Titlebook: Geometric Challenges in Isogeometric Analysis; Carla Manni,Hendrik Speleers Conference proceedings 2022 The Editor(s) (if applicable) and

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Scattered Data Approximation by LR B-Spline Surfaces: A Study on Refinement Strategies for Efficiens in some areas and is largely smooth elsewhere, LR B-splines allow the spatial distribution of degrees of freedom to follow the variations of the data set. An LRB surface approximating a data set is refined in areas where the accuracy does not meet a required tolerance. In this paper we address, in

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Completeness Characterization of Type-I Box Splines,smoothness properties. For any given type-I box spline, of specific maximum degree and order of global smoothness, our results allow to identify the local linear subspace of polynomials spanned by the box spline translates. We use the global super-smoothness properties of box splines as well as the

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THU-Splines: Highly Localized Refinement on Smooth Unstructured Splines,ion, an unstructured quadrilateral mesh is taken as the input control mesh, where the degenerated-patch method [.] is adopted in irregular regions to define .-continuous bicubic splines, whereas regular regions only involve . B-splines. Irregular regions are then smoothly joined with regular regions