I'm looking to draw outlines of 2D-closed irregular shapes with curved edges, and then compute both (a) the center of gravity (centroid) of the shape's area, and (b) the center of gravity of the shape's perimeter (i.e. the centroid of, e.g., a wire wrapped tightly around the outside of the shape). I have a late-beginner's level proficiency with Python and Matlab.
(a) and (b) are easy enough given a polygon's vertices: the centroid of a polygon's area is given by the equation here, and the centroid of a polygon's perimeter is just the average of all the line segments' midpoints weighted by the line segments' lengths. I've already written some functions to do this.
The trouble I'm having is getting/approximating those vertices from any of the ways I know how to draw a closed shape with curved edges. The best solution I've come up with so far is to use something like this matplotlib-based script to draw the curvy shape, and then call path.to_polygons(), which converts Path objects to polygons — but does so with surprisingly low resolution, such that the resulting approximation is quite poor (and too poor for my purposes — I'd like to compute those centroids fairly precisely).
So, I'm looking to either (i) find some way to increase the resolution of .to_polygons (about 10-fold), which would be satisfactory for my purposes, or (ii) try some new strategy entirely. One option would be to draw the shapes using something like Adobe Illustrator and then get an approximation of their vertices via some plugin or maybe an image processing toolbox (but I have no clue how to do either of those things). Another would be to draw the shape using some toolbox/library that already has built-in functions for finding the centroids of areas and perimeters (I've seen some having the former, but none with the latter). But I'm sure there are many other options out there that I haven't considered.
