Through a geometncal approach of the blossoming pnnciple, we achieve a dimension élévation process for extended Chebyshev spaces Applied to a nested séquence ofsuch spaces included in a polynomial one, this allows to compute the Bézier points from the initial Chebyshev-Bézier points This method leads to interesting shape effects © Elsevier, Paris

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We consider special rational triangular Bézier surfaces of degree 2 on the sphere in standard form and show that these surfaces are parameterized by chord lengths. More precisely, it is shown that the ratios of the three distances of a point to the patch vertices and the ratios of the distances of the parameter point to the three vertices of the (suitably chosen) domain triangle are identical. ...

In this paper, an efficient algorithm for automatic outline capture of digital character images is presented. This method is well suited for non-Roman languages like Arabic, Urdu, Persian, etc. Contemporary word processing systems store shapes of the characters in terms of their outlines, and outlines are expressed as cubic Bezier curves. The process of capturing outlines includes steps detecti...

An algorithm is presented that generates developable Bézier surfaces through a Bézier curve of arbitrary degree and shape. The algorithm has two important advantages. No (nonlinear) characterizing equations have to be solved and the control of singular points is guaranteed. Further interpolation conditions can be met.  2003 Elsevier B.V. All rights reserved.

In this paper, we propose a novel raindrop shape model for the detection of view-disturbing, adherent raindrops on inclined surfaces. Whereas stateof-the-art techniques do not consider inclined surfaces because they assume the droplets as sphere sections with equal contact angles, our model incorporates cubic Bézier curves that provide a low dimensional and physically interpretable representati...

15 Parametric Curves And Surfaces 15.1 Parametric Curves Designing Curves • We don’t want only polygons. • Curves are used for design. Users require a simple set of controls to allow them to edit and design curves easily. • Curves should have infinite resolution, so we can zoom in and still see a smooth curve. • We want to have a compact representation. Parametric functions are of the form x(t)...

In this paper, we present arc-length estimations for quadratic rational Bézier curves using the length of polygon and distance between both end points. Our arc-length estimations coincide with the arc-length of the quadratic rational Bézier curve exactly when the weight w is 0, 1 and∞. We show that for all w > 0 our estimations are strictly increasing with respect to w. Moreover, we find the pa...

In this paper, we present arc-length estimations for quadratic rational Bézier curves using the length of polygon and distance between both end points. Our arc-length estimations coincide with the arc-length of the quadratic rational Bézier curve exactly when the weight w is 0, 1 and∞. We show that for all w > 0 our estimations are strictly increasing with respect to w. Moreover, we find the pa...