带两个形状参数的类三次三角Bézier曲线  

QUASI CUBIC TRIGONOMETRIC Bézier CURVE WITH TWO SHAPE PARAMETERS

作　　者：李军成[1] 宋来忠[2] 龙志文[1] 

机构地区：[1]湖南人文科技学院数学系,湖南娄底417000 [2]三峡大学理学院,湖北宜昌443002

出　　处：《计算机应用与软件》2010年第2期218-220,共3页Computer Applications and Software

摘　　要：给出了一种基于三角函数的类三次三角Bézier曲线,并简称为QCT-Bézier曲线,其基函数由四个带两个形状参数的三角多项式组成。由四个顶点控制的QCT-Bézier曲线不仅具有类似于三次Bézier曲线的诸多性质,而且其形状可通过修改两个形状进行局部或整体调节,方便设计不同形状的曲线。选取适当的形状参数,可使两条QCT-Bézier曲线段在连接点处满足C3拼接。另外,在适当条件下,QCT-Bézier曲线无需有理形式即可精确地表示圆弧、椭圆弧、抛物线弧等二次曲线。A kind of quasi cubic trigonometric Bezier curve based on trigonometric function, in short, QCT-Bezier curve, is presented in this paper. Its basic function is constructed by four trigonometric polynomials with two shape parameters each. The four vertices controlled QCT-Bezier curve has a lot of properties similar to cubic Brzier curve, and its shape can be locally or globally adjusted by modifying two shape parameters, which is convenient for designing curves in different shape. Properly choosing shape parameters can satisfy C^3 stitching of two- piece QCT-BEzier at their joints. In addition, in appropriate condition, the QCT-BEzier curve can represent other quadratic curves such as circle arc, elliptic arc and parabola arc accurately without rational form.

关 键 词：三角曲线 BÉZIER曲线 形状参数 二次曲线 曲线设计 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术] TP391.41[自动化与计算机技术—计算机科学与技术]