四维轴测图计算机显示的数学基础

THE MATHEMATIC FUNDAMENTAIS FOR DISPLAYING THE FOUR-DIMENSIONAL AXONOMETRIC DRAWING USING COMPUTER

作者在1983年提出了“四维正等轴测投影”的思想之后,本文又提出了四维轴测图计算机显示的数学方法,研究了四维空间旋转变换及变换规律和方法;并对四维正等轴测轴进行了优化处理,找到一种既简便又较直观的四维正等轴测图的轴向角及变形系数。

In this paper,a mathematic method to display the axonometric drawings of the four-dimensionalobjects by computer is presented.It is a compound transformation of rotating and orthographic projec-tion for geometric elements in four-dimensional space.Thus the four-dimensional isometric drawingscan be obtained.The rotating transformation and its regulerity are studied systematically.And the four-dimensional isometric axes are optimized.A simple and clear shaft angle and distortional coefficient ofeach axis in the four-dimensional isometric drawings are obtained.Therefore,a new way to study andsolve problems in four-dimensional space′s provided.This method can be developed from 4-D into theN-dimensional space.