Construction of Generalized λμ-Ball Curves of Degree n

In Computer Aided Geometric Design (CAGD), the representation of curves and surfaces is a research focus. Benefiting from the fast computing speed and excellent properties of the basic functions, the Ball curves and surfaces have been widely used and deeply studied. In this paper, a generalized Ball curve with two parameters is constructed and discussed, called λμ-Ball curves. Firstly, based on the cubic Ball basic function with shape parameters, we derive the λμ-Ball basis functions of degree n by using the recursive algorithm. Then, the properties of λμ-Ball basis functions are discussed. Finally, the G
¹
continuity conditions of the generalized λμ-Ball curve are given. The results show that λμ-Ball curve can be adjusted more flexibly by modifying the shape parameters and describing the complex geometry under the G
¹
continuity conditions.