Study On Generalized Ball Curves And Surfaces

Free curves/surfaces defined in different topological structure have different expressions in CAGD, and generalized Ball curves are more efficient than Bézier curves in calculation, the degree elevation and reduction。This dissertation focuses on the research about the generalized Ball curves/surfaces。Firstly, the extension of Wang-Said type generalized curves is provided by introducing some shape parameters。By changing the values of those shape parameters, the shape of these new curves can be adjusted locally or entirely, and Said-Ball curve with multiple shape parameters is provided。The extension of Wang-Ball surface is made to get a kind of new surface over triangular domain by introducing a shape parameter。Secondly, this paper presents a family of new curves which unify the representations of Bézier curve and Wang-Ball curve。The corresponding degree elevation scheme, recursive algorithm and explicit conversion formulae between this new family of curves and Bézier curve are given。Finally, a family of new basis is offered to unify the Berntein basis, Wang-Ball and Said-Ball basis。In addition, the corresponding degree elevation scheme and recursive algorithm are presented。...