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Variational surface design under normal field guidance

  • Wu, Weidong (Department of Mathematics, Zhejiang University) ;
  • Yang, Xunnian (Department of Mathematics, Zhejiang University)
  • Received : 2014.11.25
  • Accepted : 2014.12.17
  • Published : 2015.07.01

Abstract

This paper proposes a novel method for shape design of a Bezier 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 Bezier 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.

Keywords

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