带形状参数的三次三角DP曲线的构造  

Construction of the cubic trigonometric DP curve with shape parameters

作　　者：彭兴璇[1] 王研 宋九锡 PENG Xingxuan;WANG Yan;SONG Jiuxi(School of Mathematics, Liaoning Normal University, Dalian 116029, China)

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《辽宁师范大学学报（自然科学版）》2022年第1期6-12,共7页Journal of Liaoning Normal University:Natural Science Edition

摘　　要：以Delgado和Pena在2003年所给出的一类全新的DP-NTP曲线理论为基础,构造了一类带形状参数的三次三角DP曲线.该曲线具有三次多项式DP曲线的优良性质,基函数是一组规范全正基,而且还带有两个形状参数,这使得曲线具有更强、更加灵活的表现能力,增强了曲线的形状控制能力,也更适用于曲线设计.另外,在非有理形式情形下,该曲线能精确地表示圆、椭圆、抛物线等圆锥曲线,并且给出了圆周曲线、椭圆和抛物线的精确表示算例,验证了所得研究结论的有效性.In this paper,based on the theory of DP-NTP curve given by Delgado and Pena in 2003,a set of cubic trigonometric DP curve with shape parameters is presented.The curve has good properties of the cubic DP curve.The basis is a set of normalized totally positive basis.It has two parameters.The introduction of shape parameters enhances the shape control ability of the curve,which is better for curve design.And in the case of non-rational function,the conic section such as circle,ellipse and parabola can be accurately represented.In the paper the examples for the circle,ellipse and parabola are given,which show the effectiveness of the theory.

关 键 词：DP曲线 三角多项式曲线 形状参数 

分 类 号：O241.5[理学—计算数学]