A trigonometric curve is a real plane curve where each coordinate is given parametri-cally by a truncated Fourier series. The trigonometric curves frequently arise in various areas of mathematics, physics, and engineering. Some trigonometric curves can be also represented implicitly by bivariate polynomial equations. In this paper, we give algorithms for (a) simplifying a given parametric repre...

The partial fraction decomposition method is explored to establish several interesting trigonometric function identities, which may have applications to the evaluation of classical multiple hypergeometric series, trigonometric approximation and interpolation. 1. Outline and introduction Recently, in an attempt to prove, through the Cauchy residue method, Dougall’s theorem (Dougall [6, 1907], se...

This paper studies the merits of using knot interval notation for B-spline curves, and presents formulae in terms of knot intervals for common B-spline operations such as knot insertion, differentiation, and degree elevation. Using knot interval notation, the paper introduces MD-splines, which are B-spline-like curves that are comprised of polynomial segments of various degrees (MD stands for “...