The John A. Gregory Award is currently the highest award in the field of Geometric Design. It is presented to one or more individuals for Fundamental Contributions to the Field of Geometric Modelling . The laureates are chosen by a committee operating privately. Their names are announced once every three years. A central criterion in making selections for this award is the laureate's lifetime impact on the field.
John Gregory was one of the founders of the discipline of Computer Aided Geometric Design (CAGD), a discipline whose name arose out of seminal meeting held in 1974 at The University of Utah where John was a key participant.
John's roots were in Numerical Analysis. The lively atmosphere in the topic of the finite element method provided by his advisor John Whiteman at Brunel sparked some of his early research. John Gregory worked in many areas of CAGD and Numerical Analysis, as is shown by his membership on editorial boards of both types of journal.John's CAGD research, particularly distinguished by its gracefulness, can be categorized as belonging to six areas. Best known for Gregory's Square, he introduced a method that correctly interpolates boundary data where vexing twist incompatibilities are inherently present. Gregory's Square is used worldwide, and inspired considerable subsequent research.
Done jointly with Barnhill, John's first published research established error bounds computable in terms of originally furnished information for bivariate interpolants. These new error bounds were of far greater utility for finite element approximation.
John's convex combination patches avoid certain "incompatibilities", e.g., twist incompatibilities for bicubic patches, which are inherent from the mathematical composition of interpolants involving derivatives. In addition to rectangular patches, he also introduced elegant triangular and simplicial patches for interpolants in three and four dimensions, respectively.
His work on rational splines, carried out with several of his students, focused on shape preserving curve methods, including monotone and convex data preserving methods. Additionally, his research on subdivisions schemes concerning "Corner cutting methods" and their convergence for curves and surfaces involved collaborations with other outstanding leaders.
The sixth area listed above, polygonal patches, involved a combination of ideas: Gregory (with his student Peter Charrot and others) developed tangent-plane continuous triangular, pentagonal and n-sided patches. Some are compatibly corrected patches and some are convex combination patches. A second part of this story is that John brought Jorg Hahn to Brunel University to work on higher order geometric continuity of surface patches. Their collaboration produced a general theory which, when specialized to the polygonal patch case, permits the smooth (C²) filling of polygonal patch holes in otherwise rectangular networks. This addresses what is frequently called the "suitcase corner problem".
John participated in many CAGD conferences. Because his exceptionally clear presentations always set a high standard, he was frequently chosen as the first speaker, especially at the famous Oberwolfach conferences.
The extraordinary ability to listen and to synthesize his thoughts with those of others made John an ideal partner and excellent collaborator. These qualities, coupled with his well known kindness, made him an ideal colleague and friend who not only achieved new research results, but also brought many others into the area.
John died suddenly March 26, 1993, at the age of 48.
(The above remarks are abstracted from the preface written by Robert Barnhill and Hans Hagen for a special dedicated issue of the CAGD Journal (Vol 13, 1996, 789-791), where John served as an Associate Editor.)