二次曲面简便化简方法解析

在立体几何中,二次曲面的化简是非常重要的问题,课本中一般利用不变量来判断二次曲面的类型及形状.用不变量化简二次曲面,不易写出坐标变换及直角坐标系间的对应关系.本文在传统二次曲面解法的基础上面,提出两种化简步骤,正交配方化简法与主径面化简法.第一种方法相对更容易理解,但计算相对较为复杂;第二种方法计算相对简单,但由于引入主径面、渐进方向等相关概念,较为抽象,不易理解.

Explanation of Simplification Method of Quadric Surface

In Solid geometry,simplification of quadric surface is a very important problem.In the textbook,invariant ia used to determine the type and shape of quadric surface.It is not easy to show the corresponding relation between the transformation of coordinates and right triangle coordinates.This paper offers two methods of simplification: quadrature formula simplification and main surface simplification.The first one is relatively easy to understand but calculation is relatively complex.The second one is relatively easy to calculate but more abstract and not easy to understand because of the introduction of concept of main surface and the progressive direction.