The six-dimensional space SE (3) is traditionally associated with the space of configurations
of a rigid solid (a subset of Euclidean three-dimensional space R3). But a solid itself can be
also considered to be a set of configurations, and therefore a subset of SE (3). This
observation removes the artificial distinction between shapes and their configurations, and
allows formulation and solution of a large class of problems in mechanical design and
manufacturing. In particular, the configuration product of two subsets of configuration space …