Convergence properties of a geometric mesh smoothing algorithm

2014/11/14 by Dimitris Vartziotis, Vartziotis, Dimitris, Doris Bohnet +1 · 1 citation
Computer Science · Engineering · #3D Shape Modeling and Analysis #Computational Geometry and Mesh Generation #Computer Graphics and Visualization Techniques #FOS: Mathematics #Metric Geometry (math.MG) #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1411.3869

openalex publication_date 2014/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Algebraic Mesh Quality Metrics

Cited by

• Curvature transformation

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