| Abstract | In Computer Aided Design, the definition of the shape of an actual object has been found to be more suitable in terms of parametric curves and surfaces than nonparametric ones. From a design point of view, it is convenient if the shape of a curve or surface can be controlled in a predictable way by changing only a few parameters. Bezier curves and surfaces partially satisfy this need. Therefore, the Bezier model, consisting of curves, rectangular and triangular surfaces, has been used extensively in Computer Aided Design and Computer Aided Geometric Design. However, in recent years, the Ball model has been found to be more suitable in a number of situations than the Bezier model, for examples, degree elevation and reduction. The present study aims to investigate further the important properties of this model. To this purpose, an algorithm for generating rational Ball curves is first developed. The Pythagorean hodograph of rational Ball curves is then investigated. Recognizing the fact that any rectangular polynomial surface of degree (m+n) in the parameter, :1 and v can be treated as a Bezier or Ball rectangular surface of degree (m, n), the study establishes the conversion formulas between the control points of a Bezier surface and the corresponding Ball surface. Similarly, the conversion formulas between a Bezier triangular surface and the corresponding Ball triangular surface are derived. Finally, since triangles are more widely applicable than rectangles and the existing algorithm for generating a point on a Ball triangular surface is found to be more efficient than the de Casteljau algorithm for obtaining a point on the correSponding Bezier triangular surface, it may be desirable to convert rectangular surfaces into Ball triangular surfaces. Using existing results concerning the conversion of Bezier rectangular surfaces into Bezier triangular surfaces, two approaches are proposed in this work to convert a Ball rectangular surface into a Ball triangular surface. It is shown that both give the same results. The results obtained in this study provide all needed formulae for a designer to go from one model to the other, depending on the suitability of such model in practical situations. |