A family of $C^1$ Clough-Tocher spline spaces on $C^0$ piecewise quadratic domain partitions

Grošelj, Jan (author), Knez, Marjetka (author)

The paper addresses the construction of $C^1$ splines on a curved domain that is parametrized by a $C^0$ piecewise geometry mapping composed of quadratic Bézier triangles. The $C^1$ 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 $C^1$ splines on triangulations.

• Language: English
• Keywords: quadratic triangle, quadratic triangulation, isogeometric functions, Clough-Tocher refinement, spline space, dimension, basis functions
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2025
• Number of pages: Str. 368-389
• Numbering: Vol. 234
• PID: 20.500.12556/RUL-168013
• UDC: 519.6
• ISSN on article: 0378-4754
• DOI: 10.1016/j.matcom.2025.03.006
• COBISS.SI-ID: 230027267
• Publication date in RUL: 25.03.2025

Record is a part of a journal

• Title: Mathematics and computers in simulation : transactions of IMACS
• Shortened title: Math. comput. simul.
• Publisher: Elsevier, International Association for Mathematics and Computers in Simulation
• ISSN: 0378-4754
• COBISS.SI-ID: 25913088

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• License: CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
• Link: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Description: The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.