Control vectors for splines. (January 2015) - Kosinka, Jiří; Sabin, Malcolm A.; Dodgson, Neil A.
Abstract: Traditionally, modelling using spline curves and surfaces is facilitated by control points. We propose to enhance the modelling process by the use of control vectors . This improves upon existing spline representations by providing such facilities as modelling with local (semi-sharp) creases, vanishing and diagonal features, and hierarchical editing. While our prime interest is in surfaces, most of the ideas are more simply described in the curve context. We demonstrate the advantages provided by control vectors on several curve and surface examples and explore avenues for future research on control vectors in the contexts of geometric modelling and finite element analysis based on splines, and B-splines and subdivision in particular. Highlights: We extend traditional splines based on control points by incorporating control vectors. Our paradigm allows combining several spline constructions into one formulation. We can model curves and surfaces that are not possible with existing techniques.