Closed rational trigonometric curves and surfaces
A general method of obtaining a set of basis functions is presented in order to describe curves as combinations of control points and basis functions. The starting point is in a set of basis functions and a set of corresponding weights. The basis functions are normalized by their weighted sum, obtaining a new set of basis functions, which is called, in this paper, quotient bases. Representatives of quotient bases are the rational Bernstein and B-spline functions. Several properties of rational curves/surfaces are shown to hold for this general case. Further, the rational counterpart of cyclic curves/surfaces is specified. Some applications show how rational trigonometric basis can be used for the exact description of some famous closed curves and surfaces: lemniscate of Bernoulli, Zhukovsky airfoil profile, Boy surface, Dupin cyclide.
rational Bernstein and B-spline functions
scientific article; zbMATH DE number 5724558
scientific article