Variational surface design under normal field guidance. Issue 3 (9th March 2015)

• Record Type: Journal Article
• Authors: Wu, Weidong; Yang, Xunnian
• Is Part Of: Journal of computational design and engineering. Volume 2:Issue 3(2015)
• Page Start: 129
• Page End: 136
• Publication Date: 2015-03-09
• Subjects: Membrane energy functional -- Thin plate energy functional -- Normal vector field -- Geometric modeling; Engineering -- Data processing -- Periodicals; Computer-aided design -- Periodicals; Computer-aided design; Engineering -- Data processing; Electronic journals; Electronic journals; Periodicals; 620.0042
• DOI: 10.1016/j.jcde.2015.03.001
• Languages: English
• ISSNs: 2288-4300

Abstract

Abstract: This paper proposes a novel method for shape design of a Bézier surface with given boundary curves. The surface is defined as the minimizer of an extended membrane functional or an extended thin plate functional under the guidance of a specified normal field together with an initial prescribed surface. For given boundary curves and the guiding normal field, the free coefficients of a Bézier surface are obtained by solving a linear system. Unlike previous PDE based surface modeling techniques which construct surfaces just from boundaries, our proposed method can be used to generate smooth and fair surfaces that even follow a specified normal field. Several interesting examples are given to demonstrate the applications of the proposed method in geometric modeling.