Figure 6.

We decompose the configuration space of a rigid body into a product of orientational and translational subspaces (SO(3) and , respectively). The orientation space is subdivided into a finite number of neighborhoods, and each of them is projected into translational space. The sphere on the left is a simplified illustration of SO(3); the green and yellow patches represent overlapping orientation neighborhoods (U_i and U_j). Their respective slice approximations are visualized on the right (Sl^a(U_i) and Sl^a(U_j), in green and yellow, respectively).