Geometric continuity between adjacent Bézier patches and their constructions Original Research Article

In this paper, the necessary and sufficient conditions for two adjacent Bézier surface patches of arbitrary degrees joining Gn-continuously along a common boundary curve are presented. These conditions are represented directly by the two surface patches, or via an intermediate surface patch. Configurations of the coefficient functions attached to the adjacent Bézier patches are obtained. Based on these results, an algorithm to compute the order of continuity between two given Bézier patches along a common boundary curve is presented. The Gn compatibility conditions which involve the coefficient functions and the control points of the two adjacent Bézier patches are developed. Examples for the construction of G1- and G2-continuous Bézier patches are given to illustrate the conditions developed.