4. Subdivision diagrams

We have seen that parametric models of B-splines curves and surfaces describe the underlying shapes well. They allow local or global modifications by manipulating control points. Their disadvantages lie in the need for numerical calculations to determine the geometric elements of the model, difficult control of geometric continuity between adjacent parametric curves/surfaces and consistency between surfaces: each surface is described independently of the others. Other models exist for representing a 3D object, notably subdivision models. These models are based on polyhedral models. They allow complex, "smooth" surfaces to be modeled using subdivision steps. A subdivision surface is a boundary surface defined by an infinite number of refinement operations, applied to a coarse control mesh also known as a control polyhedron. A subdivision scheme defines an iterative process for recursively...