Smoothing Game

TL;DR

This paper proposes a novel mesh smoothing method based on a game-theoretic approach where geometric elements are treated as players seeking to optimize their regularity through strategic translations.

Contribution

It introduces a new framework modeling mesh smoothing as a game where elements act as players with utility functions, extending traditional smoothing techniques.

Findings

Conceptual framework for game-theoretic mesh smoothing

Potential for incorporating complex quality measures

Ongoing research with promising initial ideas

Abstract

We want to introduce another smoothing approach by treating each geometric element as a player in a game: a quest for the best element quality. In other words, each player has the goal of becoming as regular as possible. The set of strategies for each element is given by all translations of its vertices. Ideally, he would like to quantify this regularity using a quality measure which corresponds to the utility function in game theory. Each player is aware of the other players' utility functions as well as their set of strategies, which is analogous to his own utility function and strategies. In the simplest case, the utility functions only depend on the regularity. In more complicated cases this utility function depends on the element size, the curvature, or even the solution to a differential equation. This article is a sketch of a possible game-theoretical approach to mesh smoothing and still on-going research.