vor.max_bound[1] + 0.1)

plt.show()

这篇关于着色Voronoi图的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！