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Local reparametrization by approximating lines of curvature

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  • Malinen, Mika

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.

Suggested Citation

  • Malinen, Mika, 2022. "Local reparametrization by approximating lines of curvature," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 275-290.
    • Handle: RePEc:eee:matcom:v:201:y:2022:i:c:p:275-290
    DOI: 10.1016/j.matcom.2022.05.016
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