Designing Approximate Minimal Ruled Surfaces with a Given Geodesic

With the applications in garment manufacture,shoe making industry and material cutting,in this paper we give an algorithm to design approximate minimal ruled surfaces passing through a given geodesic.By combining the method of surface design passing through a given geodesic and the constructive technique of approximate minimal surfaces,we represent ruled surfaces in a parametric form with two parametric variables and optimize the surface representation by a variational method.Then we discuss the result with arc parameter and general parameter respectively.Finally,some examples are presented to demonstrate the efficiency of the proposed method.