论文标题
平滑游戏
Smoothing Game
论文作者
论文摘要
我们想通过将每个几何元素视为游戏中的玩家来介绍另一种平滑方法：寻求最佳元素质量。换句话说，每个玩家的目标是变得尽可能规律。每个元素的一组策略均由其顶点的所有翻译给出。理想情况下，他想使用与游戏理论中实用程序功能相对应的质量度量来量化这种规律性。每个玩家都知道其他玩家的实用程序功能以及他们的一组策略，这类似于他自己的实用功能和策略。在最简单的情况下，实用程序功能仅取决于规律性。在更复杂的情况下，该效用函数取决于元素大小，曲率甚至差分方程的解决方案。本文是一种可能的游戏理论方法的草图，以进行融化和仍在进行的研究。
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.
