S–λS–λ bases and S–λS–λ curves

In this paper, a class of discrete distributions called S–λS–λ distributions is presented and the corresponding S–λS–λ basis functions are constructed from these distributions by means of the technique of generating functions and transformation factors. These basis functions generate S–λS–λ curves. We show that S–λS–λ curves include Bézier curves, Poisson curves, rational Bézier curves and a lot of other curves. Therefore the research in this paper provides a unified scheme for dealing with these well-known curves. We study some important properties of the S–λS–λ basis functions and S–λS–λ curves. Furthermore, by means of the technique of generating functions, a new convenient and practical method for local changes of S–λS–λ curves is proposed.

► We introduce a broad class of discrete distributions called S–λS–λ distributions.
► We construct S–λS–λ basis functions by the technique of generating functions.
► We construct S–λS–λ curves and show that they include many important curves used in CAD.
► We study some important properties of the S–λS–λ basis functions and S–λS–λ curves.
► We propose a new convenient and practical method for local changes of S–λS–λ curves.