DYNAMIC CATMULL-CLARK SUBDIVISION SURFACES

Recursive subdivision schemes have been extensively used in computer g raphics, computer-aided geometric design, and scientific visualization for modeling smooth surfaces of arbitrary topology. Recursive subdivi sion generates a visually pleasing smooth surface in the limit from an initial user-specified polygonal mesh through the repeated applicatio n of a fixed set of subdivision rules. In this paper, we present a new dynamic surface model based on the Catmull-Clark subdivision scheme, a popular technique for modeling complicated objects of arbitrary genu s. Our new dynamic surface model inherits the attractive properties of the Catmull-Clark subdivision scheme, as well as those of the physics -based models. This new model provides a direct and intuitive means of manipulating geometric shapes, and an efficient hierarchical approach for recovering complex shapes from large range and volume data sets u sing very few degrees of freedom (control vertices). We provide an ana lytic formulation and introduce the ''physical'' quantities required t o develop the dynamic subdivision surface model which can be interacti vely deformed by applying synthesized forces. The governing dynamic di fferential equation is derived using Lagrangian mechanics and the fini te element method. Our experiments demonstrate that this new dynamic m odel has a promising future in computer graphics, geometric shape desi gn, and scientific visualization.