Special issue: Mathematical methods for CAD

In this special issue of Computer-Aided Design, mathematical and geometrical methods are presented for a set of problems in computer-aided design. In particular, the issue contains seven papers that deal with topics in the synthesis and analysis of surfaces and solids. The first three papers deal with topics in surface design. A basic problem in shape design is the fitting of smooth surfaces over a given mesh of curves, e.g. cubic B6zier curves. In the first paper, Liu and Son present two methods for interpolating the mesh by G 1 smooth rectangular B6zier patches. Next, the assessment of surface quality is dealt with, and Beier and Chen in their paper propose a highlight-line model for the smoothness evaluation of surfaces. The third paper, by Aono, Breen and Wozny, describes the kernel of a computeraided lamination system for fitting woven-cloth fabric (composite ply) on curved surfaces. Such modelling techniques are also important in the light of layered manufacturing, which provides the capability to build 3D objects by 'stacking' 2D surfaces (or layers). The remaining four papers are on solids. The fourth and fifth papers are concerned with representations and conversions. The reconstruction of contours of solids from digitized (voxel) data is important in computeraided inspection, and this is the topic of the paper by G a ~ , Sehraek and Kwok. A procedure for spatial enumeration to CSG conversion, in an integrated system that automatically derives the shape and topology of structural components, is described in the paper by Chirebdast and Palmlamla'os. Swept volumes are useful for a host of CAD/CAM applications, and, in the sixth paper, Blaekmore, Leu and Silila extend the sweep-differential method to incorporate deformations in swept-volume analysis. Finally, Srinivas and Dutta, in the last paper, consider the cyclide (a variable-radius torus), and outline methods for the synthesis of geometrically complex objects using smoothly joined pieces of cyclides. In the preparation of this special issue, I have received help from many individuals. Thanks are due to all the referees for their timely and meticulous reviews. Les Piegl's help and advice throughout the process was very useful. Finally, I had several interactions with Karen Hemingway, Shirley Wakley and Clare Rumsey at Butterworth-Heinemann; they were simply a pleasure to work with and have been most helpful.