将一个匀称的多边形切割成 N 个同样大小的多边形

问题描述

我有一个匀称的多边形.我想将这些多边形切割成 n 个多边形，它们都有或多或少相同大小的区域.大小相同最好，但近似值也可以.

我尝试使用这两种方法

这是在shape_to_points之后:

这是在points_to_voronoi

之后

然后我们可以对 voronoi 进行三角测量:

I have a Shapely polygon. I want to cut these polygon into n polygons, which all have more-or-less equally sized areas. Equally sized would be best, but an approximation would be okay too.

I have tried to use the two methods described here, which both are a step in the right direction by not what I need. Both don't allow for a target n

I looked into voronoi, with which I am largely unfamiliar. The resulting shapes this analysis gives would be ideal, but it requires points, not a shape as input.

解决方案

This is the best I could manage. It does not result in equal surface area per polygon, but it turned out to work for what I needed. This populates a shape with a specific number of points (if the parameters are kept constant, the number of points will be too). Then the points are converted to a voronoi, which was then turned into triangles.

# Voronoi doesn't work properly with points below (0,0) so set lowest point to (0,0)
shape = affinity.translate(shape, -shape_a.bounds[0], -shape_a.bounds[1])

points = shape_to_points(shape)

vor = points_to_voronoi(points)

triangles = MultiPolygon(triangulate(MultiLineString(vor)))



def shape_to_points(shape, num = 10, smaller_versions = 10):
    points = []

    # Take the shape, shrink it by a factor (first iteration factor=1), and then
    # take points around the contours
    for shrink_factor in range(0,smaller_versions,1):
        # calculate the shrinking factor
        shrink_factor = smaller_versions - shrink_factor
        shrink_factor = shrink_factor / float(smaller_versions)
        # actually shrink - first iteration it remains at 1:1
        smaller_shape = affinity.scale(shape, shrink_factor, shrink_factor)
        # Interpolate numbers around the boundary of the shape
        for i in range(0,int(num*shrink_factor),1):
            i = i / int(num*shrink_factor)
            x,y =  smaller_shape.interpolate(i, normalized=True).xy
            points.append( (x[0],y[0]))

    # add the origin
    x,y = smaller_shape.centroid.xy
    points.append( (x[0], y[0]) ) # near, but usually not add (0,0)

    points = np.array(points)
    return points


def points_to_voronoi(points):
    vor = Voronoi(points)
    vertices = [ x for x in vor.ridge_vertices if -1 not in x]
    # For some reason, some vertices were seen as super, super long. Probably also infinite lines, so take them out
    lines = [ LineString(vor.vertices[x]) for x in vertices if not vor.vertices[x].max() > 50000]
    return MultiLineString(lines)

This is the input shape:

This is after shape_to_points:

This is after points_to_voronoi

And then we can triangulate the voronoi:

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