When this special issue was in the planning stage, the intended title was 'surface design'. Considering the areas where active research is going on and that are of practical interest, the 'shape' arena seemed a promising candidate for a special issue. Let us investigate how and why this area has gained importance.
Classical CAD surface design methods produced B6zier and B-spline, Coons and Gordon surfaces (plus a variety of more 'exotic' methods). The development of these methods was accomplished by the early seventies. While the original developments all took place in an industrial setting, subsequent analysis was carried out by mathematicians. They were (and are) being trained in the 'modern' way of avoiding geometric issues and concentrating on the abstract and algebraic. Not surprisingly, the quality of a surface generation method was measured by its polynomial precision or by its continuity class. Both terms, of course, are nothing but meaningless to a designer whose acquaintance with mathematics is via descriptive geometry.
Starting in the early eighties, it was realized that numerical analysis is ffot the only area of mathematics that could contribute to surface design. Geometric issues gained importance, the most obvious one being the concept of geometric continuity, which is a geometric abstraction of the algebraic concept of differentiability. The first developments in this field focused on curves, which are now reasonably well understood. Geometric continuity for surfaces is still an active area of research, the reason being the simple fact that surfaces are much harder to understand than curves. The articles by Boehm and Jones in this issue both deal with the concept geometric continuity.
In terms of classical numerical analysis, Coons and Gordon surfaces were treated in terms of Boolean sums and operators endowed with a lattice structure. Being involved with the abstract properties of these surfaces, researchers overlooked the simple fact that they could not cope with many practical situations. Often the input geometry to these surface schemes suggests a surface shape that is close to what a designer would