The design and geometric processing of free form curves and surfaces can be greatly facilitated by gaining an understanding of their visual appearance. For example, the concepts of convex and spiral shapes link the visual appearance of a curve to its synthesis and processing and thus can be used to develop effective techniques to improve the use of curves in a computer environment. The project develops further definitions to categorize free form surfaces based on shape properties and develops these into useful techniques for the design and processing of surfaces. These techniques will have a common mathematical basis and this will help to merge the design and engineering of parts.
