Centroid of a polygon made of geographic coordinates

[Anonymous]

Hi,

Please suggest an algorithm for determining the centroid of a polygon made of geographic coordinates?

Position {lat, lon}
Polygon = vector of Positions

Can your solution for a finding the intersection of of two geodesics (based on a gnomonic projection) be utilised to find the centroid of a triangle made of geodesics? If so, I have an algorithm in my mind that is based on decomposing the polygon into triangles like so:
1. Connect the first vertex with all others (except last) to form a fan of triangles.
2. Compute the centroid of these triangles. The centroids of these triangles represent another polygon
3. Repeat the process this the polygon is thus reduced to a triangle. The centroid of this triangle is a centroid of the original polygon

What do you think about this method?

Any suggestions or corrections are appreciated. Thanks

VG

[Charles Karney]

There are three problems with your suggested scheme:

The gnomonic projection is a bad starting point because it badly distorts areas. An equal area projection, e.g., Albers conic, is a better choice. But understand that this would only "work" if your polygon had a relatively small extent, say 100 km or less.

Your proposed triangulation scheme then has the problem (a) that it will be slow, O(n^2), I think, and (b) that it's wrong since you don't weight the vertices of the succeeding triangles according to the area of their parents.

I recommend using the formula for the centroid of a polygon (Google this!).

[Anonymous]

Thanks for your suggestions. I'll look into Albers Conic projections.