Dynamic Catmull-Clark subdivision surfaces

Recursive subdivision schemes have been extensively used in computer graphics, computer-aided geometric design, and scientific visualization for modeling smooth surfaces of arbitrary topology. Recursive subdivision generates a visually pleasing smooth surface in the limit from an initial user-specified polygonal mesh through the repeated application 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 genus. 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 using very few degrees of freedom (control vertices). We provide an analytic formulation and introduce the “physical” quantities required to develop the dynamic subdivision surface model which can be interactively deformed by applying synthesized forces. The governing dynamic differential equation is derived using Lagrangian mechanics and the finite element method. Our experiments demonstrate that this new dynamic model has a promising future in computer graphics, geometric shape design, and scientific visualization.