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Bézier surfaces of minimal internal energy. (English) Zbl 1141.65343

Martin, Ralph (ed.) et al., Mathematics of surfaces XI. 11th IMA international conference, Loughborough, UK, September 5–7, 2005. Proceedings. Berlin: Springer (ISBN 3-540-28225-4/pbk). Lecture Notes in Computer Science 3604, 318-335 (2005).
Summary: 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.
For the entire collection see [Zbl 1086.68006].

MSC:

65D17 Computer-aided design (modeling of curves and surfaces)
65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
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