Kinematic interpretation of quaternionic–Bézier curves and surfaces is revealed. This combination of kinematic and geometric modeling methods is used to characterize orbits of quadratic surfaces in the Study quadric under the kinematic map as certain Darboux cyclides. In particular, earlier unknown rational parametrizations of one-oval Darboux cyclides are found.

中文翻译：

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Darboux cyclides的运动学解释

揭示了四元-贝塞尔曲线和表面的运动学解释。运动学和几何学建模方法的这种组合被用来将运动学图谱下二次方研究中二次曲面的轨道表征为某些达布克斯环。特别是发现了一个椭圆形的Darboux环化物的早期未知的有理参数化。