Direct manipulation and interactive sculpting of PDE surfaces

This paper presents an integrated approach and a unified algorithm that combine the benefits of PDE surfaces and powerful physics-based modeling techniques within one single modeling framework, in order to realize the full potential of PDE surfaces. We have developed a novel system that allows direct manipulation and interactive sculpting of PDE surfaces at arbitrary location, hence supporting various interactive techniques beyond the conventional boundary control. Our prototype software affords users to interactively modify point, normal, curvature, and arbitrary region of PDE surfaces in a predictable way. We employ several simple, yet effective numerical techniques including the finite-difference discretization of the PDE surface, the multigrid-like subdivision on the PDE surface, the mass-spring approximation of the elastic PDE surface, etc. to achieve real-time performance. In addition, our dynamic PDE surfaces can also be approximated using standard bivariate B-spline finite elements, which can subsequently be sculpted and deformed directly in real-time subject to intrinsic PDE constraints. Our experiments demonstrate many attractive advantages of our dynamic PDE formulation such as intuitive control, real-time feedback, and usability to the general public.