基于五点分段的一类三角多项式曲线  

A Class of Trigonometric Polynomial Curves on Five-Point Piecewise Scheme

作　　者：李明珠[1] 陈丽娟[1] 张莉[2] 

机构地区：[1]青岛理工大学理学院,青岛266033 [2]山东农业大学信息科学与工程学院,泰安271018

出　　处：《青岛理工大学学报》2009年第1期112-116,共5页Journal of Qingdao University of Technology

摘　　要：提出了一类新的分段三角多项式曲线,给出了加权三角多项式曲线,表示式结构简单,能用于曲线设计.与四次B样条曲线类似,每段三角多项式曲线由5个控制点生成.对于等距节点,一次和二次三角多项式曲线是C1连续的,三次三角多项式曲线是C3连续的.利用该类分段三角多项式,给出了开曲线和闭曲线的构造方法,并提出了分段三角多项式可精确、灵活地表示椭圆.This paper presents a new class of piecewise trigonometric polynomial curves and a weighted trigonometric polynomial curve which has simple structure and can be used to design curves. Analogous to the four B-spline curves, each curve segment is generated by five consecutive control points. For equidistant knots, the trigonometric polynomial curves of first and second degrees are C^1 continuous, and those of third degree are C^3 continuous. This trigonometric polynomial can be used to construct open and closed curves. Moreover, the class of piecewise trigonometric polynomial curves can be accurate and flexible to express ellipse.

关 键 词：曲线构造 三角多项式 样条曲线 

分 类 号：O241.5[理学—计算数学]