The word optimal is used in different ways in mesh generation.  It could mean that the output is in some sense, "the best mesh" or that the algorithm is, by some measure, "the best algorithm".  One might hope that the best algorithm also produces the best mesh, but maybe some tradeoffs are necessary.  In this talk, I will survey several different notions of optimality in mesh generation and explore the different tradeoffs between them.  The bias will be towards Delaunay/Voronoi methods.

Note that I have made some corrections from the version presented at SoCG. Specifically, I had presented the analyssi for why the feature size intergral counts the vertices size in a quality mesh. This was meant to be simple, but it ignores the fact that one must first prove the algorithm produces verties that are spaced according to the feature size. As this may have been confusing, I updated the slides and added a note.