Determining the possible positions and motions of objects based on their geometry is fundamental to reasoning about the physical world, for example in robot planning or mechanical design. Existing techniques are based on the geometry of object boundaries and limited in the degrees of freedom they allow, or in the object shapes that can be considered. In this paper, I present a technique which is based on the topology of objects and space, and does not require a closed-form representation of object boundaries. The technique is simpler, more efficient and more robust than techniques based on geometry. However, it is limited to objects which can be represented as the union of convex subparts.
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