A Simple Affine-Invariant Spline Interpolation over Triangular Meshes

László L. Stachó
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László L. Stachó: Bolyai Institute, University of Szeged, Aradi Vértanúk tere 1, 6725 Szeged, Hungary

Mathematics, 2022, vol. 10, issue 5, 1-8

Abstract: Given a triangular mesh, we obtain an orthogonality-free analogue of the classical local Zlámal–Ženišek spline procedure with simple explicit affine-invariant formulas in terms of the normalized barycentric coordinates of the mesh triangles. Our input involves first-order data at mesh points, and instead of adjusting normal derivatives at the side middle points, we constructed the elementary splines by adjusting the Fréchet derivatives at three given directions along the edges with the result of bivariate polynomials of degree five. By replacing the real line R with a generic field K , our results admit a natural interpretation with possible independent interest, and the proofs are short enough for graduate courses.

Keywords: polynomial 𝒞 1 -spline; triangular mesh; first-order data; affine invariance over fields (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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