圆环面正轴测计算机绘图的数学模型

MATHEMATICAL PATTERN FOR DRAWING THE ORTHOGRAPHIC AXONOMETRIC PROJECTION OF A TORUS WITH A COMPUTER

本文运用图解法,在对圆环面正轴测投影的曲线性质进行投影分析的基础上,导出了圆环面正轴测投影外形线的参数方程;给出了产生尖点的几何条件和判别式;解决了尖点和虚实线分界点的定位问题.为圆环面正轴测投影的计算机绘图提供了可靠的数学依据.

The authors have derived a prametric equation of the contour curve by the graphic method and through the analysis of its na- ture on the orthographic axonometric projection of a torus.In this paper a geometrical condition leading to the tip point and a dis- criminant is given,and the orientation of the tip point and dashed and real points of division is supplied.In addition,it is mathe- matically proved that there exists a practical possibility of drawing the orthographic axonometric projection of a torus with a computer.