A class of generalized quadratic B-splines with local controlling functions

作者：Xie, Qi; Huang, Yiting^*

来源：AIMS Mathematics, 2023, 8(10): 23472-23499.

DOI：10.3934/math.20231193

• quadratic Bernstein-like functions
• quadratic B-splines
• extended Chebyshev spaces
• C & quot
• continuity
• curve design

In this work, a class of generalized quadratic Bernstein-like functions having controlling functions is constructed. It contains many particular cases from earlier papers. Regarding the controlling functions, sufficient conditions are given. Corner cutting algorithms and the accompanying quadratic Bezier curves are discussed. A class of generalized quadratic B-splines possessing controlling functions is proposed. Some important properties for curve and surface design are proved. Sufficient conditions for C2 continuity, C3 continuity and C" continuity are also given. Some applications of the constructed B-splines in R2 and R3 are presented, which show the ability to adjust the shape of the curves flexibly and locally. These applications show that generalized quadratic Bsplines can be easily implemented and serve as an alternative strategy for modeling curves.