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.