3种带形状参数的二次三角样条曲线  

Three kinds of quadratic trigonometric spline curves with shape parameter

作　　者：严兰兰[1,2] 黄涛[1] 梁炯丰[3] 

机构地区：[1]东华理工大学数学与信息科学学院,江西抚州344000 [2]东华理工大学放射性地质与勘探技术国防重点学科实验室,江西抚州344000 [3]东华理工大学土木与环境工程学院,江西抚州344000

出　　处：《合肥工业大学学报（自然科学版）》2010年第4期632-636,共5页Journal of Hefei University of Technology：Natural Science

摘　　要：构造了3种带参数的三角样条基,基于这3组基定义了3种三角样条曲线。与二次B样条曲线类似,这3种曲线的每一段都由相继的3个控制顶点生成。这3种曲线具有许多与二次B样条曲线类似的性质,但它们的连续性都比二次B样条曲线更好。对于等距节点,在一般情况下,这3种曲线都整体C2连续,在特殊条件下它们都可达C3连续。另外,这3种曲线都具有比二次B样条曲线更好的对控制多边形的逼近性。Three kinds of trigonometric spline bases are constructed in this paper. Based on these bases, three kinds of trigonometric spline curves are defined. As each piece of these trigonometric spline curves is generated by three consecutive control points, these curves retain many properties of the quadratic B-spline curve, but they have higher order of continuity than the quadratic B-spline curve. For equidistant knots, these curves are C2 continuous, and they are Ca continuous under special conditions. Besides, these curves are closer to the control polygon than the quadratic B-spline curve.

关 键 词：三角基 样条曲线 形状参数 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]