Bézier surfaces of minimal internal energy

Authors:
Yongwei Miao;Huahao Shou;Jieqing Feng;Qunsheng Peng;A. Robin Forrest
Affiliations:
State Key Lab. of CAD&CG, Zhejiang University, Hangzhou, P.R.China;College of Science, Zhejiang University of Technology, Hangzhou, P.R.China;State Key Lab. of CAD&CG, Zhejiang University, Hangzhou, P.R.China;State Key Lab. of CAD&CG, Zhejiang University, Hangzhou, P.R.China;School of Computing Sciences, University of East Anglia, Norwich, U.K.
Venue:
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Year:
2005

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Abstract

In this paper the variational problems of finding Bézier surfaces that minimize the bending energy functional with prescribed border for both cases of triangular and rectangular are investigated. As a result, two new bending energy masks for finding Bézier surfaces of minimal bending energy for both triangular and rectangular cases are proposed. Experimental comparisons of these two new bending energy masks with existing Dirichlet, Laplacian, harmonic and average masks are performed which show that bending energy masks are among the best.