RECURSIVE G(K) TRANSFORMATIONS BETWEEN ADJACENT BEZIER SURFACES

In this paper, explicit conditions of G(k) continuity between Bezier s urfaces are given. We concentrate on the structures of G(k) transforma tions between adjacent Bezier surfaces Q and show that a general G(k) transformation can be represented recursively with the composition of k cardinal G(k) transformations. We can thus construct a new Bezier su rface Q from a given Bezier surface R such that Q and R meet with G(k) continuity by recursively applying simple geometric transformations w hich have intuitive geometric meaning for k times. When these simple G (k) transformations are also polynomial preserving, each of them is ac tually determined by three real constants which are called shape param eters. The structures of G(k) transformations are explored and describ ed. Since the G(k) conditions between two Bezier surfaces are finally expressed with the explicit relationship of the related control points , these results can be used directly in closed surface modeling, surfa ce blending and surface connecting.