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A new approach to discrete conical curves

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4 Author(s)
Becker, J.-M. ; Univ. Jean Monnet St Etienne, France ; Mennessier, C. ; Figueiredo, O. ; Odin, D.

Conics drawing is an important issue in image processing and CAD. Many methods exist, but few are based on linear iterative methods Xn+1 = SXn for the computation of points belonging to a conic with equation XTCX = 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.

Published in:

Signals, Circuits and Systems, 2005. ISSCS 2005. International Symposium on  (Volume:1 )

Date of Conference:

14-15 July 2005