曲面片的可展切曲面及其映射分析

摘要

论文以微分几何可展曲面理论为基础,提出了过曲面曲线构造其可展切曲面的方法,得出了可展切曲面的表达形式,对可展切曲面进行了分类,通过建立两曲面间的映射关系,实现了它们间整体与局部的映射分析,较准确地把握曲面的变形情况,并通过实例对方法进行了验证.曲面片可展切曲面的方法可以应用于曲面设计、曲面近似展开和纹理映射等方面.%Based on the developable curved surface theory of differential geometry, the method to construct the developable tangent curved surface passed a curve on a curved surface is put forward, the expression form and type division of the developable tangent curved surface is given, the overall and partial mapping analysis between two surfaces is realized through establishing the mapping relationship of them and the deformation of surface is grasped accurately. The method is validated by example and can be applied to the design and approximate development of curved surface and surface texture mapping.