6533b7dbfe1ef96bd1270896

RESEARCH PRODUCT

Bézier surfaces of minimal area: The Dirichlet approach

Juan Monterde

subject

Bézier surfacePure mathematicsMinimal surfaceAerospace EngineeringBézier curveComputer Science::Computational GeometryTopologyComputer Graphics and Computer-Aided DesignDirichlet distributionsymbols.namesakeComputer Science::GraphicsModeling and SimulationComputer Science::MultimediaAutomotive EngineeringsymbolsMathematics

description

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

yearjournalcountryeditionlanguage
2004-02-01Computer Aided Geometric Design
https://doi.org/10.1016/j.cagd.2003.07.009