如何使用Shapely获取MultiPolygon内每个点的列表

Question

我有以下几点MultiPolygon：

MULTIPOLYGON (
(
(10.8849956 49.8901705, 10.8849507 49.8902499, 10.884969 49.8902588, 10.8851033 49.8903298, 10.8851183 49.8903132, 10.88512882654868 49.8903054, 10.8851246 49.8903054, 10.8851246 49.8902754, 10.8851546 49.8902754, 10.8851546 49.89028643275958, 10.8853289 49.8901612, 10.885421 49.8901035, 10.8854414638889 49.8900896, 10.8854205 49.8900896, 10.8854205 49.8900596, 10.8854505 49.8900596, 10.8854505 49.89008346226415, 10.885527 49.8900315, 10.885519 49.8899952, 10.8854851 49.8899903, 10.8853164 49.8899957, 10.8852419 49.8899981, 10.8851711 49.8899919, 10.8851165 49.8899814, 10.8850728 49.8899652, 10.8850692 49.8899713, 10.8849925 49.8900275, 10.8850251 49.890083, 10.8850275 49.8901159, 10.8850185 49.8901733, 10.8849956 49.8901705),
(10.8852028 49.8901715, 10.8852328 49.8901715, 10.8852328 49.8902015, 10.8852028 49.8902015, 10.8852028 49.8901715),
(10.8852889 49.8900884, 10.8853146 49.8900884, 10.8853146 49.8901184, 10.8853078 49.8901184, 10.8853078 49.8901337, 10.8852808 49.8901337, 10.8852808 49.8901463, 10.8852508 49.8901463, 10.8852508 49.8901346, 10.8852239 49.8901346, 10.8852239 49.8901046, 10.8852305 49.8901046, 10.8852305 49.8900815, 10.8852589 49.8900815, 10.8852589 49.8900812, 10.8852889 49.8900812, 10.8852889 49.8900884),
(10.8851133 49.890201, 10.8851433 49.890201, 10.8851433 49.890231, 10.8851133 49.890231, 10.8851133 49.890201),
(10.8849849 49.8902202, 10.8850149 49.8902202, 10.8850149 49.8902502, 10.8849849 49.8902502, 10.8849849 49.8902202)
),

(
(10.8852605 49.8901112, 10.8852605 49.8901115, 10.8852539 49.8901115, 10.8852539 49.8901163, 10.8852778 49.8901163, 10.8852778 49.8901112, 10.8852605 49.8901112)
)
)

如何获得包含每个（唯一）点的平面列表？列表项不必是 Shapely Points，它们也可以是元组。我真的不明白如何迭代这个结构。

Answer 1

不幸的是，Shapely 不提供立即从MultiPolygon对象中提取所有点的功能。相反，您必须首先迭代 a 的各个多边形MultiPolygon，然后提取每个 的各个点Polygon。

人们可以想出不同的方法来解决这个问题。例如，如果您知道没有一个多边形有孔，您可以简单地执行以下操作：

points = []
for polygon in multipolygon:
    points.extend(polygon.exterior.coords[:-1])

注意[:-1]防止复制第一个顶点。如果您想要更简洁的语法并且不关心每个多边形有一个重复点，则可以将其删除。
这也可以使用带有两个循环的列表理解写在一行中：

points = [point for polygon in multipolygon for point in polygon.exterior.coords[:-1]]

或在以下人员的帮助下itertools.chain.from_iterable：

from itertools import chain

points = list(chain.from_iterable(polygon.exterior.coords[:-1] for polygon in multipolygon))

通常，当多边形可以包含孔时，例如，我们可以编写以下函数来从内部环中提取坐标：

def to_coords(multipolygon):
    for polygon in multipolygon:
        yield from polygon.exterior.coords[:-1]
        yield from chain.from_iterable(interior.coords[:-1] for interior in polygon.interiors)

用法示例：

mp = MultiPolygon([Polygon([(0, 0), (1, 0), (1, 1), (0, 1)]),
                   Polygon([(2, 0), (3, 0), (3, 1), (2, 1)], 
                           holes=[[(2.25, 0.25), (2.75, 0.25), (2.75, 0.75), (2.25, 0.75)]])])

points = list(to_coords(mp))
# [(0.0, 0.0), (1.0, 0.0), (1.0, 1.0), (0.0, 1.0),
#  (2.0, 0.0), (3.0, 0.0), (3.0, 1.0), (2.0, 1.0), 
#  (2.25, 0.25), (2.75, 0.25), (2.75, 0.75), (2.25, 0.75)]

人们可以更进一步地将其概括为任何输入几何体（Python 3.7）：

from functools import singledispatch
from itertools import chain
from typing import (List, 
                    Tuple,
                    TypeVar)

from shapely.geometry import (GeometryCollection,
                              LinearRing,
                              LineString,
                              Point,
                              Polygon)
from shapely.geometry.base import (BaseGeometry,
                                   BaseMultipartGeometry)

Geometry = TypeVar('Geometry', bound=BaseGeometry)


@singledispatch
def to_coords(geometry: Geometry) -> List[Tuple[float, float]]:
    """Returns a list of unique vertices of a given geometry object."""
    raise NotImplementedError(f"Unsupported Geometry {type(geometry)}")


@to_coords.register
def _(geometry: Point):
    return [(geometry.x, geometry.y)]


@to_coords.register
def _(geometry: LineString):
    return list(geometry.coords)


@to_coords.register
def _(geometry: LinearRing):
    return list(geometry.coords[:-1])


@to_coords.register
def _(geometry: BaseMultipartGeometry):
    return list(set(chain.from_iterable(map(to_coords, geometry))))


@to_coords.register
def _(geometry: Polygon):
    return to_coords(GeometryCollection([geometry.exterior, *geometry.interiors]))

用法示例：

from shapely.geometry import (MultiLineString,
                              MultiPoint,
                              MultiPolygon)

geometry_objects = [Point(0, 0),
                    LineString([(0, 0), (1, 1)]),
                    LinearRing([(0, 0), (1, 0), (1, 1)]),
                    Polygon([(0, 0), (1, 0), (1, 1), (0, 1)], 
                            holes=[[(0.25, 0.25), (0.75, 0.25), (0.75, 0.75), (0.25, 0.75)]]),
                    MultiPoint([(0, 0), (1, 1)]),
                    MultiLineString([LineString([(0, 0), (1, 1)]), LineString([(2, 0), (3, 1)])]),
                    MultiPolygon([Polygon([(0, 0), (1, 0), (1, 1), (0, 1)]),
                                  Polygon([(2, 0), (3, 0), (3, 1), (2, 1)], 
                                          holes=[[(2.25, 0.25), (2.75, 0.25), (2.75, 0.75), (2.25, 0.75)]])]),
                    GeometryCollection([Point(0, 0), LineString([(0, 0), (1, 1)])])]

for geometry in geometry_objects:
    print(f"For {geometry.wkt}\nwe got:\n"
          f"{to_coords(geometry)}\n")

输出：

points = []
for polygon in multipolygon:
    points.extend(polygon.exterior.coords[:-1])