双参数曲面族的包络与单参数曲面族的二次包络

The Enveloping of Bi-parametric Surface Family and the Quadratic Enveloping of Singl-parametric Surface Family

摘要: 本文主要讨论以隐式及参数式给出的双参数曲面族的包络和单参数曲面族的二次包络,以及这两种包络之间的关系,从而得到了通过求双参数曲面族的包络去求出单参数曲面族的二次包络的简便方法,和与此等价的其他包络条件。

Abstract: This paper presents an approach to the enveloping of biparametric surf-ace family and the quadratic enveloping of single-parametric surface family. Both are expressed in terms of implicite or parametvic equations. A simple method fov solving the quadratic enveloping through solving of a bi-param-etric surface family and the equivalent enveloping conditions are established.