This paper presents a contact analysis algorithm for pairs of rigid, curved, planar parts based on configuration space computation. The algorithm is part of a dynamical simulator for planar systems with changing contact topologies. The configuration space of a pair of parts is a data structure that encodes the contact configurations for all pairs of part features. The configuration spaces of the interacting pairs in the mechanical system are constructed before the simulation. At each time step, the simulator queries the configuration spaces for contact changes instead of performing collision detection. The simulator demonstrates the efficacy of the configuration space approach to contact analysis. It achieves real-time performance on systems with complex contact geometry, curved parts, and changing contacts.

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