Gregory-type patches bounded by low degree integral curves for G~2 continuity

摘要

G~2 continuity of free-form surfaces is sometimes very important in engineering applications. The conditions for G~2 continuity to connect two Bezier patches were studied and methods have been developed to ensure it. However, they have some restrictions on the shapes of patches of the Bezier-patch formulation. Gregory patch is a kind of free-form surface patch which is extended from Bezier patch so that four first derivatives on its boundary curves can be specified without restrictions of the compatibility condition. Several types of Gregory patches have been developed for integral, rational, and NURBS boundary curves. In this paper, we propose some integral boundary Gregory-type patches bounded by cubic and quartic curves for G~2 continuity.