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Construction of C^2 cubic splines on arbitrary triangulations
[article]
2021
arXiv
pre-print
In this paper, we address the problem of constructing C^2 cubic spline functions on a given arbitrary triangulation 𝒯. To this end, we endow every triangle of 𝒯 with a Wang-Shi macro-structure. The C^2 cubic space on such a refined triangulation has a stable dimension and optimal approximation power. Moreover, any spline function in such space can be locally built on each of the macro-triangles independently via Hermite interpolation. We provide a simplex spline basis for the space of C^2
arXiv:2110.07907v1
fatcat:i5qlrbl6czg5fgt3vx36rppusq