Copyright (c) Susan Laflin. August 1999.

This topic is not covered either by the second-year text by Hearn and Baker or by Rogers and Adams. However both Chapter 9 of Rooney and Steadman and also Chapter 10 of Foley et al give good discussions. Since they are very different, it would be a good idea to read both of them.

There are many commercial packages for various aspects of Geometric Modelling. In fact, the newcomer would find the situation similar to that described in the Royal Society meeting in 1971, except that then the available software was smaller and cheaper. There is some guidance on choice of software, for example the courses at Cranfield which are charged at commercial rates but are still much less than the cost of the mistakes which might otherwise be made.

The range of packages which used to be available in the Apollo laboratory at Elms Rd gave a good idea of the usual range. These included a "Design Office Graphics System" (usually referred to as DOGS); a Numerical Control system (DOGS-NC); a sculptured surface modeller (SWANS or Surface With A Nice Shape); a finite element analysis package (PAFEC-FE) and a solid modelling package (BOXER). We have already referred to some sculptured surface modellers, namely UNISURF and POLYSURF which both use Bezier Surfaces and NMG (or Numerical Master Geometry) from British Aerospace which uses bi-cubic surface patches extensively.

For a more recent survey of the software and applications in this area, the text by Rooney and Steadman, which is used for the Open University course, will give you a good introduction. To go into this area more fully, you should consult some of the Engineering departments rather than Computer Science. This section of the course will consider the basic principle underlying much of the work in this area.

When we come to study geometric modelling, we find there are three main types of method. These are:

a. Cellular Methods.

The first section discusses Cellular Methods and their use in modelling packages. These methods require the use of compression techniques .

b. Half-Space Methods.

The next section discusses Half-space Methods and the logical operations necessary to combine these half spaces to produce descriptions of objects in three-dimensions.

c. Boundary-Representation Methods.

The next section introduces Boundary-Representation Methods and discusses how objects may be described in this format.

The final section considers the use of graphs to describe three-dimensional objects and includes an example of the use of Euler's Rule to verify objects so described.

References

"Introduction to Computer Graphics" J. D. Foley, A. vanDam, S. K. Feiner, J.F.Hughes and R.L.Phillips. Addison Wesley. 1994. ISBN 0-201-60921-5.

"Principles of Computer-aided Design" Joe Rooney and Philip Steadman. Pitman/Open University. 1987. ISBN 0-273-02672-0.

The Proceedings of the Royal Society, Series A, for February 1971 contained the papers from a meeting on `Computer Aids in Mechanical Engineering Design'. This included a paper by Bezier on his `Unisurf' package used by the Renault car company to design their car bodies. Although it is not obvious from the paper, this was the earliest use of Bezier surfaces, which were invented for this package. Another paper described the `Multiobject' package by Armit, which used the same equations. The paper by Sabin, discribing the `Numerical Master Geometry' in use at the British Aircraft Corporation, shows the extensive use of Bicubic Surface tiles in their work because they are particularly concerned to get the extra smoothness of functions which can only be guaranteed by bicubic or higher-order patches.