Polynomial representations, such as Bezier curves, B-splines or NURBS, form the basis of numerous surface modelling packages. Although they possess properties that result in fast, efficient software, they have some limitations in terms of the shapes that can be modelled and the nature of the controls they offer the user. This paper presents a new, point-based approach to modelling that is guaranteed to produce high quality surfaces whilst providing a simpler, more intuitive user interface. These qualities make the method ideal for such applications as graphical design or animation where there is a need to produce pleasing images with minimum time and effort.

Key words: geometric modelling, computer graphics, geometric control, curvature continuous