New algorithms for evaluating parametric surface

Through generalization of mathematical model of surface lofting program in the CONSURF system, the definitions for two generalized Ball surfaces and t heir recursive algorithms are given. Furthermore, the conversion algorithms from Bezier surface to these two generalized Ball surfaces are presented. On the basis of these algorithms, two more efficient algorithms for evaluat ing parametric surfaces are also derived. One uses generalized Ball forms d irectly for evaluating surface, and the other converts the given Bezier sur face to a generalized Ball surface firstly, and then evaluates the surface. Both theoretical analysis and example computations show that the two new a lgorithms are more efficient than the de Casteljau algorithm. Especially wh en Wang-Ball surface is used, the time complexity is reduced from cubic to quadratic of the degree of the surface. If these algorithms are applied to displaying, interactive rendering, designing, intersection-finding, offsett ing and approximating for surfaces, considerable economic results can he ac hieved.