Title :
Finite difference surface representation considering effect of boundary curvature
Author :
You, Lihua ; Zhang, Jian J.
Author_Institution :
Nat. Centre for Comput. Animation, Bournemouth Univ., Poole, UK
Abstract :
Surface representation using the solution to a partial differential equation (PDE) is an important topic of computer graphics and computer-aided design. In existing references, various free-from surfaces were created with a 4th-order PDE, which is only able to meet the tangential conditions at the surface boundaries. The need for a 6th-order PDE in surface modelling arises in two situations: one is to generate surfaces with curvature continuity and the other is to use curvature values as a user handle for surface shape manipulation. In this paper, we introduce such a 6th-order PDE for free-form surface generation and develop a finite difference method to solve this PDE. We also investigate the effects of boundary curvature and the vector-valued shape parameters on the surface shape. It was found that their variation has a strong influence on the shape of the surfaces and that, therefore, they can be used as flexible user handles
Keywords :
computational geometry; finite difference methods; partial differential equations; vectors; 6th-order partial differential equation; boundary curvature; computer graphics; computer-aided design; curvature continuity; curvature values; finite-difference surface representation; flexible user handles; free-form surface generation; surface boundaries; surface modelling; surface shape; surface shape manipulation; tangential conditions; vector-valued shape parameters; Computer graphics; Deformable models; Elasticity; Finite difference methods; Finite element methods; Partial differential equations; Shape; Solid modeling; Spline; Surface cracks;
Conference_Titel :
Information Visualisation, 2001. Proceedings. Fifth International Conference on
Conference_Location :
London
Print_ISBN :
0-7695-1195-3
DOI :
10.1109/IV.2001.942089
