Approximating Surfaces in R³ by Meshes with Guaranteed Regularity

2020/01/24 by Joel Hass, Hass, Joel, Maria Trnková +1
Computer Science · Engineering · #3D Shape Modeling and Analysis #53A10 (Primary) #57M50 (Secondary) #57R22 #Advanced Numerical Analysis Techniques #Computational Geometry (cs.CG) #Computational Geometry and Mesh Generation #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Geometric Topology (math.GT)

paper · pdf · doi:10.48550/arxiv.2001.09081

openalex publication_date 2020/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the problem of approximating a surface F in R³ by a high quality mesh, a piecewise-flat triangulated surface whose triangles are as close as possible to equilateral. The MidNormal algorithm generates a triangular mesh that is guaranteed to have angles in the interval [49.1^o, 81.8^o]. As the mesh size e→ 0, the mesh converges pointwise to F through surfaces that are isotopic to F. The GradNormal algorithm gives a piecewise-C¹ approximation of F, with angles in the interval [35.2^o, 101.5^o] as e→ 0. Previously achieved angle bounds were in the interval [30^o, 120^o].

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