A local simplex spline basis for C3 quartic splines on arbitrary triangulations

Tom Lyche, Carla Manni and Hendrik Speleers

Applied Mathematics and Computation, 2024, vol. 462, issue C

Abstract: We deal with the problem of constructing, representing, and manipulating C3 quartic splines on a given arbitrary triangulation T, where every triangle of T is equipped with the quartic Wang–Shi macro-structure. The resulting C3 quartic spline space has a stable dimension and any function in the space can be locally built via Hermite interpolation on each of the macro-triangles separately, without any geometrical restriction on T. We provide a simplex spline basis for the space of C3 quartics defined on a single macro-triangle which behaves like a B-spline basis within the triangle and like a Bernstein basis for imposing smoothness across the edges of the triangle. The basis functions form a nonnegative partition of unity, inherit recurrence relations and differentiation formulas from the simplex spline construction, and enjoy a Marsden-like identity.

Keywords: C3 quartic splines; B-splines; Simplex splines; Wang–Shi macro-structure; Triangulations (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:462:y:2024:i:c:s009630032300499x

DOI: 10.1016/j.amc.2023.128330

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