Interactive curve design using digital French curves

Abstract

In the real world designers often use French curves or sweeps to create or edit curves to bring out a personal style or reflect a corporate standard in all their designs. A French curve is a general term for a pre-defined curve template used to create high quality 2D drawings or sculpt 3D models. Research in interactive curve and surface design is continually moving toward direct manipulation of the objects being defined. This paper describes a system in which digital French curves, represented by planar cubic NURBS curves, interactively create and sculpt curves and surfaces that comprise the design of an object. The approach is especially relevant in the early stages of conceptual design to beautify and simplify curves obtained from quick gestural sketches. Algorithmically, the contributions of this paper are twofold. We describe an efficient technique for approximating a planar parametric curve by a small set of elliptic arcs. Proximity computation to the approximating ellipses is simple and efficient, greatly improving the interactivity of the sculpting paradigm. We also describe a simple approach to smoothly replace sections of design curves with sections of the French curve. The results are illustrated within a design system using a puck that provides simultaneous position and orientation information to control the digital sweep, allowing the user the same physical feel and efficiency of motion of a real sweep.