ABSTRACT. The theory of 'geometric continuity' within the subject of CAGD is reviewed. In particular, we are concerned with how parametric surface patches for CAGD can be pieced together to form a smooth C k surface. The theory is applied to the problem of filling an n-sided hole occurring within a smooth rectangular patch complex. A number of solutions to this problem are surveyed.
A polygonal patch method is described which can be used to fill a polygonal hole within a given k'th order continuous rectangular patch complex. The method is relatively easy to implement, since it only requires C k extensions of the rectangular patch complex defined in terms of the rectangular patch parameterizations. The method is illustrated by reference to C 2 bicubic B-spline surfaces.
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