空间有理曲线的μ基及曲线隐式化  

The μ-Basis and Implicitization of Rational Space Curves

作　　者：申立勇[1] 

机构地区：[1]华东师范大学软件学院上海高可信计算重点实验室,上海200062

出　　处：《计算机辅助设计与图形学学报》2009年第7期900-904,共5页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(90718041);中国科学院数学机械化重点实验室开放课题

摘　　要：空间有理曲线是计算机辅助几何设计中常用曲线,以空间曲线为研究对象,讨论其μ基形式,并用μ基方法快速隐式化一类曲线.首先给出μ基定义和一些基本性质,之后基于μ基方法分析给出空间曲线μ基的符号公式,进一步讨论了用μ基方法隐式化空间有理曲线.通过对结式性质的细致分析,得出一类空间曲线快速隐式化的结果,这类曲线隐式的仿射簇可以用μ基的两两单变量结式表示,对不满足条件的情况给出了反例.Rational space curves are widely used in geometric modeling, this paper studies the μ- basis of the space curves and computes the algebraic varieties based on theμ-basis. The μ-basis plays a bridging role between the parametric expression and implicit expression. After the definition tl-basis is given, the paper presents the symbolic formula to compute the t^-basis. In addition, based on the discussion of resultants, we obtain a class of space curves which can be implicitized by univariate resultant computations on the μ-basis. A typical counterexample is also proposed when the restriction is unsatisfied.

关 键 词：空间曲线 仿射簇 隐式化 μ基 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术] TP391.72[自动化与计算机技术—计算机科学与技术]