The Plateau-Bézier Problem
نویسنده
چکیده
We study the Plateau problem restricted to polynomial surfaces using techniques coming from the theory of Computer Aided Geometric Design. The results can be used to obtain polynomial approximations to minimal surfaces. The relationship between harmonic Bézier surfaces and minimal surfaces with free boundaries is shown.
منابع مشابه
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 surf...
متن کاملDegree Reduction of Disk Wang-Bézier Type Generalized Ball Curves
A disk Wang-Bézier type generalized Ball curve is a Wang-Bézier type generalized Ball curve whose control points are disks in a plane. It can be viewed as a parametric curve with error tolerances. In this paper, we discuss the problem of degree reduction of disk Wang-Bézier type generalized Ball curve, that is, bounding disk Wang-Bézier type generalized Ball curves with lower degree disk Wa...
متن کاملApproximation methods for the Plateau-Bézier problem
The stretching energy functional and the bending energy functional are widely used for approximating the solution of the Plateau-Béizer Problem. This paper presents another two simple methods by using the extended stretching energy functional and the extended bending energy functional. The resulting surface obtained by the new methods will have a smaller area. Comparisons are made with both the...
متن کاملDegree Reduction of Disk Wang-Bézier Type Generalized Ball Curves
A disk Wang-Bézier type generalized Ball curve is a Wang-Bézier type generalized Ball curve whose control points are disks in a plane. It can be viewed as a parametric curve with error tolerances. In this paper, we discuss the problem of degree reduction of disk Wang-Bézier type generalized Ball curve, that is, bounding disk Wang-Bézier type generalized Ball curves with lower degree disk Wa...
متن کاملOn Bézier surfaces in three-dimensional Minkowski space
0. Introduction A Bézier surface is defined using mathematical spline functions whereby the resulting surface has a compact analytic description. This enables such surfaces to be easily manipulated, and they also have greater continuity properties. Bézier curves and surfaces are commonly used in computer-aided design [1,2], image processing [3,4], and finite elementmodeling (e.g. [5–7]). Many o...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003