Normalized B-basis of the space of trigonometric polynomials and curve design

A normalized B-basis of the space of trigonometric polynomials of degree n is presented. Some interesting properties of the basis functions are given. Based on the basis, symmetric trigonometric polynomial curves like Bézier curves are constructed. The trigonometric polynomial curves present the shape of their control polygons well. Thus the theoretics and methods are proposed for curve representation of the trigonometric polynomial space. By adding additional control points, the given graph examples show that the trigonometric polynomial curves are nearer their control polygons than the Bézier curves for the same parametric variable and the same degree.