Bézier surfaces of minimal area: the Dirichlet approach. (English) Zbl 1069.65559

Summary: The Plateau-Bézier problem consists in finding the Bézier surface with minimal area from among all Bézier surfaces with prescribed border. An approximation to the solution of the Plateau-Bézier problem is obtained by replacing the area functional with the Dirichlet functional. Some comparisons between Dirichlet extremals and Bézier surfaces obtained by the use of masks related with minimal surfaces are studied.


65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
65D17 Computer-aided design (modeling of curves and surfaces)
68U07 Computer science aspects of computer-aided design
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[1] Arnal, A.; Lluch, A.; Monterde, J., Triangular Bézier surfaces of minimal area, (), 366-375
[2] Cosı́n, C.; Monterde, J., Bézier surfaces of minimal area, (), 72-81 · Zbl 1055.68119
[3] do Carmo, M.P., Differential geometry of curves and surfaces, (1976), Prentice-Hall International Englewood Cliffs, NJ · Zbl 0326.53001
[4] Farin, G., Curves and surfaces for computer aided geometric design. A practical guide, (2001), Morgan Kaufmann San Mateo, CA
[5] Farin, G.; Hansford, D., Discrete coons patches, Comput. aided. geom. design, 16, 691-700, (1999) · Zbl 0997.65033
[6] Gray, A., Modern differential geometry of curves and surfaces with Mathematica, (1998), CRC Press Boca Raton, FL · Zbl 0942.53001
[7] Greiner, G., Blending surfaces with minimal curvature, (), 163-174
[8] Monterde, J., The plateau-Bézier problem, (), 262-273 · Zbl 1274.65047
[9] Moreton, H.P.; Séquin, C.H., Functional minimization for fair surface design, (), 167-176
[10] Nitsche, J.C.C., Lectures on minimal surfaces, vol. 1, (1989), Cambridge Univ. Press Cambridge · Zbl 0202.20601
[11] Osserman, R., A survey of minimal surfaces, (1986), Dover New York · Zbl 0209.52901
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