python: elegant way of finding the GPS coordinates of a circle around a certain GPS location

Question

I have a set of GPS coordinates in decimal notation, and I'm looking for a way to find the coordinates in a circle with variable radius around each location.

Here is an example of what I need. It is a circle with 1km radius around the coordinate 47,11.

What I need is the algorithm for finding the coordinates of the circle, so I can use it in my kml file using a polygon. Ideally for python.

Answer 1

Use the formula for "Destination point given distance and bearing from start point" here:

http://www.movable-type.co.uk/scripts/latlong.html

with your centre point as start point, your radius as distance, and loop over a number of bearings from 0 degrees to 360 degrees. That will give you the points on a circle, and will work at the poles because it uses great circles everywhere.

Answer 2

see also Adding distance to a GPS coordinate for simple relations between lat/lon and short-range distances.

this works:

import math

# inputs
radius = 1000.0 # m - the following code is an approximation that stays reasonably accurate for distances < 100km
centerLat = 30.0 # latitude of circle center, decimal degrees
centerLon = -100.0 # Longitude of circle center, decimal degrees

# parameters
N = 10 # number of discrete sample points to be generated along the circle

# generate points
circlePoints = []
for k in xrange(N):
    # compute
    angle = math.pi*2*k/N
    dx = radius*math.cos(angle)
    dy = radius*math.sin(angle)
    point = {}
    point['lat']=centerLat + (180/math.pi)*(dy/6378137)
    point['lon']=centerLon + (180/math.pi)*(dx/6378137)/math.cos(centerLat*math.pi/180)
    # add to list
    circlePoints.append(point)

print circlePoints

Answer 3

It is a simple trigonometry problem.

Set your coordinate system XOY at your circle centre. Start from y = 0 and find your x value with x = r. Then just rotate your radius around origin by angle a (in radians). You can find the coordinates of your next point on the circle with Xi = r * cos(a), Yi = r * sin(a). Repeat the last 2 * Pi / a times.

That's all.

UPDATE

Taking the comment of @poolie into account, the problem can be solved in the following way (assuming the Earth being the right sphere). Consider a cross section of the Earth with its largest diameter D through our point (call it L). The diameter of 1 km length of our circle then becomes a chord (call it AB) of the Earth cross section circle. So, the length of the arc AB becomes (AB) = D * Theta, where Theta = 2 * sin(|AB| / 2). Further, it is easy to find all other dimensions.