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.
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Arnal, A., Lluch, A., Monterde, J.: Triangular Bézier surfaces of minimal area. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (eds.) ICCSA 2003. LNCS, vol. 2669, pp. 366–375. Springer, Heidelberg (2003)
Brunnett, G., Hagen, H., Santarelli, P.: Variational design of curves and surfaces. Surv. Math. Industry 3(27), 1–27 (1993)
Cosín, C., Monterde, J.: Bézier surfaces of minimal area. In: Sloot, P.M.A., Tan, C.J.K., Dongarra, J., Hoekstra, A.G. (eds.) ICCS-ComputSci 2002. LNCS, vol. 2330, pp. 72–81. Springer, Heidelberg (2002)
do Carmo, M.P.: Differential Geometry of Curves and Surfaces. Prentice-Hall International, Englewood Cliffs (1976)
Farin, G., Hansford, D.: Discrete Coons patches. Computer Aided Geometric Design 16(7), 691–700 (1999)
Floater, M., Reimers, M.: Meshless parameterization and surface reconstruction. Computer Aided Geometric Design 18(2), 77–92 (2001)
Gallier, J.: Curves and Surfaces in Geometric Modeling. Morgan Kaufmann publishers, San Francisco (2000)
Greiner, G., Loos, J., Wesselink, W.: Data dependent thin plate energy and its use in interactive surface modeling. Computer Graphics Forum 15(3), 175–186 (1996)
Hagen, H.: Variational principles in curve and surface design. In: Fisher, R.B. (ed.) Proceedings of the 5th IMA Conference on the Mathematics of Surfaces, Edinburgh, pp. 169–190. Clarendon Press, Oxford (1994)
Monterde, J.: The Plateau-Bézier problem. In: Wilson, M.J., Martin, R.R. (eds.) Mathematics of Surfaces. LNCS, vol. 2768, pp. 262–273. Springer, Heidelberg (2003)
Monterde, J.: Bézier surfaces of minimal area: The Dirichlet approach. Computer Aided Geometric Design 21(2), 117–136 (2004)
Petitjean, S.: A survey of methods for recovering quadrics in triangular meshes. ACM Comput. Surv. 34(2), 211–262 (2002)
Schneider, R., Kobbelt, L.: Geometric fairing of irregular meshes for free-form surface design. Computer Aided Geometric Design 18(4), 359–379 (2001)
Terzopoulos, D., Platt, J., Barr, A., Fleischer, K.: Elastically deformable models. In: ACM SIGGRAPH 1987, pp. 205–214 (1987)
Veltkamp, R., Wesselink, W.: Modeling 3d Curves of minimal energy. Computer Graphics Forum 14(3), 97–110 (1995)
Veltkamp, R., Wesselink, W.: Variational modeling of triangular Bézier surfaces. Technical reports of Utrecht University, report no: UU-CS-1996-40 (1996)
Welch, W., Witkin, A.: Variational surface modeling. In: ACM SIGGRAPH 1992, pp. 157–166 (1992)
Welch, W., Witkin, A.: Free-Form shape design using triangulated surfaces. In: ACM SIGGRAPH 1994, pp. 247–256 (1994)
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Miao, Y., Shou, H., Feng, J., Peng, Q., Forrest, A.R. (2005). Bézier Surfaces of Minimal Internal Energy. In: Martin, R., Bez, H., Sabin, M. (eds) Mathematics of Surfaces XI. Lecture Notes in Computer Science, vol 3604. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11537908_19
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DOI: https://doi.org/10.1007/11537908_19
Publisher Name: Springer, Berlin, Heidelberg
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