Higher-degree super-smooth $C^1$ splines over a Powell-Sabin refined triangulation

Grošelj, Jan (author)

The paper provides a generalization of $C^1$ quadratic splines over a Powell-Sabin refined triangulation to $C^1$ splines of any degree greater than two. The splines are constructed by imposing maximal super-smoothness at Powell-Sabin triangle split points and reproduce polynomials to the highest possible degree. The spline spaces are characterized by functionals that induce a B-spline representation over a triangulation, i.e., a representation of splines in terms of locally supported nonnegative basis functions that form a partition of unity. This makes the considered splines readily applicable in computer aided geometric design, function approximation problems, and finite element methods for solving partial differential equations.

• Language: English
• Keywords: $C^1$ splines over triangulations, Powell–Sabin splines, B-spline representation
• 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: 2026
• Number of pages: Str. 382-406
• Numbering: Vol. 243
• PID: 20.500.12556/RUL-180837
• UDC: 519.6
• ISSN on article: 0378-4754
• DOI: 10.1016/j.matcom.2025.11.035
• COBISS.SI-ID: 272036355
• Publication date in RUL: 18.03.2026

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

Licences

• 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.

Projects

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: P1-0294
• Name: Računsko intenzivne metode v teoretičnem računalništvu, diskretni matematiki, kombinatorični optimizaciji ter numerični analizi in algebri z uporabo v naravoslovju in družboslovju