A generalized Cayley transform relationship between orthogonal orientation matrices and skew-symmetric matrices has been introduced. This generalized transform depends on a scalar parameter that can be manipulated to generate a (Cayley) family of attitude coordinates in three-dimensional space. One class of Cayley attitude coordinates, the IPs, is special. The IPs removes the need of shadow parameters and switching logic when parameterizing orientation. They are are a natural partition and recollection of the traditional modified Rodrigues parameters and their shadows.
