可调的类三次Bzier三角曲线  

Modifiable Quasi Cubic Bézier Trigonometric Curves

作　　者：李军成[1] 陈国华[1] 杨笃庆[1] 

机构地区：[1]湖南人文科技学院数学系,湖南娄底417000

出　　处：《计算机工程与科学》2010年第3期69-71,共3页Computer Engineering & Science

基　　金：湖南人文科技学院资助项目(2008QN012)

摘　　要：本文给出了一种基于函数1、sinu、cosu和sin2u的可调类三次参数曲线,由四个顶点控制的曲线不仅具有类似于三次Bzier曲线的诸多性质,而且其形状可由一个参数进行调节,使得该曲线具有更强的表现能力。为便于自由曲线的设计,还讨论了两段曲线的拼接条件。结果表明,该曲线在拼接方面比三次Bzier曲线具有优越性,在适当选取形状参数时,两条曲线可在连接点处达到C3拼接,其拼接条件也比三次Bzier曲线简单得多,因此该曲线更适用于曲线造型。另外,该曲线无需有理形式即可精确地表示圆、椭圆、抛物线等二次曲线,方便实际应用。A modifiable quasi cubic curve based on functions 1, sinu, cosu, sin2 u is presented in this paper. The curve is controlled by four points, and it has a lot of similar characteristics to the cubic Bezie curve, and its shape can be adjusted by a parameter, which makes the curve have more powerful expression ability. For designing free curves, the continuity condition of two-piece curves is discussed. As a result, the continuity of the curve is better than the cubic Bezier curve, two-piece curves can be Ca continuous when choosing a proper shape parameter, and the continuity condition of the curve is simpler than the cubic Bezier curve. In addition, the curve can represent elliptic curves, parabola and other conical curves without using a rational form, which is helpful for practical applications.

关 键 词：三角曲线 Bzier曲线 可调 拼接性 二次曲线 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]