A Class of Trigonometric Polynomial Curves on Four-Point Piecewise Scheme
基于四点分段的一类三角多项式曲线

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.