Partial Said-Ball curves: A new type of generalized Ball curves

Abstract

Ball basis was introduced for cubic polynomials by Ball, then generalized for polynomials of higher degree by Wang and Said. In this paper we present theorems and algorithms about constructing a new type of generalized Ball curves: Partial Said-Ball curves; investigate the properties and Bézier representation of the new curves; give the transforming matrixes between the basis of new curves and Bernstein basis which constructing Bézier curves. Furthermore, the shape differences between the new curves and the other existent generalized Ball curves are demonstrated through examples.