Over the years I have spent many happy but largely fruitless hours attempting to construct a genuinely independent interpolation algorithm. Here, for the delectation of math funners, is my innovatory technique for building Bezier-like closed-curve splines, recently disinterred for service in another ovipository thread. Suppose we are given n control points P_i for i = 0,...,n-1, [as Cartesian 2-vectors in the plane, homogeneous 4-vectors in space, or whatever]. We wish to construct a closed curve Q(u), passing near(?) to each control as 0 <= u <= 1, with Q(0) = Q(1) and similarly for all derivatives. Consider the weight functions f_i(u) = (2/n)*cos(Pi*(u - i/n))^2 : these are analytic, periodic over 0 <= u <= 1, and for all u sum to 1 over 0 <= i <= n-1. Furthermore f_i is nonnegative, and has its maximum at u = i/n. So a reasonable looking spline function might be Q(u) = \sum_i f_i(u) P_i. Exercise: prove that, whatever the controls, Q(u) is always an ellipse! Fred Lunnon