Convergence properties of a geometric mesh smoothing algorithm
For researchers in mesh generation and computational geometry, this work provides theoretical convergence guarantees for a practical smoothing algorithm.
The paper presents a geometric mesh smoothing algorithm and proves its convergence for planar triangle meshes, introducing dynamical methods to analyze such algorithms.
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.