过测地线的近似极小直纹曲面设计

Designing Approximate Minimal Ruled Surfaces with a Given Geodesic

为了在服装鞋帽制造业及材料剪裁中采用过给定测地线且具有近似最小面积的直纹曲面,提出一种直纹曲面算法.该算法将过给定测地线的曲面设计和近似极小曲面的逼近技术进行有机结合,把直纹曲面表示成含2个参变量的形式;利用变分法的思想进行最优化,并分别在弧长参数和一般参数下对其进行了讨论.最后通过一些实例验证了文中算法的正确性和有效性.

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.