Direct manipulation and interactive sculpting of PDE surfaces

This paper presents an integrated approach and a unified algorithm that com bine the benefits of PDE surfaces and powerful physics-based modeling techn iques within one single modeling framework, in order to realize the full po tential of PDE surfaces. We have developed a novel system that allows direc t manipulation and interactive sculpting of PDE surfaces at arbitrary locat ion, hence supporting various interactive techniques beyond the conventiona l boundary control. Our prototype software affords users to interactively m odify point, normal, curvature, and arbitrary region of PDE surfaces in a p redictable way. We employ several simple, yet effective numerical technique s including the finite-difference discretization of the PDE surface, the mu ltigrid-like subdivision on the PDE surface, the mass-spring approximation of the elastic PDE surface, etc. to achieve real-time performance. In addit ion, our dynamic PDE surfaces can also be approximated using standard bivar iate B-spline finite elements, which can subsequently be sculpted and defor med directly in real-time subject to intrinsic PDE constraints. Our experim ents demonstrate many attractive advantages of our dynamic PDE formulation such as intuitive control, real-time feedback, and usability to the general public.