ABSTRACT
Subdivision algorithms are similar to fractal procedures. In the standard fractal algorithm, we begin with a compact set C0 and iterate over a collection of contractive transformations W to generate a sequence of compact sets Cnþ1 ¼ W Cnð Þ that converge in the limit to a fractal shape C1 ¼ Limn!1Cn. In subdivision procedures, we start with a set P0 (usually either a control polygon or a control polyhedron, or as we shall see shortly a quadrilateral or triangular mesh) and recursively apply a set of rules S to generate a sequence of sets Pnþ1 ¼ S Pnð Þ of the same general type as P0 that converge in the limit to a smooth curve or surface P1 ¼ Limn!1Pn.
