C 2 Gregory patch

Abstract

G² continuity of free-form surfaces is sometimes very important in engineering applications. The conditions for G2 continuity between two Bezier patches has been studied and methods developed to ensure such continuity. However, certain restrictions on the shapes of such patches arise within the Bezier-patch formulation. The Gregory patch is a kind of free-form surface patch which is an extension of the Bezier patch such that cross-boundary first derivatives can be specified without restrictions on the compatibility condition. In this paper, we extend the idea of the Gregory patch and develop a formulation for the C² Gregory patch. The properties of the C² Gregory patch are discussed as well as its connection with a Bezier patch and a G² continuous interpolation method based upon such patches.