| Many important geometric reasoning problems are characterized by the interdependence of configurations (spatial positions and orientations) of moving parts. Examples of such problems include mechanism workspace computation, spatial planning in the presence of obstacles, computing sweeps over curves or surfaces, shape synthesis, and packaging with motion constraints, among others. We propose the paradigm of configuration modeling by introducing new operations that effectively address the formulation of such problems by treating shapes and their configurations as subsets of the six dimensional configuration space of rigid motions SE(3). Earlier configuration space approaches have been considered impractical since they do not scale to realistic parts moving in a six dimensional configuration space. We support our formulations by providing efficient and robust computations for their solution via convolution algebras. The proposed computational approach is fast, highly parallelizable, and has been implemented on graphics hardware. These results suggest that configuration modeling is the proper and practical setting to formulate and solve configuration related geometric reasoning problems. |
