Following the process from the 2D World Generator the next step is to select some of the larger drainage basins and make them Endorheic basins. This requires the placement of randomly generated shapes for the bodies of water the rivers will drain into, each body should fit within the bounds of the drainage basin without it being cutoff unnaturally by the perimeter of the basin. In order to do this I plan to project the selected basin onto a plane and then use the same method for 2D feature placement that I used previously.
The projection is pretty straight-forward. I find the center of mass of the selected faces or vertices by averaging the points and rotate that position to the top pole of the sphere, from there I just do a straight projection to a plane that is on XZ axis. After the points are projected I can scale the 2D projection to whatever resolution is needed. Below are some of the larger basins in a data set. The first image in each pair is a projection of the vertices while the second image in each pair puts a point at the center of each hex/pentagon face instead. From these it is easy to compare overlays using the projection as a mask to see what features will fit inside, that feature can then be mapped back to the original vertex or hex that the pixel is representing.
These projections will also be useful later for UV mapping and procedural texture generation. The next thing to do is place some bodies of water.