The thesis is concerned with describing new ways of using computers to create images of 3-dimensional designs. It also introduces novel methods for manufacturing some of these designs using numerically controlled machine tools. The work began as an extension of an existing surface design package called 'DUCT'. This was a program capable of holding descriptions of subtly curved surfaces, but which could only display them using line drawings. It was the first task of the author to examine different methods for depicting surfaces and then to decide which one was the most suitable for use in conjunction with industrial design work. Once done, this led on to ways in which the rendering methods could be improved. These improvements then enabled the package to be used in new application areas such as realistic image synthesis for advertising and animation. In tandem with this, new methods were developed for verifying the machining paths generated by DUCT for use on 3-axis milling machines. The methods developed for machining path verification were then extended to give improved techniques for the generation of such machining paths. The new approach allowed the manufacture of objects which were beyond the scope of previous surface design systems. The work on depicting objects manufactured using a 3-axis milling machine drew attention to the related problem of depicting realistic terrain. The author improved the existing methods for defining detailed surfaces such as mountains, and then went on to suggest new techniques for rendering such terrain in perspective. The new algorithms led naturally to the possibility of implementation on parallel computers and a paper study was made of the trade-offs involved in choosing different parallel computing architectures.