Check if point is within radius of another point with Shapely

Question

I've successfully used Shapely with python to check if a point is within one of a set of polygons in a .shp file but now would like to check if a point is within a circle of radius x miles from another point - how can I achieve this with Shapely?

I'd imagine I have to create a circle with radius x miles from my reference point and then check if each of my other points intersects with that new circle - I'm ok with checking the intersection but how do I create a circle with radius x miles given my coordinates are in lat/long?

I read a question that suggests I need to change projections but not sure what this means or how to apply it to my problem: creating circle with radius in metres

My example is in Africa btw, not the US (the above question mentions the US local state plane as a 'reference system' but not sure what that means)...

Answer 1

To effectively use shapely it is important to first project your coordinates into a projected coordinate system that is appropriate to your region, for example, epsg:27700 if you are based in the UK. A good way to do this is using pyproj:

import pyproj as proj

# setup your projections
crs_wgs = proj.Proj(init='epsg:4326') # assuming you're using WGS84 geographic
crs_bng = proj.Proj(init='epsg:27700') # use a locally appropriate projected CRS

# then cast your geographic coordinate pair to the projected system
x, y = proj.transform(crs_wgs, crs_bng, input_lon, input_lat)

You can then go about using your projected coordinate pairs to create circles and test for point within, or you could simply use the distance method. [EDIT: Remember that units are now those of your projected coordinate system.]

from shapely import geometry

# create your two points
point_1 = geometry.Point(x_1, y_1)
point_2 = geometry.Point(x_2, y_2)

# create your circle buffer from one of the points
distance = 1000
circle_buffer = point_1.buffer(distance)

# and you can then check if the other point lies within
if point_2.within(circle_buffer):
    print('point 2 is within the distance buffer of point 1')
# or similarly
if circle_buffer.contains(point_2):
    print('circle buffer contains point 2')

# but a simpler method is to simply check the distance
if point_1.distance(point_2) < distance:
    print('point 1 is within the distance of point 2')