Overview

Formally, subdivision is a method of obtaining a smooth surface as a limit of an infinite sequence of successive refinements.

Even though many people associate computer modelling with the “traditional” splines, subdivision is used widely in Computer Aided Geometry and Design.

The advantages that subdivision surfaces techniques have over the traditional modelling makes it an indispensable feature in most commercial modelling and animation packages (Maya, Side Effects Houdini)

The main gain of using subdivision is that it works on arbitrary topology and it does not need a parameter field (rectangular or triangular) which constraints the surface to fixed topology. Also animating a deformable surface (e.g. lip sinking) is a lot easier using a subdivision approach (http://www.caligari.com/Help/Tutorials/tS5TutorialMovies.asp?Cate=HTutorials , http://www.mrl.nyu.edu/~dzorin/sig99/). Since subdivision generate non-parametric surfaces, it may be hard in general to apply some of the features that are trivial to do on a parametric surface (e.g. texture mapping, normals, tangents)

A subdivision scheme is strictly defined by its refining that can be split into two parts:

• Geometry Split – the geometry mesh is refined
• Averaging step – the positions of the vertices are recomputed.

While the method can be apply to any kind of geometric primitive, my projects focuses on the subdivision of triangular meshes.