Techniques for interactive design using the PDE method

TLDR

Interactive design of practical surfaces using the PDE method is considered. We present efficient techniques for constructing surfaces of practical significance interactively in real time. The PDE method models surface design as a boundary value problem with elliptic operators, where boundary conditions control internal shape and a closed‑form solution enables real‑time interactive manipulation. Surfaces produced by this method are smooth and fair.

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.