Convergence properties of a geometric mesh smoothing algorithm

TL;DR

This paper introduces a geometric mesh smoothing algorithm, analyzing its convergence properties and demonstrating effectiveness on planar triangle meshes, with a focus on its dynamical behavior.

Contribution

It presents a new geometric transformation-based smoothing algorithm and provides a convergence analysis, including dynamical methods applicable to various algorithms.

Findings

Proves effectiveness for certain planar triangle meshes

Introduces dynamical methods for analyzing algorithm dynamics

Provides insights into convergence properties of geometric smoothing

Abstract

We describe a simple geometric transformation of triangles which leads to an efficient and effective algorithm to smooth triangle and tetrahedral meshes. Our focus lies on the convergence properties of this algorithm: we prove the effectivity for some planar triangle meshes and further introduce dynamical methods to study the dynamics of the algorithm which may be used for any kind of algorithm based on a geometric transformation.