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.
Lyche, T., Manni, C., Speleers, H. (2024). A local simplex spline basis for C3 quartic splines on arbitrary triangulations. APPLIED MATHEMATICS AND COMPUTATION, 462 [10.1016/j.amc.2023.128330].
A local simplex spline basis for C3 quartic splines on arbitrary triangulations
Manni C.
;Speleers H.
2024-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.