A local tangential lifting differential method for triangular meshes

Jyh-Yang Wu, Mei-Hsiu Chi and Sheng-Gwo Chen

Mathematics and Computers in Simulation (MATCOM), 2010, vol. 80, issue 12, 2386-2402

Abstract: In this note we present a local tangential lifting (LTL) algorithm to compute differential quantities for triangular meshes obtained from regular surfaces. First, we introduce a new notation of the local tangential polygon and lift functions and vector fields on a triangular mesh to the local tangential polygon. Then we use the centroid weights proposed by Chen and Wu [4] to define the discrete gradient of a function on a triangular mesh. We also use our new method to define the discrete Laplacian operator acting on functions on triangular meshes. Higher order differential operators can also be computed successively. Our approach is conceptually simple and easy to compute. Indeed, our LTL method also provides a unified algorithm to estimate the shape operator and curvatures of a triangular mesh and derivatives of functions and vector fields. We also compare three different methods : our method, the least square method and Akima’s method to compute the gradients of functions.

Keywords: Local tangential polygon; Gradient; Laplacian; Curvatures (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:80:y:2010:i:12:p:2386-2402

DOI: 10.1016/j.matcom.2010.06.001

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