任意螺旋线拓扑数值解法

A Topological Numerical Solution of Arbitrary Helix

根据拓扑原理,找到任意曲线的同胚圆,并造出与其相应的圆柱螺旋线,将此圆柱螺旋线和任意曲线螺旋线通过同胚关系关联起来,推导任意螺旋线方程,根据这一方程编制程序,计算几种非圆柱螺旋线.结果表明,螺旋线形状优美,和相应的曲线形状匹配,说明本文的算法合理,程序可靠,在一定程度上填补了这方面研究的空白.

According to the principle of topology,the homeomorphism circle of an arbitrary curve was found and the cylindrical spiral was created correspondingly.An equation which is uesed to describe an arbitrary spiral was deduced through homeomorphism relation with the cylindrical spiral.Several non cylindrical spirals were computed by program coded according to the equation and displayed graphically.Results show that the shape of the spirals are beautiful and matches well with the curves.All these prove that the algorithm presented in the paper is reasonable and the program is reliable.In a sense,the work done in this paper fills the gap in this research field.