Designing B-Spline Surfaces with Haptics Based on Variational Technique

Abstract

Due to their 3D nature, many CAD B-Spline surfaces are difficult to design and edit with traditional 2D interfaces, e.g., a 2D mouse. Based on an energy minimization method or variational B-Spline technique, the paper presents the technique of using a haptic device to design B-Spline surfaces. Under complex constraints and without any pre-calculation, the variational B-Spline technique used in the system can solve virtually all practical B-Spline surfaces in a matter of milliseconds. Such results are much more efficient and powerful than previous work in the variational B-Spline field. By using a haptic interface, the system allows a user in a natural 3D environment to directly manipulate/design constraints, e.g., points and curves, and in real time, the system generates energy-minimization B-Spline surfaces in response to haptic operations. The discussed technique delivers all the performance and capacity required for using haptics to design high-quality B-Spline surfaces, and haptic-based surface operations provide a powerful method for designing B-Spline surfaces.

Haptic Assembly and Prototyping: An Expository Review

“…In a follow-up study [237,238] they used 'shape control functions' to simulate surface deformations which yield a linear system of constraints solved by the singular value decomposition (SVD) method. Later in Hebei University of Technology, Liu also implemented variational B-spline (VBS) techniques and real-time energy minimization (using Hebei's VBS kernel) for surface hole filling [234,240] and for interactive surface editing [233,235] into DesignWorks. 22 A Phantom Desktop device (6 DOF input, 3 DOF output) was used for all applications.…”

“…The later versions of Virtual DesignWorks[236,238] was called De-signWorks[233,235] in subsequent publications.…”