  We study the rigidity of body-and-cad frameworks which capture the majority
of the geometric constraints used in 3D mechanical engineering CAD software. We
present a combinatorial characterization of the generic minimal rigidity of a
subset of body-and-cad frameworks in which we treat 20 of the 21 body-and-cad
constraints, omitting only point-point coincidences. While the handful of
classical combinatorial characterizations of rigidity focus on distance
constraints between points, this is the first result simultaneously addressing
coincidence, angular, and distance constraints. Our result is stated in terms
of the partitioning of a graph into edge-disjoint spanning trees. This
combinatorial approach provides the theoretical basis for the development of
deterministic algorithms (that will not depend on numerical methods) for
analyzing the rigidity of body-and-cad frameworks.
