心射球面投射在球面多边形拼接中的应用研究

针对球面等边多边形包覆拼接建模及出现拼接重叠等问题，分析了心射球面投射原理和共球面等边多面体的结构特征，提出了共球面等边多面体作心射球面投射的方法。由于共球面等边多面体和球面多边形包覆拼接之间存在一一对应的关系，只要找到相应顶点特征的共球面等边多面体，即可通过心射球面投射实现球面等边多边形的包覆拼接。以实例的形式通过图解共球面等边多面体的几何关系，实现了在SolidWorks环境下球面等边多边形拼接设计建模。

A Study on the Gnomonic Projection Applied to Spherical Polygons Joint

An approach is first posed by using gnomonic projection, based on the problem remaining unresolved, which is about the coating joint modeling and the joint overlap of spherical equilateral polygon. Because of the one-to-one correspondence between the equilateral polyhedra and the joint overlap of spherical equilateral, the problem can be resolved with an analysis of the principle about gnomonic projection and the structural characteristics of equilateral polyhedra, as long as the equilateral polyhedra are found with a corresponding vertex characteristic. Through diagrammatizing the geometrical relationship of equilateral polyhedra with instance, it achieves the modeling in spherical equilateral polygon joints under the SolidWorks environment.