Playing to Par: Reinforcement Learning for Provably Optimal Quadrilateral Block Decompositions

A quadrilateral block decomposition of a planar domain is judged by whether it is complete, whether its elements are well shaped, and how many of its vertices are irregular, with the discrete Gauss-Bonnet identity enforcing a provable lower bound on total vertex irregularity. The work applies reinforcement learning to reach provably optimal quadrilateral block decompositions.

A quadrilateral block decomposition of a planar domain is judged by whether it is complete, whether its elements are well shaped, and how many of its vertices are irregular. The last has a provable floor: the discrete Gauss-Bonnet identity enforces a lower bound on the total vertex irregularity of a