Abstract
In this paper, the constraints on the homogeneous surface belonging to a certain rational surface are derived which are both necessary and sufficient to ensure that the rational surface is nth-order geometric continuous. This gives up the strong restriction that requires the homogeneous surface to be as smooth as the rational surface. Further the conditions for the rectangular rational Bézier patches are developed, and some simple and practical sufficient conditions are presented which might give a valid means for the construction of GC n connecting surfaces.
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