Advanced Graphics Study Guide

Advanced Graphics, Dr Neil Dodgson, University of Cambridge Computer Laboratory
Part II course, 2000


Part 4: Other 3D modelling mechanisms
A: Generative models
B: Converting swept objects to polygons
C: Constructive Solid Geometry
D: Implicit surfaces, voxels and marching cubes
E: Subdivision surfaces
...back to part 3 | on to part 5...

4E) Subdivision surfaces

Subdivision schemes work by taking a coarse polygon mesh and introducing new vertices to create a finer mesh. Iterating this process several times creates a very fine mesh of polygons. Given that we are interested in drawing things only to a certain level of accuracy (there is no point in having polygons that are much smaller than pixels), the easily understood subdivision idea has definite benefits over the mathematically complicated B-spline methods. In fact, as will be explained in lectures, two of the subdivision schemes (Doo-Sabin and Catmull-Clark) produce, in the limit, B-spline surfaces (uniform quadratic and uniform cubic respectively).

Subdivision schemes have been around for a long time. Subdivision methods for curves were first mathematically analysed in 1947. Their use in computer graphics dates from 1974 when Chaikin used them to derive a simple algorithm for generating curves quickly. In 1978 Doo and Sabin (quadratic) and Catmull and Clark (cubic) generalised Chaikin's work from curves to surfaces. Much work has been done since then, but it seems that it is only in the last five years that subdivision schemes have had widespread use.

Some of the mathematical detail of subdivision surfaces is given in SMEG section 5.

Exercises
  1. Do the "constructive" exercises at the end of SMEG section 5.1.
  2. Explain how Doo-Sabin subdivision works for an arbitrary polygon mesh.


Part 4: Other 3D modelling mechanisms
A: Generative models
B: Converting swept objects to polygons
C: Constructive Solid Geometry
D: Implicit surfaces, voxels and marching cubes
E: Subdivision surfaces
...back to part 3 | on to part 5...


Neil Dodgson | Advanced Graphics | Computer Laboratory

Source file: p4e.html
Page last updated on Thu Sep 14 16:58:09 BST 2000
by Neil Dodgson (nad@cl.cam.ac.uk)