Key developments in computer-aided geometric design

Abstract

Computer-aided geometric design (CADG) is concerned with the mathematical and computational aspects of Computer-aided design (CAD). The word ‘geomeric’ reflects the major ingredient of CAD mathematics. Geometry is one of the oldest disciplines of mathematics; it is almost as old as mankind. Through the centuries up until the beginning of the 20th century, geometry had an excellent position among other mathematical fields. Unfortunately, in this century, scientists and teachers neglected the field for most part; geometry was not an active topic of research and the geometry curriculum was cut down to a minimum (if not to zero). Thanks to the advent of computers in engineering, a new applied geometry has emerged to underpin computer-aided design. In the late 1950s and early 1960s, the subject was researched by (and known to) engineers and technical people only. In 1971, P J Davis proposed that there be a conference on ‘graphics and mathematics’. The University of Utah hosted the first conference in 1974 whose proceedings were entitled ‘Computer Aided Geometric Design’. Although this year can be considered as the ‘official’ birthday of CAGD, the development of CAGD techniques go back to the early 1960s when people started to work on CAD projects, and developed methods suitable for computer application. This survey attempts to summarize the most important techniques developed in the last 20–25 years. The ‘point system’ with which these methods were selected was based on the application and usefulness, and not on the beauty of mathematics involved.