Techniques for interactive design using the PDE method

Abstract

Interactive design of practical surfaces using the partial differential equation (PDE) method is considered. The PDE method treats surface design as a boundary value problem (ensuring that surfaces can be defined using a small set of design parameters). Owing to the elliptic nature of the PDE operator, the boundary conditions imposed around the edges of the surface control the internal shape of the surface. Moreover, surfaces obtained in this manner tend to be smooth and fair. The PDE chosen has a closed form solution allowing the interactive manipulation of the surfaces in real time. Thus we present efficient techniques by which we show how surfaces of practical significance can be constructed interactively in real time.