Local reparametrization by approximating lines of curvature

Mika Malinen

Mathematics and Computers in Simulation (MATCOM), 2022, vol. 201, issue C, 275-290

Abstract: Although a surface parametrization by orthogonal curvilinear coordinates offers many benefits, ways to construct them are not immediate. The utility of lines of curvature for constructing such representations globally is severely limited by the presence of umbilical points, but a collection of local parametrizations may suffice in applications. Here we develop a practical method to obtain a local reparametrization of a piecewise parametric surface model by consistently accurate lines of curvature coordinates. Our analysis of possible instabilities occurring at an isolated umbilical point indicates that a slight modification of the original patches may suffice to ensure that the configuration of the reparametrized surface always stays regular. We give explicit representations of differential geometric quantities which are particularly useful in treating finite element formulations defined on surfaces.

Keywords: Line of curvature; Orthogonal curvilinear coordinate; Surface; Reparametrization; Umbilical point; Shell (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:201:y:2022:i:c:p:275-290

DOI: 10.1016/j.matcom.2022.05.016

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