Interpolating Movements Using CAGD Tools

The idea is to perform interpolations with quaternions or quaternionic functions each one of whom represents a movement. We present several antecedents of different methods to perform interpolations with quaternions and other antecedents of the its use considering the fact that they represent movements for example to define surfaces in different ways. The paper is however focused on the quaternionic version of Sibson interpolant on the surface of the sphere where the scattered data are moving vortices of some fluid.