Shapes and Topology

Topology, or the part of it that is most closely related to CG, is the study of surface properties that remain the same regardless of deformations made to an object. When working with nurbs, it is especially useful to understand these properties because nurbs surfaces are made from a very small number of topological types. If you understand these surface types, you will be able to more quickly construct your target object out of nurbs surfaces (Fig. 14.1).

All nurbs primitives are four-sided. This is a topological limitation. To use them effectively, you will have to be able to see this four-sided topology in everything you intend to build. The easiest way to accomplish it is to remember the unfolded carton from the first exercise. When you look at objects, analyze your target to dis- cern how it will unfold in two-dimensional space. By doing this, you will be able to understand its topology, and know how to build the object using four-sided nurbs surfaces.