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Modeling Nonconvex Constraints Using Linear Complementarity

Many physical simulators linearize contact constraints such that each contact constraint defines a half-space in the configuration space of the effected objects. By modeling contact constraints as infinitely extending half spaces it is only possible to approximate regions in configuration space that are locally convex. This implicit assumption of local convexity introduces artifacts in the results of the simulation. We present a new method for modeling regions of configuration space that are locally nonconvex using a linear complementarity formulation. From this we show that we can now accurately represent any general polytope using linear complementarity.