与给定多边形相切的一类代数三角混合样条曲线  

A Class of Algebraic Trigonometric Blending Spline Curves with Tangent of Given Polygon

作　　者：尹晓莎[1] 王成伟[2] 

机构地区：[1]北京服装学院材料科学与工程学院,北京100029 [2]北京服装学院基础教学部,北京100029

出　　处：《北京服装学院学报（自然科学版）》2016年第3期65-71,共7页Journal of Beijing Institute of Fashion Technology：Natural Science Edition

基　　金：北京服装学院科学研究一般项目资助(2014A-14)

摘　　要：提出了一种带形状参数的代数三角混合样条曲线,该曲线不仅与三次均匀B样条曲线具有相似的性质,而且在控制顶点保持不变时,其形状可通过形状参数的取值进行调整.描述了一种与给定多边形相切的代数三角混合可调的样条曲线的算法.在算法中,所有代数三角混合可调的样条曲线的控制点可以通过对多边形的顶点简单计算产生.所构造的曲线对多边形具有保形性,曲线可以局部修改.最后给出了两个算例,实例表明算法是有效可行的.In this paper, a class of algebraic trigonometric blending spline curves is proposed. These curves inherit the major advantages of the cubic uniform B-spline curves;meanwhile their shape can be adjusted by using shape parameters when the control vertices are fixed. An algorithm for con- structing algebraic trigonometric blending adjustable spline curves which is tangent to the given poly- gon is also described. The control points of the algebraic trigonometric blending adjustable spline curves to he constructed can be generated by simple computations from the vertices of the given poly- gon. The constructed curvesare shape-preserving to the polygons, the local modifications to the spline curves can be completed by simply adjusting the corresponding control parameters. Finally, two examples were given, which demonstrated that the algorithm was effective and feasible.

关 键 词：CAGD 代数三角混合样条曲线 多边形 形状参数 

分 类 号：O241.3[理学—计算数学]