一组基于三角函数的类三次参数曲线

Class of quasi-cubic parametric curves based on trigonometric functions

给出了一组基于函数空间{1,sin,cos,sin2}的类三次三角参数曲线,称之为QCT-曲线,主要包括QCT-Ferguson曲线、QCT-Bézier曲线及均匀QCT-B样条曲线。讨论了QCT-曲线的性质、应用及相互之间的关系。事实表明,QCT-曲线不仅具有三次多项式曲线的诸多性质,而且在一定条件下可相互转化。另外,QCT-曲线无需有理形式即可精确地表示圆、椭圆、抛物线等二次曲线弧。

A class of quasi-cubic trigonometric parametric curves based on {1, sinu, cosu, sin^2u} is presented, which are called QCT-curves, including QCT-Ferguson curve, QCT-Bézier curve and uniform QCT-B spline curve. Then, the properties, application and relationship of QCT-curves are discussed. QCT-curves have the same characteristic with traditional cubic polynomial curves, and they is converted into each other in proper condition, furthermore they can represent the arc of circle, arc of ellipse, arc of parabola and other quadratic curves without using rational form.