四维画法几何中的曲线投射法

CURVE PROJECTION IN DESCRIPTIVE GEOMETRY OF FOUR DIMENSIONS

本文是研究以曲线作为辅助投射线,对四维空间中的点、直线、平面等几何元素进行投影变换的问题。文中采用了以平面为投射轴,以平面曲线为投射线的方法建立曲线投射的变换模型。并给出了两个实例,说明用此方法可解决些用一般四维画法几何的方法难以解决的问题。

This paper discusses the problem of transforming geometric elements in four dimensions using curves as projective lines.The transformation model of curve projection is successfully built which uses a plane as the projective axis and curves in a plane as projective lines.Two examples are given to illustrate that this method might be helpful to solve some of problems which are difficult for general methods.