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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.

MSC:

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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