基于Kirov定理的带可控参数的多结点造型方法  

Many-Knot Spline Interpolation Scheme with Controllable Parameters with Kirov’s Theorem

作　　者：马辉[1] 宋瑞霞[2] 王小春[3] 

机构地区：[1]澳门科技大学资讯科技学院 [2]北方工业大学理学院,北京100041 [3]北京林业大学理学院,北京100083

出　　处：《工程图学学报》2006年第3期73-78,共6页Journal of Engineering Graphics

基　　金：国家自然科学基金重点资助项目(60133020);国家"九七三"资助项目(G2002CB312104;2004CB318000);北京市教委科技发展计划面上资助项目(km200610009011)

摘　　要：基于Kirov定理,利用多结点样条函数,研究一类带有可控参数的曲线曲面造型方法。该方法是在普通的多结点样条中加入可控参数,通过调节这些参数可以控制插值曲线(面)在各型值点的切向量(切平面或法向量),从而达到满意的曲线(面)造型效果。该方法保持了多结点样条的基数型和局部性特点,特别是局部性使得可以只对插值曲线(面)作局部调整而不会影响整体,这有助于CAD或CAGD领域的工程人员去设计、调整曲线(面)的形状。Based on Kirov＇s Theorem, applying many-knot spline functions, one kind of curve or surface modeling method with tangent vectors or normal vectors, by which some local shapes of curves or surfaces can be controlled, has been introduced. Adding some adjustable parameters to the general many-knot spline, a new kind of interpolating curve or surface is constructed. At control points, if we can control the tangent vectors of fitting curves or normal vectors of interpolation surfaces by adjusting these parameters, the better fitting curves or interpolation surfaces can be obtained. The scheme maintains the advantages of common many-knot spline （cardinal-type, local-support）. Thus it maybe helps engineers in the field of CAD/CAGD to design and adjust fitting curves or interpolation surfaces.

关 键 词：计算机应用 计算机辅助几何设计 B样条 多结点样条 Kirov定理 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]