A local tangential lifting differential method for triangular meshes. (English) Zbl 1195.65021
Summary: 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 S.-G. Chen and J.-Y. Wu [Comput. Aided Geom. Des. 21, No. 5, 447–458 (2004; Zbl 1069.53502)] 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.
MSC:
| 65D18 | Numerical aspects of computer graphics, image analysis, and computational geometry |
Citations:
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