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Higher-degree super-smooth C1 splines over a Powell–Sabin refined triangulation

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  • Grošelj, Jan

Abstract

The paper provides a generalization of C1 quadratic splines over a Powell–Sabin refined triangulation to C1 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.

Suggested Citation

  • Grošelj, Jan, 2026. "Higher-degree super-smooth C1 splines over a Powell–Sabin refined triangulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 243(C), pages 382-406.
    • Handle: RePEc:eee:matcom:v:243:y:2026:i:c:p:382-406
    DOI: 10.1016/j.matcom.2025.11.035
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    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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