Should we be flipping our triangle clockwise or counterclockwise?
If you're working with a triangular mesh, does it matter? :) Otherwise, just pick a direction. Counter-clockwise would probably be a wise choice. So would clockwise.
In the context of the assignment, counter-clockwise.
I was wondering where I had seen the name Delaunay before — realized he created Delaunay triangulation (https://en.wikipedia.org/wiki/Delaunay_triangulation), the standard method for turning point clouds into triangular meshes. Is this sort of Delaunay remeshing equivalent (or effectively similar to) to just considering the vertices of the mesh as a point cloud and running Delaunay triangulation in terms of the overall characteristics and quality of the mesh? Seems like we have a bit more info (local connectivity) here that makes this superior to just starting with a point cloud, but I'm having trouble understanding to what extent we preserve local connectivity patterns/treat them as accurate during the remeshing process.