在 Multipolygons 中使用 shapely 创建矩形多边形

Question

我正在寻找一种方法来在多多边形内沿一条线创建一组多边形（rechtangles），并像在绘图中一样均匀地间隔它们。

我尝试生成点并将它们用作多边形的中点，但问题是通过创建均匀间隔的点栅格，除了 180 度之外，它无法以任何其他方向旋转。

example

given 是一个多多边形形状的对象，多边形由宽度和高度以及每个多边形之间的垂直和水平间距定义。 多边形只能放置在多多边形内，不能相交。

额外的问题：也许有一种方法可以将它们沿矢量放置，以便可以旋转线条。

Answer 1

如果您的间距和矩形尺寸以米为单位。请尝试以下操作。

import folium
import geopy
import numpy as np
from shapely.geometry import Polygon, MultiPoint


def get_rectangle_points(coordinates, bearing, width, height):
    start = geopy.Point(coordinates)
    hypotenuse = np.hypot(width/1000, height/1000)
    d = geopy.distance.distance(kilometers=hypotenuse/2)

    opposite_angle = np.degrees(np.arctan(width/height))
    northeast_angle = 0 - opposite_angle
    southwest_angle = 180  - opposite_angle
    northwest_angle = opposite_angle
    southeast_angle = 180 + opposite_angle

    points = []
    for angle in [northeast_angle, northwest_angle, southwest_angle, southeast_angle]:
        point = d.destination(point=start, bearing=angle+bearing)
        coords = (point.latitude, point.longitude)
        #coords = (point.longitude, point.latitude)
        points.append(coords)

    return points

lat_point_list = [50.854457, 52.518172, 50.072651, 48.853033, 50.854457]
lon_point_list = [4.377184, 13.407759, 14.435935, 2.349553, 4.377184]

polygon_geom = Polygon(zip(lon_point_list, lat_point_list))

latmin, lonmin, latmax, lonmax = polygon_geom.bounds

v = 100 #vertical spacing in meters
h = 500 #horizontal spacing in meters
height = 20000
width = 50000

vertical_spacing = geopy.units.degrees(arcminutes=geopy.units.km(meters=2*v+height)) #spacing in degrees
horizontal_spacing = geopy.units.degrees(arcminutes=geopy.units.km(meters=2*h+width)) #spacing in degrees
x, y = np.round(np.meshgrid(np.arange(latmin, latmax, horizontal_spacing), np.arange(lonmin, lonmax, vertical_spacing)),4)
points = MultiPoint(list(zip(x.flatten(),y.flatten())))
valid_points = []
valid_points.extend([i for i in points if polygon_geom.contains(i)])

map_coords = [polygon_geom.centroid.y, polygon_geom.centroid.x]

webmap = folium.Map(map_coords, zoom_start=6)
folium.GeoJson(polygon_geom).add_to(webmap)

for point in valid_points:
    coords = (point.y, point.x)
    rect_coords = get_rectangle_points(coords, 0, width, height) #increase bearing to rotate rectangle    
    folium.Polygon(rect_coords, color='red').add_to(webmap)

webmap.save('webmap.html')