A ternary subdivision scheme for generating trigonometric splines and its application to geometric modeling

In this paper, we present a ternary non-stationary subdivision scheme for generating trigonometric splines of order n with uniform knots. As a particular cases for n = 3 and n = 4, we obtain ternary subdivision schemes for generating quadratic and cubic trigonometric splines respectively. These schemes, at every level retain all the points of the previous level if the initial control points lie on the graph of a function which is a linear combination of cos((n-1)x) and sin((n-1)x).