Abstract
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 extends well and we present its application in the case of 2D and 3D Bézier curves as well as Bézier triangle patches and tensor-product surface patches.
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© 1999 Springer-Verlag Berlin Heidelberg
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Figueiredo, O., Hersch, R.D., Reveillès, JP. (1999). Digitization of Bézier Curves and Patches using Discrete Geometry. In: Bertrand, G., Couprie, M., Perroton, L. (eds) Discrete Geometry for Computer Imagery. DGCI 1999. Lecture Notes in Computer Science, vol 1568. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49126-0_30
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DOI: https://doi.org/10.1007/3-540-49126-0_30
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