两个二次曲面间的二次GC^0及三次GC^1阶光滑混合拼接的代数方法  

A Blending Surface Smoothly Connects with Two Quadratic Surfaces

作　　者：周晓[1] 

机构地区：[1]安徽省芜湖师范专科学校数学系

出　　处：《信阳师范学院学报（自然科学版）》1996年第2期133-139,共7页Journal of Xinyang Normal University(Natural Science Edition)

摘　　要：本文在Ｊ．ｗａｒｒｅｎ等人的基础上，利用数值代数和算法交换代数知识为工具，分析讨论了两个二次曲面问ＧＣ~ｏ，ＧＣ~１阶光滑混合拼接的二次多项式及三次多项式的问题。按ＣＡＧＤ解决问题的顺序（即由控制曲面到混合拼接），解决了两个二次曲面间存在一个二次曲面与它们同时相交且支线是平面二次曲线的问题，并在此基础上，从理论上到具体实现上解决两个二次曲面间用一个三次曲面混合拼接问题．In this paper,by algebraic numerical calculus and by computing commutatirealgebra,we consider the following problem to look for a blending surface meeting to twoquadratic surface with order GC,GC1 rescaling continuity. We show that between two irreducibe quadratic surfaces. z (g1 ),z(g2),there exists a quadratic ruled surface z (g) with order Gc rescaling continuily and there exists a cubic blending surface z(f) which is tangent(with order GC1 rescaling continuity) to z(gl ) and z(g2)'We also discuss some principles and skills in constructing such a class of surfaces. Thegiven examples show that our method is very simple and efficient.

关 键 词：秩 素理想 二次曲面 三次曲面 光滑拼接 

分 类 号：O182.1[理学—数学]