Approximating Surfaces in R^3 by Meshes with Guaranteed Regularity

01/24/2020

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by   Joel Hass, et al.

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We study the problem of approximating a surface F in R^3 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-C^1 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].