New shape control tools for rational Bézier curve design
Andriamahenina Ramanantoanina  1@  , Kai Hormann  2  
1 : Universita della Svizerra italiana
2 : Universitá della Svizzera Italiana

Bézier curves are indispensable for geometric modeling and computer graphics. They have numerous favourable properties and provide the user with intuitive tools for editing the shape of a parametric polynomial curve, for example, by modifying the control points P_0, ..., P_n. Even more control and flexibility can be achieved by associating a shape parameter alpha_i with each control point P_i and considering rational Bézier curves, which comes with the additional advantage of being able to represent all conic sections exactly. In this talk, we explore the editing possibilities that arise from expressing a rational Bézier curve in barycentric form, defined by a set of triplets (Q_i, beta_i, t_i) of interpolation points Q_i, weights beta_i, and nodes t_i. In particular, we show how to convert back and forth between the Bézier and the barycentric form, we discuss the effects of modifying the constituents (interpolation points, weights, nodes) of the barycentric form, and we study the connection between point insertion in the barycentric form with degree elevation of the Bézier form.

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