...

Prior to the advent of subdivision surfaces, non-uniform rational b-splines (or NURBS) were the industry standard when it came to the creation of smooth surfaces. They remain a popular choice for animation, especially when working with programs that have excellent NURBS modeling workflows.

Like subdivision surfaces, NURBS are inherently smooth surfaces and suffer none of the faceting artifacts that are associated with polygonal approximations. In fact, RenderMan will always efficiently render a NURB as a smooth surface. Unlike subdivision surfaces, however, NURBS have a inherent topological constraint: a NURB's control surface is a rectangular mesh of rows and columns. While this means a NURB's parametric space for texturing is easy to understand (it's a rectangle!), it also means that when creating a complex organic shape like a human character, it is now the job of the modeler to divide that complex shape into a collection of rectangular pieces, each of which is a separate NURB. Moreover, if more detail is required at some section of the mesh which requires the addition of extra knots (an intersection of a row and a column), additional rows and columns must be added across the entire NURB in order to satisfy the rectangular mesh constraint. This can very quickly lead to unwieldy models.

...