Abstract

Standard free-form splines such as B-splines and NURBS are widely employed in a wide range of CAD/CAM systems. Conventional geometric modeling and design techniques using these popular splines often requires tedious control-point manipulation and/or painstaking constraint specification (for functional requirements) via unnatural mouse-based computer interfaces. In this paper, we propose a novel and natural haptic interface and present a physics-based geometric modeling approach that supports the interactive sculpting of spline-based virtual material. Our desktop modeling system permits both expert and non-expert users to interactively deform virtual materials with real properties using force feedback. Using commercially available (and low-cost) haptic devices, modelers can feel the physically realistic presence of virtual spline objects such as B-splines throughout the design process. Our haptics-based B-spline is a special case of more powerful dynamic NURBS (D-NURBS) models. We develop various haptic sculpting tools to expedite the deformation of B-spline surfaces with haptic feedback and constraints. The most significant contribution of this paper is that point, normal, and curvature constraints can be specified interactively and modified naturally using forces. To achieve the real-time sculpting performance, we devise a novel dual representation for B-spline surfaces in both physical and mathematical space: the physics-based mass-spring model is mathematically constrained by the B-spline surface throughout the sculpting session.