Shapely 多边形与 Matplotlib 楔形的交集

Question

在这种情况下，我正在绘制 matplotlib.patches.Wedge objects and also buffered shapely.geometry.LineString 个对象。我需要计算这两个对象的重叠区域。但是，Wedge 是一个 matplotlib.wedges 对象，不能与 Shapely 的 .intersection() 方法一起使用。

我该怎么做？这是一些代码：

from shapely.geometry import LineString
from matplotlib.patches import Wedge
from matplotlib import pyplot as plt
from descartes.patch import PolygonPatch

width = 5
radius = 1
rich = 1

circle_patch = Wedge((0, 0), radius+3,
                     0, 360, 3)

fig, ax = plt.subplots()

ax.add_patch(circle_patch)

ax.plot(0, 0, 'xr')
plt.autoscale()

coords = [
    [0, 0],
    [0, 1],
    [0, 2],
    [1, 2],
    [2, 2]
]

stick = LineString(coords)

stick_patch = PolygonPatch(stick.buffer(0.5))

ax.add_patch(stick_patch)

x, y = stick.xy
ax.plot(x, y, 'r-', zorder=1)

plt.show()

area = stick.buffer(0.5).intersection(circle_patch).area

P.S。必须是环状，不能是圆形

Answer 1

想通了。 matplotlib.patches class 的 ._path.vertices 成员为您提供楔形对象的坐标数组，然后您可以将其与 Shapely 的 LinearRing class 一起使用像这样创建一个 Shapely 对象：

from shapely.geometry import LineString, LinearRing
from matplotlib.patches import Wedge

width = 5
radius = 1
rich = 1

circle_patch = Wedge((0, 0), radius,
                     0, 360,)

ring_coords = circle_patch._path.vertices
ring_coords = ring_coords[(ring_coords[:, 0] != 0) & (ring_coords[:, 1] != 0)]

ring = LinearRing(ring_coords)

但是它确实需要对坐标数组进行操作，我认为这不是最可靠的方法，但它对我有用。此外，环并不完全平滑，但我相信可以使用某些或其他 Numpy 或 Scipy 函数对坐标数组进行一些平滑处理。

编辑： 要创建单个楔形线，必须删除楔形的 width 成员。然而，这可以在以后使用 Shapely 的 buffer() 函数重新合并。

Answer 2

最简单的解决方案是不使用 Matplotlib 补丁并首先使用 Shapely 构建 wedge-polygon：

import matplotlib.pyplot as plt
from descartes.patch import PolygonPatch
from shapely.geometry import LineString, Point

outer_circle = Point(0, 0).buffer(4)
inner_circle = Point(0, 0).buffer(1)
wedge = outer_circle.difference(inner_circle)

stick = LineString([(0, 0), (0, 2), (2, 2)])
buffered_stick = stick.buffer(0.5)

intersection = buffered_stick.intersection(wedge)

wedge_patch = PolygonPatch(wedge)
stick_patch = PolygonPatch(buffered_stick, alpha=0.5, hatch='/')
intersection_patch = PolygonPatch(intersection, alpha=0.5, hatch='.')

fig, ax = plt.subplots()
ax.add_patch(wedge_patch)
ax.add_patch(stick_patch)
ax.add_patch(intersection_patch)
plt.autoscale()

如果出于某种原因，这是不可能的，并且您必须使用 Matplotlib 的 Wedge，那么我可以想出两种方法来获得它与 Shapely 多边形的交叉区域。在这两个中，我首先将补丁转换为形状多边形。您仅使用 Matplotlib 获得交叉区域。

1) 使用 .get_path() method on the Matplotlib's patch from which you can extract vertices as a NumPy array and convert it to a Shapely polygon using asPolygon:

import matplotlib.pyplot as plt
from descartes.patch import PolygonPatch
from matplotlib.patches import Wedge
from shapely.geometry import asPolygon, LineString

wedge_patch = Wedge(center=(0, 0), 
                    r=4,
                    theta1=0, 
                    theta2=360, 
                    width=3)
stick = LineString([(0, 0), (0, 2), (2, 2)])
buffered_stick = stick.buffer(0.5)

wedge_path = wedge_patch.get_path()
wedge_polygon = asPolygon(wedge_path.vertices).buffer(0)
intersection = buffered_stick.intersection(wedge_polygon)

stick_patch = PolygonPatch(buffered_stick, alpha=0.5, hatch='/')
intersection_patch = PolygonPatch(intersection, alpha=0.5, hatch='.')

fig, ax = plt.subplots()
ax.add_patch(wedge_patch)
ax.add_patch(stick_patch)
ax.add_patch(intersection_patch)
plt.autoscale()

请注意我应用于楔形多边形的 buffer(0)。这是 Shapely 中从无效多边形中创建有效多边形的常用技巧。在中，从 ring_coords.

中删除零时，您会做类似的事情

2) 通过访问 Wedge 属性：center、r 和 width，并使用它们重新创建多边形：

import matplotlib.pyplot as plt
from descartes.patch import PolygonPatch
from matplotlib.patches import Wedge
from shapely.geometry import LineString, Point

wedge_patch = Wedge(center=(0, 0), 
                    r=4,
                    theta1=0, 
                    theta2=360, 
                    width=3)
stick = LineString([(0, 0), (0, 2), (2, 2)])
buffered_stick = stick.buffer(0.5)

outer_circle = Point(wedge_patch.center).buffer(wedge_patch.r)
inner_circle = Point(wedge_patch.center).buffer(wedge_patch.r - wedge_patch.width)
wedge_polygon = outer_circle.difference(inner_circle)
intersection = buffered_stick.intersection(wedge_polygon)

stick_patch = PolygonPatch(buffered_stick, alpha=0.5, hatch='/')
intersection_patch = PolygonPatch(intersection, alpha=0.5, hatch='.')

fig, ax = plt.subplots()
ax.add_patch(wedge_patch)
ax.add_patch(stick_patch)
ax.add_patch(intersection_patch)
plt.autoscale()

所有解决方案都提供相同的视觉输出。

并且所有方法给出大致相同的区域：

>>> intersection.area
3.3774012986988513  # 1st case
3.3823210603713694  # 2nd case and the original without Matplotlib

Shapely 多边形与 Matplotlib 楔形的交集

Intersection of a Shapely polygon with a Matplotlib wedge

python

intersection

matplotlib

shapely