投影变换在解题中的研究比较

Projection Change in Problem Solving Research Comparison

当直线、平面等几何元素在投影面体系中处于一般位置时,求解它们的定位问题(交点、交线)或度量问题(距离、角度、实形)的作图都比较复杂;而当几何元素处于特殊位置时,问题就易于解决.投影变换就是研究如何改变空间几何元素与投影面的相对位置,或者改变投影方向,以达到简化解题的目的.笔者探讨了几种解题方法,针对一部分典型题采用一题多解的手段来比较其难易与优劣.

When the abstract geometric elements and so on straight line, plane are in the general position when the projecting plane system, solves their localization question （point of intersection, intersection） or the measure question （is away from, angle, solid shape） the mapping quite to be complex, but when the geometric element is in the special position, the question easy to solve. How is the projection change studies changes the space geometric element and the projecting plane relative position, or the change projection direction, achieves the simplified problem solving the goal. This article discusses several problem solving methods, uses a topic multi-solution in view of a part of standard topic the method to compare its difficulty and the fit and unfit quality.