在矩形的联合中找到孔？

我在单位正方形（红色）内和周围有许多随机矩形（黑色），需要提取单位正方形内未被任何矩形覆盖的所有多边形区域。

看起来这可以用 Shapely 来完成，当我得到矩形（绿色）的并集时，我已经达到了这一点，但我不知道如何从单位正方形中减去它并检索多边形列表。

这是我生成测试数据的代码：

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()

基本上，您想要获取“联合”多边形与大正方形的差异，然后对结果进行多边形化以获得单独的、单独的多边形。例如：

#-- 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，基于你的：

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()