Quaternion rational Bézier curves - Zube, Severinas (Lietuvos matematikos rinkinys, 2011)
We extended the rational Bézier model for space curve, by allowing quaternion weights. These curves are Möbius invariant and have halved degree with respect to real Bézier curves. This simplify the analysis of curves. In general, these curves are in four dimensional space. We analyze when the quadratically parameterized quaternion curve is in usual three dimensional subspace.
Keywords: circle; inversion; quaternion; weight point