Α-B-splines non-stationary subdivision schemes for grids of arbitrary topology design. (November 2022) - Barrera, D.; Lamnii, A.; Nour, M.-Y.; Zidna, A.
Abstract: This paper proposes a new class of B-spline-like functions that blend trigonometric and hyperbolic functions. A new family of non-stationary subdivision schemes of order k ≥ 3 has been built using the refinement of these B-splines. The schemes yield a C k − 2 limit curve that represents the spline. A tensor-product subdivision approach is used to produce a limit surface from an initial mesh with regular vertices. For extraordinary vertices, new rules are proposed. Except at extraordinary points, where they are C 1 continuous, the scheme generates C k − 2 continuous limit surfaces. The proposed scheme is a particular case of many well-known curve and surface subdivision schemes. Some examples are given to demonstrate how well the new schemes perform in generating various shapes of limit curves and surfaces. Graphical abstract: Highlights: C k − 2 limits surfaces except at a number of extraordinary vertices where is C 1 . Reproduction of sphere, torus, conical shapes and more kinds of limit surfaces. Easy control of the shape of the limit surface, only by varying the shape parameter. By changing the two tension parameters several forms of limit surfaces are generated.