# Playing to Par: Reinforcement Learning for Provably Optimal Quadrilateral Block Decompositions > Source: > Published: 2026-09-29 11:30:00+00:00 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