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.

贝塞尔曲线对于几何建模和计算机图形必不可少。它们具有许多有利的特性，并为用户提供了用于编辑参数多项式曲线形状的直观工具。通过将形状参数与每个控制点相关联并考虑有理贝塞尔曲线，可以实现更大的控制和灵活性，这具有能够精确表示所有圆锥截面的附加优点。在本文中，我们探索了以重心形式表示有理贝塞尔曲线所带来的编辑可能性。特别是，我们展示了如何在Bézier和重心形式之间来回转换，我们讨论了修改重心形式的组成部分（节点，插值点，权重）的效果，我们研究了重心形式的点插入与Bézier形式的度高之间的联系。此外，我们分析了重心形式对评估曲线的有利性能。