基于四点分段的一类三角多项式曲线

提出了一类m(m=1,2,3)次分段三角多项式曲线，通过引入形状参数，给出了加权三角多项式曲线，与三次B样条曲线类似。每段三角多项式曲线由4个相继的控制点生成，对于等距节点的情形，所提出的三角多项式曲线是C^2m-1连续；给出了三角开曲线和闭曲线的构造方法。论述了椭圆的表示方法，给出了三角多项式曲线与三次B样条曲线的对比，通过改变次数m或调整形状参数，可以得到不同程度地接近于控制多边形的曲线，因此，所给曲线的生成方法是一种结构简单和使用方便的曲线生成方法。

A Class of Trigonometric Polynomial Curves on Four-Point Piecewise Scheme

A class of piecewise trigonometric polynomial curves of degree m(m=1,2,3) is presented in this paper. Weighted trigonometric polynomial curves are given by using a shape parameter. Analogous to the cubic B-spline curves, each trigonometric polynomial curve segment is generated by four consecutive control points. For equidistant knots, the given trigonometric polynomial curves of degree m are C 2m-1 continuous. The construction methods of an open and a closed trigonometric polynomial curves are described. The given curves can be used to generate ellipses conveniently. The comparisons between the trigonometric polynomial curves and the cubic B-spline curves are given. By choosing m or the shape parameter, the trigonometric polynomial curve can approach to the given control polygon in a different way. Therefore, the construction method of the trigonometric polynomial curves is simple and useful for curve design.