  The proper handling of 3D orientations is a central element in many
optimization problems in engineering. Unfortunately many researchers and
engineers struggle with the formulation of such problems and often fall back to
suboptimal solutions. The existence of many different conventions further
complicates this issue, especially when interfacing multiple differing
implementations. This document discusses an alternative approach which makes
use of a more abstract notion of 3D orientations. The relative orientation
between two coordinate systems is primarily identified by the coordinate
mapping it induces. This is combined with the standard exponential map in order
to introduce representation-independent and minimal differentials, which are
very convenient in optimization based methods.
