Interpolation of unit vectors

Summary. Time series of unit vectors occur in geophysics as palaeomagnetic poles or poles of relative motion in plate tectonics, and it is often required to trace a smooth curve through the individual points. A simple method is given for interpolating such time series based on cubic splines. The curve obtained is smooth (e.g. possesses continuous curvature) and does not depend on the choice of coordinate axes. An extension with the same desirable properties is given for the case where the given data are inexact.