FEM-based dynamic subdivision splines

Recent years have witnessed a dramatic growth in the use of subdivision schemes for graphical modeling and animation, especially for the representation of smooth, often complex, shapes of arbitrary topology. Nevertheless, conventional interactive approaches to subdivision objects can be extremely laborious and inefficient. Users must carefully specify the initial mesh and/or painstakingly manipulate the control vertices at different levels of the subdivision hierarchy to satisfy a diverse set of functional requirements and aesthetic criteria in the modeled object. This modeling drawback results from the lack of direct manipulation tools for the limit geometric shape. To improve the efficiency of interactive design, we have developed a unified finite element method (FEM) based dynamic methodology for arbitrary subdivision schemes by marrying principles of computational physics and finite element analysis with powerful subdivision geometry. Our dynamic framework permits users to directly manipulate the limit surface obtained from any subdivision procedure via simulated "force" tools. Our experiments demonstrate that the new unified FEM-based framework promises a greater potential for subdivision techniques in geometric modeling, finite element analysis, engineering design, computer graphics and other visual computing applications.