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...
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
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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...