A family of C1 Clough–Tocher spline spaces on C0 piecewise quadratic domain partitions

Jan Grošelj and Marjeta Knez

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 234, issue C, 368-389

Abstract: The paper addresses the construction of C1 splines on a curved domain that is parametrized by a C0 piecewise geometry mapping composed of quadratic Bézier triangles. The C1 splines are assembled from polynomials of a chosen total degree greater than or equal to four, and their construction is based on the Clough–Tocher splitting technique that ensures locality. In particular, the splines are locally characterized by an interpolation problem described by Hermite data, which resembles the standard macro-element concepts developed for C1 splines on triangulations.

Keywords: Quadratic triangle; Quadratic triangulation; Isogeometric functions; Clough–Tocher refinement; Spline space; Dimension; Basis functions (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:234:y:2025:i:c:p:368-389

DOI: 10.1016/j.matcom.2025.03.006

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