A new approach to discrete conical curves

Conics drawing is an important issue in image processing and CAD. Many methods exist, but few are based on linear iterative methods X_n+1 = SX_n for the computation of points belonging to a conic with equation X^TCX = z. This paper studies these methods in a systematic way. It shows that S and C are linked by S = ±exp(θJC), where J is the π/2 rotation matrix and θ controls the points´ density. Different linear properties are established, especially a bijective connection with simple processes on the unit circle or unit hyperbola. Moreover, an efficient drawing algorithm for elliptic and hyperbolic arcs is derived.