A physics-based framework for subdivision surface design with automatic rules control

The recent non-uniform subdivision approach extends traditional uniform subdivision schemes with variable rules, offering additional shape parameters (such as knot spacings) for feature control. Despite its flexibility, shape modification based on non-uniform subdivision usually requires designers to interactively adjust a large number of degrees of freedom (DOFs) to achieve the desired shapes, which can often be laborious. This paper extends the principle of variational subdivision and integrates the non-uniform subdivision schemes with powerful physics-based shape sculpting techniques, providing a universal method for arbitrary subdivision schemes with adjustable rules. The subdivision control points and knot spacings evolve in response to the shape deformation resulting from the numerical integration of Lagrangian dynamics equation or the optimization of shape energy functional. Thus, our system allows users to manipulate the desired shape in a direct and intuitive fashion. In addition, we propose a novel and efficient discrete functional evaluation method for polygonal meshes or point clouds of arbitrary topology based on implicit functions, in which no parameterization is needed. Finally, we develop a simple prototype sculpting system demonstrating many advantages of our novel physics-based, non-uniform subdivision modeling system.