A robust, efficient and time-stepping compatible collision detection method for non-smooth contact between rigid bodies of arbitrary shape
Résumé
This paper proposes an efficient collision detection method which is compatible
with time-stepping methods in the sense that it enables the robust simulation non-smooth contact between rigid bodies with complex shapes, including industrial CAD models of various topology and in presence of conforming contact situations. It introduces a discrete representation of rigid body shapes based on dilated simplicial complexes, which generalizes the notion of triangulation to domains of arbitrary topological dimension. It also defines finite collections of point contacts between those shapes thanks to quasi-LMDs, which are defined as an extension of local minimum distances with respect to small relative rotations, between the base complexes. Smooth gap functions associated to these point contacts are defined, as well as complete and smooth generalized contact kinematics, enabling the use of non-smooth contact laws like Signorini or Coulomb. Quasi-LMDs also lead to the stable treatment of conforming contact cases. An efficient method based on 5D+1 bounding volume hierarchies for computing quasi-LMDs is presented. Finally, robustness and performance benchmarks show that our method combined with a fast time-stepping-based solver allows interactive-time simulations of complex and possibly conforming contact situations.
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