Approximating Surfaces in $R^3$ by Meshes with Guaranteed Regularity

Abstract

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 $e\to 0$, 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 $e\to 0$. Previously achieved angle bounds were in the interval $[30^o,120^o]$.

33 pages, 15 figures

References in corpus (1)

• Tiling space and slabs with acute tetrahedra