Intersect two shapely polygons on the Earth projection

Question

as i know, shapely use only cartesian coordinate system. I have two point on the earth with lat and lon coordinates. I need create buffer with 1km radius around this two points and find polygon, where this buffers intersect.

But construstion

buffer = Point(54.4353,65.87343).buffer(0.001) create simple circle, but in projection on the Earth it becomes ellipse, but i need two real circle with 1 km radius.

I think, i need convert my buffers into new projection and then intersect it, but dont now how correct do it.

score 4 · Answer 1 · answered Jul 04 '17 at 12:22

You need to do what you say. For that, you will need to use a library that handles projections (pyproj is the choice here). There is a similar question in Geodesic buffering in python

import pyproj
from shapely.geometry import MultiPolygon, Polygon, Point
from shapely.ops import transform as sh_transform
from functools import partial

wgs84_globe = pyproj.Proj(proj='latlong', ellps='WGS84')

def point_buff_on_globe(lat, lon, radius):
    #First, you build the Azimuthal Equidistant Projection centered in the 
    # point given by WGS84 lat, lon coordinates
    aeqd = pyproj.Proj(proj='aeqd', ellps='WGS84', datum='WGS84',
                       lat_0=lat, lon_0=lon)
    #You then transform the coordinates of that point in that projection
    project_coords = pyproj.transform(wgs84_globe, aeqd,  lon, lat)
    # Build a shapely point with that coordinates and buffer it in the aeqd projection
    aeqd_buffer = Point(project_coords).buffer(radius) 
    # Transform back to WGS84 each coordinate of the aeqd buffer.
    # Notice the clever use of sh_transform with partial functor, this is 
    # something that I learned here in SO. A plain iteration in the coordinates
    # will do the job too.
    projected_pol = sh_transform(partial(pyproj.transform, aeqd, wgs84_globe),
                          aeqd_buffer)
    return projected_pol

The function point_buff_on_globe will give you a polygon in lat lon that is the result of buffering the given point in the Azimuthal Equidistant Projection centered in that point (the best you can do with your requirements. Two observations:

I don't remember the units of the radius argument. I think is in meters, so if you need a 10 km buffer, you will need to pass it 10e3. But please, check it!
Beware of using this with radius to wide or points that are to far away from each other. Projections work well when the points are near to the point you are centering the projection.

Intersect two shapely polygons on the Earth projection

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