在矩形的联合中找到孔? [英] Find holes in a union of rectangles?

问题描述

我在一个单位正方形(红色)内或周围有许多随机矩形(黑色)，需要提取该单位正方形内未被任何矩形覆盖的所有多边形区域.

I have a number of random rectangles (black) in and around a unit square (red) and need to extract all the polygonal regions inside the unit square that are not covered by any rectangle.

看起来这可以用 Shapely 来完成，当我有矩形(绿色)的并集时，我已经到了这一点，但我不知道如何从单位正方形中减去它并检索一个列表多边形.

It looks like this can be done with Shapely and I've gotten to the point when I have the union of the rectangles (green) but I'm not sure how to subtract that from the unit square and retrieve a list of polygons.

这是我生成测试数据的代码:

Here is my code to generate the test data:

import pylab
import random
from matplotlib import pyplot
from shapely.geometry import Point, Polygon
from shapely.ops import cascaded_union
from descartes import PolygonPatch

def make_square(x, y, size1, size2):
    dx = [size1, -size1, -size1, size1, size1]
    dy = [size2, size2, -size2, -size2, size2]
    return [(x+sx, y+sy) for sx, sy in zip(dx, dy)]


pylab.figure()

square = make_square(0.5, 0.5, 1.0, 1.0)
a, b = zip(*square)
pylab.plot(a, b, 'r-')
polygons = []

for i in xrange(10):
    x = random.random()
    y = random.random()
    s1 = random.random()
    s2 = random.random()

    square = make_square(x, y, s1, s2)
    polygons.append(Polygon(square))
    a, b = zip(*square)
    pylab.plot(a, b, 'k-')

u = cascaded_union(polygons)
patch2b = PolygonPatch(u, fc='#00ff00', ec='#00ff00', alpha=0.5, zorder=2)
pylab.gca().add_patch(patch2b)


pylab.show()

推荐答案

基本上，您希望将合并的"多边形与大正方形的差值化，然后将结果多边形化以获得单独的、单独的多边形.例如:

Basically, you want to take the difference of your "unioned" polygons with the large square and then polygonize the result to get individual, separate polygons. For example:

#-- Get the region not covered by individual squares.
uncovered_region = Polygon(bigsquare).difference(union)

# In some cases, the result will be a single polygon...
if not isinstance(uncovered_region, MultiPolygon):
    uncovered_region = [uncovered_region]

for poly in polygonize(uncovered_region):
    patch = PolygonPatch(poly, fc='purple', alpha=0.5, zorder=2)
    ax.add_patch(patch)

作为一个完整的例子，根据您的情况:

As a full example, based on yours:

import matplotlib.pyplot as plt
import random
from shapely.geometry import Polygon, MultiPolygon
from shapely.ops import cascaded_union, polygonize
from descartes import PolygonPatch

def make_square(x, y, size1, size2):
    dx = [size1, -size1, -size1, size1, size1]
    dy = [size2, size2, -size2, -size2, size2]
    return [(x+sx, y+sy) for sx, sy in zip(dx, dy)]


fig, ax = plt.subplots()

bigsquare = make_square(0.5, 0.5, 1.0, 1.0)
a, b = zip(*bigsquare)
ax.plot(a, b, 'r-')
polygons = []

for i in xrange(10):
    x = random.random()
    y = random.random()
    s1 = random.random()
    s2 = random.random()

    square = make_square(x, y, s1, s2)
    polygons.append(Polygon(square))
    a, b = zip(*square)
    ax.plot(a, b, 'k-')

union = cascaded_union(polygons)
patch2b = PolygonPatch(union, fc='#00ff00', ec='#00ff00', alpha=0.5, zorder=2)
ax.add_patch(patch2b)

#-- Get the region not covered by individual squares.
uncovered_region = Polygon(bigsquare).difference(union)

# In some cases, the result will be a single polygon...
if not isinstance(uncovered_region, MultiPolygon):
    uncovered_region = [uncovered_region]

for poly in polygonize(uncovered_region):
    print poly
    patch = PolygonPatch(poly, fc='purple', alpha=0.5, zorder=2)
    ax.add_patch(patch)

plt.margins(0.05)
plt.show()

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