Quadratic rational Bézier curve transformation is widely used in the field of computational geometry. In this paper, we offer several important characteristics of the quadratic rational Bézier curve. More precisely, on the basis of proving its monotonicity, the necessary and sufficient conditions for transforming a quadratic rational Bézier curve into a point, line segment, parabola, elliptic arc, circular arc, and hyperbola are proved, respectively.

中文翻译：

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表达二次有理Bézier曲线的充要条件

二次有理Bézier曲线变换已广泛用于计算几何领域。在本文中，我们提供了二次有理贝塞尔曲线的几个重要特征。更确切地说，在证明其单调性的基础上，分别证明了将二次有理Bézier曲线转换为点，线段，抛物线，椭圆弧，圆弧和双曲线的必要和充分条件。