椭圆上特殊点的准确作图原理简析

A Brief Analysis of the Principle of Drawing Graphs Accurately on Special Points of Ellipses

画法几何中用八点法作椭圆时,一般是根据圆的外切四边形画出平行四边形,从而确定两对特殊的共轭直径,所画椭圆的8个特殊点中总有4个点可以比较直观地确定,而其余4个点只能近似地在相应的共轭直径上求出。本文应用仿射对应等方法,阐述了准确定出椭圆周必定经过的特殊点的位置,并提出其作图的理论根据,同时提供了多种准确快速地确定这些特殊点的方法。

When eight points method is used to draw an ellipse in the technique of drawing of geometry,a parallelogram is generally drawn according to the circumscribed parallelogram of a circle so as to locate the two special conjugate diameters.Four points among the eight special points of the ellipse can be determined by direct perceiving through the senses,but the rest points have to be got approximately on the conjugate diameter.The accurate location of the special position of an ellipse is expounded by means of similar profecting and corresponding method in this paper.The theoretical foundation of drawing graphs is given,and various approaches to locating the special points accurately and rapidly are offered as well.