Ω-Arithmetization of Ellipses

International audienceMulti-resolution analysis and numerical precision problems are very important subjects in fields like image analysis or geometrical modeling. In the continuation of our previous works, we propose to apply the method of Ω-arithmetization to ellipses. We obtain a discrete multi-resolution representation of arcs of ellipses. The corresponding algorithms are completely constructive and thus, can be exactly translated into functional computer programs. Moreover, we give a global condition for the connectivity of the discrete curves generated by the method at every scale

Computer Graphics in Rapid Prototyping Technology

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Digitization of Bézier curves and patches using discrete geometry

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

Arithmetic Discrete Parabolas

International audienceIn the present paper, we propose a new definition of discrete parabolas, the so-called arithmetic discrete parabolas. We base our approach on a non-constant thickness function and characterized the 0-connected and 1-connected parabolas in terms of thickness function. This results extend the well-known characterization of the κ-connectedness of arithmetic discrete lines, depending on the norm || ·||∞ and || ·||1 of their normal vector