3D Articulated Arms - Epicycles - Polygonal Paths - Fourier Decomposition

What is the parametric equation for a polygon? We know the parametric equation for a circle. Its { Sin(t), Cos(t) }. Exp( i t ) traces out a circle in the complex plane. ( i is the sqrt(-1) ). By adding two circles (epicycles) ... r_1 Exp( w_1 i t ) r_2 Exp( w_2 i t ) ... together we can generate more complex curves. E.g. Epicycloids, ellipse, deltoid, astroid, epitrochoid, hypocycloid, hypotrochoid, cardioid. By adding infinitely many together (almost) any path can be approximated.