Bézier surfaces of minimal area: The Dirichlet approach

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.