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Near-best \(C^2\) quartic spline quasi-interpolants on type-6 tetrahedral partitions of bounded domains

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Abstract

In this paper, we present new quasi-interpolating spline schemes defined on three-dimensional bounded domains, based on trivariate \(C^2\) quartic box splines on type-6 tetrahedral partitions and with approximation order four. Such methods can be used for the reconstruction of gridded volume data. More precisely, we propose near-best quasi-interpolants, i.e. with coefficient functionals obtained by imposing the exactness of the quasi-interpolants on the space of polynomials of total degree three and minimizing an upper bound for their infinity norm. In case of bounded domains the main problem consists in the construction of the coefficient functionals associated with boundary generators (i.e. generators with supports not completely inside the domain), so that the functionals involve data points inside or on the boundary of the domain. We give norm and error estimates and we present some numerical tests, illustrating the approximation properties of the proposed quasi-interpolants, and comparisons with other known spline methods. Some applications with real world volume data are also provided.

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  1. Dipartimento di Matematica, Università di Torino, via C. Alberto, 10, 10123, Turin, Italy

    Catterina Dagnino, Paola Lamberti & Sara Remogna

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  1. Catterina Dagnino
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  2. Paola Lamberti
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  3. Sara Remogna
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Correspondence to Sara Remogna.

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Dagnino, C., Lamberti, P. & Remogna, S. Near-best \(C^2\) quartic spline quasi-interpolants on type-6 tetrahedral partitions of bounded domains. Calcolo 52, 475–494 (2015). https://doi.org/10.1007/s10092-014-0125-9

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