Two equations are presented which express the derivative of a rational Bézier curve in terms of its control points and weights. These equations are natural generalisations of the non-rational case and various properties are found from them. Bounds on the magnitude of the derivative and the direction of the derivative (the hodograph) are obtained. Expressions for the second derivative, curvature...

In this paper, we present a geometric construction of control meshes of helicoids over trapezium domain. We first introduce the quasi-Bézier basis in the space spanned by {1, t, cos t, sin t, t sin t, t cos t}, with t ∈ [0, α], α ∈ [0, 2π). We denote the curves expressed by the quasi-Bézier basis as algebraic-trigonometric Bézier curves, for short ATBézier curves. Then we find out the transform...

The presentation of Bézier surfaces affects the results of rendering and tessellating applications greatly. To achieve optimal parameterization, we present two reparameterization algorithms using linear Möbius transformations and quadratic transformations, respectively. The quadratic reparameterization algorithm can produce more satisfying results than the Möbius reparameterization algorithm wi...

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...