参数曲线的分段近似隐式化  

Piecewise approximate implicitization of parametric curves

作　　者：李彩云[1] 朱春钢[1] 王仁宏[1] 

机构地区：[1]大连理工大学数学科学学院,辽宁大连116024

出　　处：《高校应用数学学报（A辑）》2010年第2期202-210,共9页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(60533060;10801024;U0935004);中国科学院高温气体动力学重点实验室开放基金

摘　　要：曲线的参数形式和隐式形式之间的相互转化在CAGD和造型中起着重要的作用,将参数形式的曲线转化为代数形式的曲线的过程称为隐式化.由于复杂参数曲线的精确隐式化比较困难,因此近似隐式化就显得非常重要.基于隐函数样条与异度隐函数样条,作者提出了参数曲线分段近似隐式化方法,并给出具体算法.通过实例对比,说明了此方法的简洁性和有效性.The mutual transformation between parametric equation and implicit equation of curve plays an important role in CAGD, and the procedure of finding the implicit form of a parametric equation is called implicitization. Since the exact implicitization of a parametric curve is generally complex and difficult, approximate implicitization appears very important. Based on functional spline curves（with different degrees of smoothness）, a new method for implicitization is presented. Moreover, an algorithm is given, and examples are provided to illustrate the efficiency and simplicity of the new method.

关 键 词：隐函数样条 隐式曲线 近似隐式化 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]