Abstract
Bézier curves are indispensable for geometric modelling and computer graphics. They have numerous favourable properties and provide the user with intuitive tools for editing the shape of a parametric polynomial curve. Even more control and flexibility can be achieved by associating a shape parameter with each control point and considering rational Bézier curves, which comes with the additional advantage of being able to represent all conic sections exactly. In this paper, we explore the editing possibilities that arise from expressing a rational Bézier curve in barycentric form. 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 (nodes, interpolation points, weights) of the barycentric form, and we study the connection between point insertion in the barycentric form with degree elevation of the Bézier form. Moreover, we analyse the favourable performance of the barycentric form for evaluating the curve.
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