1. A computer program product for implementing a method for interpolating rotations from a computing input device, the computer program product comprising one or more computer storage devices having computer executable instructions encoded thereon which, when executed upon one or more computer processors, perform the method comprising: receiving one or more data structures comprising two rotations, A 1 and A 2 ; expressing each rotation as a composition of two reflections, each reflection having a common initial reflection for each of the rotations, such that A 1 =R 1 R and A 2 =R 2 R 1 and each reflection R j being of the form R j =2u j u j T −I; interpolating two unit vectors, u 0 and u 1 , by u s , 0<s<1, using a standard spherical interpolation on a two-dimensional unit sphere in three-dimensions; computing interpolated rotations using the formula A S =R s R.