CAGD 2003

A DAMTP Part III lecture course on Computer-aided Geometric Design

• Admin
• Style
• Content



• Notes
• Notation (and Glossary)
• Examples
• Small Print

Admin Issues

This course is held

• during Michaelmas term 9/10/2002 to 2/12/2002
• on Tuesdays and Thursdays at 11 am in Room MR11

Because the course is relevant to other subjects there may be people from other departments or even outside the university present.

As well as the lectures there will be 2 or 3 `examples classes' for the part III students. These will be held CMS on Tuesday or possibly Thursday afternoons, at a time and place to be chosen democratically once the course has settled down.

There will be a 2 hour exam in June, good for 60 marks. In previous years the marks obtained on this course have correlated fairly well with the overall grades that candidates have gained, and so it is neither an easy option nor a particularly hard one.

I shall also set at least one essay question. We will discuss that once the course has settled down. I shall be positive if any of you have topics within the scope of the course which you would like to offer as essays. The subjects have to be defined fairly early in the term, and so any requests should be made by 17th October.

This set of web pages will be accessible at

Style

I hope to continue the style of previous years, where I have finished each lecture by posing a problem and started the next by discussing its solution.

These problems are intended to take typically about twenty minutes, but they will vary. You should never need to spend more than an hour. They will be designed to help you internalise the material of the lectures, sometimes conventionally by exercising something you have just learnt; sometimes by getting you thinking beforehand about something we are going to cover.

I hope to be able to go further in the direction of Socratic teaching by asking a lot more questions in the course of the lectures. This can only work if you cooperate. It didn't last year, so the course turned out to be a very conventional one.

Content

The subject is a branch of applied mathematics which borders on computer science and on engineering.

It deals with ways of representing shapes of smooth curves and surfaces on the computer.

It grew out of the requirements for

• analysing the behaviour/performance of cars, ships and aircraft
• driving automatic manufacturing processes.

There are three issues

• How such shapes can be represented digitally.
• How designers can create and edit representations to achieve the shapes that they want.
• How information for analysis or manufacture can be extracted from the representations.

The subject is

• focussed around constructions rather than proofs
• based on some fairly classical elementary mathematics
  • coordinates
  • differential geometry
  • calculus
  • root-finding
• and on some less elementary standard material
  • point set theory
  • algebraic geometry
  • manifolds
  • Fourier analysis
  • Eigenanalysis
• novel, with some interesting new stuff being invented right now
• applicable to jobs in Cambridge afterwards
• applicable to topics like Fluid Dynamics within DAMTP

In previous years I focussed on the techniques which were primarily designed for the manufacturing industry applications. We covered spline theory leading up to the NURBS techniques widely used in CAD/CAM systems.

Last year I switched the focus to the subdivision techniques which are likely to supplant them as standard in the next five years or so. There are a lot more new results here, and so this year's course will have a few differences from last year.

This page was last updated on 7th October 2003.
It is maintained by Malcolm Sabin <malcolm@geometry.demon.co.uk>.