一类极小曲面的几何设计

极小曲面是变分学意义下具有极小面积的曲面。它能量最小、结构稳定的优点。形如马鞍的负高斯曲率的极小曲面可作为房顶曲面的设计模型。由负高斯曲率的极小曲面设计得到房顶曲面不但外形美观，而且牢固经济。该文提出一种几何构造法，得到了一类三次多项式形式的负高斯曲率极小曲面，将其表示为三次Ｂ－Ｂ曲面，进而高次Ｂ－Ｂ曲面表示出负高斯曲率极小曲面的裁剪曲面以增加设计的灵活性。算法给出一个可变参数，通过调整该参数可改

GEOMETRIC DESIGN OF A CLASS OF MINIMAL SURFACE WITH NEGATIVE GAUSSIAN CURVATURE

A minimal surface is a kind of surface with minimum area in the sense of variation. A minimal surface has advantages of minimal energy and stable structure. A minimal surface with negative Gaussian curvature looks like a saddle. It can be used to model a roof surface,which is economic and stable and looks nice. In this paper, an effective method is presented for the construction of minimal surface possessing negative Gaussian curvature, the form of which is a parameter polynomial of degree 3. It is represented as a cubic Bernstein Bezier surface. To increase its relaxation in the design, a minimal trimmed surface is also represented as a Bernstein Bezier surface of higher degree by reparametering method. Its shape can be changed by adjusting some shape parameter.