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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
