Chapter 12

Subdivision Surfaces

Malcolm Sabin

This chapter deals with the technology of subdivision surfaces, how they can be defined and how schemes are analysed for desirable properties, thus allowing tuning of the details of the scheme for optimum behaviour.

12.1 SUBDIVISION SURFACE DEFINITIONS

The basic idea is that an initial 2-manifold network of vertices, edges and facets (often now referred to as the control polyhedron, even though the facets need not be planar, or sometimes as the mesh) can be refined by computing new vertices and joining them up to form a new polyhedron. This operation can be repeated indefinitely, and as the process continues, if the refinement construction is suitable, the polyhedron converges towards a limit ...

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