Digitization of Bezier Curves and Patches using Discrete Geometry

O. Figueiredo, J.-P. Reveillès, R.D. Hersch

Discrete Geometry for Computer Imagery, Proceedings of the 8th International Conference DGCI'99, Marne-la-Vallee, France, March 1999, Gilles Bertrand, Michel Couprie, Laurent Perroton, Eds., LNCS 1568, Springer Verlag, 388-398

Existing algorithms for rendering Bézier curves and surfaces fall into two categories: iterative evaluation of the parametric equations (generally using forward differencing techniques) or recursive subdivision. In the latter case, all the algorithms rely on an arbitrary precision constant (tolerance) whose appropriate choice is not clear and not linked to the geometry of the image grid. In this paper we show that discrete geometry can be used to improve the subdivision algorithm so as to avoid the need for any arbitrary value. The proposed approach is applied to 2D and 3D Bézier curves as well as Bézier triangle and tensor-product surface patches.

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