The construction of λμ-B-spline curves and its application to rotational surfaces

In order to provide more flexible approaches for designers, the λμ-B-spline curves are constructed as a generalization of the traditional cubic uniform B-spline curves. Possessing multiple local shape control parameters, λμ-B-spline curves not only inherit the properties of cubic uniform B-spline curves, but also exhibit better performance when adjusting its local shapes through two local shape control parameters. Particularly, to adjust and control the shapes of rotational surfaces more elegantly, the λμ-B-spline rotational surfaces with two local shape parameters are presented and utilized. A rotational surface is produced by combining λμ-B-spline with a transfinite vector valued rational interpolation function. Further, the properties of rotational surfaces, as well as its applications in rotational surface designs, are explored. Finally, the modeling examples are supplied to illustrate the proposed method in admitting the easy control of the shape of a surface, which suggest the much wider applications to the pattern design system of apparel CAD/CAM.