TABLE OF CONTENTS Bicubic patches (integral ones) have enjoyed enormous popularity. Another type of surface, the Coons patch, never became quite as popular because of problems people had with a correct specification of certain twist vectors (see [57] for details.) The twist problem was first fixed by J. Gregory in 1972, still in the context of Coons patches. What really made his idea recognized and successful was, however, a modification by Chiyokura and Kimura as described in [33] and [32]. The following sections will focus on that approach; for the original literature, see Barnhill [14], Barnhill and Gregory [15], and Gregory [83]. [1]
J. Gregory has contributed more to the field of Geometric Modeling than just the patches that now bear his name. He also obtained fundamental results in the areas of interpolatory subdivision, n-sided patches, and shape preserving interpolation. John Gregory died in March 1993, at the age of 47.
[1]In the earlier literature, Gregory patches are typically referred to as "Gregory squares".
Consider the problem that is illustrated by Fig. 14.1: two (integral) bicubic B zier patches A and B are given. A third one is sought such that we achieve C 1 continuity across all patch boundaries.
The C 1 conditions between rectangular B zier patches determine all points in the desired patch with one exception: the pair of points marked by squares. Of those two, the point 
