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

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.