Python 检查地理点是在多边形内部还是外部
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Check if geo-point is inside or outside of polygon
提问by Federico Gentile
I am using python and I have defined the latitudes and longitudes (in degrees) of a polygon on the map.
My goal is to check if a generic point Pof coordinates x,yfalls within such polygon. I would like therefore to have a function that allows me to check such condition and return Trueor Falseif the point is inside or outside the polygon.
我正在使用 python 并且我已经定义了地图上多边形的纬度和经度（以度为单位）。我的目标是检查通用P坐标点是否x,y落在这样的多边形内。因此，我希望有一个函数可以让我检查这种条件并返回，True或者False该点是否在多边形内部或外部。
In this example the point is outside so the result would be False
在这个例子中，点在外面，所以结果是 False
Question: Is there a library/package that allows to reach my goal? if yes which one do you recommend? would you be able to give a small example on how to use it?
问题：是否有一个库/包可以实现我的目标？如果是，你推荐哪一个？你能举一个关于如何使用它的小例子吗？
Here is the code I have written so far:
这是我到目前为止编写的代码：
import numpy as np
# Define vertices of polygon (lat/lon)
v0 = [7.5, -2.5]
v1 = [2, 3.5]
v2 = [-2, 4]
v3 = [-5.5, -4]
v4 = [0, -10]
lats_vect = np.array([v0[0],v1[0],v2[0],v3[0],v4[0]])
lons_vect = np.array([v0[1],v1[1],v2[1],v3[1],v4[1]])
# Point of interest P
x, y = -6, 5 # x = Lat, y = Lon
## START MODIFYING FROM HERE; DO NOT MODIFY POLYGON VERTICES AND DATA TYPE
# Check if point of interest falls within polygon boundaries
# If yes, return True
# If no, return False
In order to plot the polygon and the point of interest I used cartopy and I wrote the following lines of code:
为了绘制多边形和兴趣点，我使用了 cartopy 并编写了以下代码行：
import cartopy.crs as ccrs
import matplotlib.pyplot as plt
ax = plt.axes(projection=ccrs.PlateCarree())
ax.stock_img()
# Append first vertex to end of vector to close polygon when plotting
lats_vect = np.append(lats_vect, lats_vect[0])
lons_vect = np.append(lons_vect, lons_vect[0])
plt.plot([lons_vect[0:-1], lons_vect[1:]], [lats_vect[0:-1], lats_vect[1:]],
color='black', linewidth=1,
transform=ccrs.Geodetic(),
)
plt.plot(y, x,
'*', # marker shape
color='blue', # marker colour
markersize=8 # marker size
)
plt.show()
Note:
注意：
- points are connected to each other by Great Circles!
- I have researched in the internt and I ended up finding some similar questions like this onebut I had no success since they all use of
.shpfiles which I do not have.
- 点通过大圆圈相互连接！
- 我研究的Internt的，我最终找到了一些类似的问题像这样的，但我没有成功，因为它们都使用的
.shp是我没有的文件。
回答by Federico Gentile
Here is a possible solution to my problem.
这是我的问题的可能解决方案。
- Geographical coordinates must be stored properly. Example
np.array([[Lon_A, Lat_A], [Lon_B, Lat_B], [Lon_C, Lat_C]]) - Create the polygon
- Create the point to be tested
- Use
polygon.contains(point)to test if point is inside (True) or outside (False) the polygon.
- 必须正确存储地理坐标。例子
np.array([[Lon_A, Lat_A], [Lon_B, Lat_B], [Lon_C, Lat_C]]) - 创建多边形
- 创建要测试的点
- 使用
polygon.contains(point)如果点在内部测试（True）或外部（False）的多边形。
Here is the missing part of the code:
这是代码的缺失部分：
from shapely.geometry import Point
from shapely.geometry.polygon import Polygon
lons_lats_vect = np.column_stack((lons_vect, lats_vect)) # Reshape coordinates
polygon = Polygon(lons_lats_vect) # create polygon
point = Point(y,x) # create point
print(polygon.contains(point)) # check if polygon contains point
print(point.within(polygon)) # check if a point is in the polygon
Note: the polygon does not take into account great cycles apparently, therefore it is necessary to split the edges into many segments thus increasing the number of vertices.
注意：多边形显然没有考虑大循环，因此需要将边分成许多段从而增加顶点数。
Special case: If point lies on borders of Polygon特殊情况：如果点位于多边形的边界上
E.g. print(Polygon([(0, 0), (1, 0), (1, 1)]).contains(Point(0, 0)))will fail
例如print(Polygon([(0, 0), (1, 0), (1, 1)]).contains(Point(0, 0)))会失败
So one can use
所以可以使用
print(polygon.touches(point)) # check if point lies on border of polygon
回答by lfvv
Another way to do it is by using the even-odd algorithm explained in this link https://wrf.ecse.rpi.edu//Research/Short_Notes/pnpoly.htmlThe python code is given in wikipedia https://en.wikipedia.org/wiki/Even–odd_rule
另一种方法是使用此链接中解释的奇偶算法https://wrf.ecse.rpi.edu//Research/Short_Notes/pnpoly.html维基百科https://en 中给出了 python 代码。 wikipedia.org/wiki/Even–odd_rule
Folks, just remember that the ORDER OF POINTS that make the polygon MATTER! I mean, different order results in different polygons.
伙计们，请记住使多边形变得重要的点顺序！我的意思是，不同的顺序会导致不同的多边形。
