Generate polygon shaped as a circle if projected using Web Mercator, in Python?

Question

I need to solve problem very similar to Generating polygon representing rough 100km circle around latitude/longitude point using Python? but subtly different.

I need a shape that will be a circle once projected in Web Mercator - not in reality.

Working answer ( https://gis.stackexchange.com/a/268251/45061 ) is not generalizable, as it relies on https://github.com/jwass/geog that will not allow doing what I am trying to do.

Answer 1

Despite it being an abomination in so many ways, Pseudo/Spherical (Web) Mercator is a projection after all, so basic math on the Cartesian plane applies:

import math

R = 6378137.0


def LL2SM(ll):
  return [math.radians(ll[0]) * R, math.log(math.tan(math.pi / 4 + math.radians(ll[1]) / 2)) * R]

def SM2LL(xy):
  return [math.degrees(xy[0] / R), math.degrees(2 * math.atan(math.exp(xy[1] / R)) - math.pi / 2.0)]

def VERTEX(cxy, a, r):
  return [cxy[0] + r * math.cos(math.radians(a)), cxy[1] + r * math.sin(math.radians(a))]


def main():
  vertices = 32

  center = [13.0, 52.0]
  radius = 100000

  circle = []

  _angle = 360.0/vertices
  for vertex in range(0, vertices):
    sm = LL2SM(center)
    cv = VERTEX(sm, vertex*_angle, radius)
    ll = SM2LL(cv)

    circle.append(ll)

  # do sth. with your circle
  print(circle)


if __name__ == "__main__":
    main()

This POC script

1. transforms a pair of Longitude/Latitude (center) into EPSG:3857 coordinates (LL2SM())
2. generates vertices amount of points on a circle with a given radius (in meter) around center, using its parametric equations (VERTEX())
3. transforms each vertex' coordinates back to Longitude/Latitude (SM2LL())

circle will then hold coordinate arrays ([Longitude, Latitude]) which, when transformed again to EPSG:3857, will form a circle around center.

Obviously, you can skip transforming back to Longitude/Latitude if you want.

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You haven't specified any software environment other than Python, so I leave translating this into the framework of your choice to you; this includes generating an actual Polygon, for which there likely are built-in functions.

Edit:

...
# do sth. with your circle
wkt_polygon = ''.join(['POLYGON((', ','.join([' '.join(map(str, ll)) for ll in circle + [circle[0]]]), '))'])

print(wkt_polygon)

will output a Polygon as valid Well Known Text representation.