Dynamic smooth subdivision surfaces for data visualization

Abstract

Recursive subdivision schemes have been extensively used in computer graphics 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 (1978) subdivision scheme, which is a very popular method to model complicated objects of arbitrary genus because of many of its nice properties. Our new dynamic surface model inherits the attractive properties of the Catmull-Clark subdivision scheme as well as that of the physics-based modeling paradigm. This new model provides a direct and intuitive means of manipulating geometric shapes, a fast, robust and hierarchical approach for recovering complex geometric shapes from range and volume data 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 in real time. The governing dynamic differential equation is derived using Lagrangian mechanics and a finite element discretization. Our experiments demonstrate that this new dynamic model has a promising future in computer graphics, geometric shape design and scientific visualization.