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Fast contact evolution for piecewise smooth surfaces Kry, Paul G.

Abstract

Dynamics simulation of smooth bodies in contact is a critical problem in physically based animation and interactive virtual environments. We describe a technique which uses reduced coordinates to evolve a single continuous contact between Loop subdivision surfaces. The incorporation of both slip and no-slip friction into our algorithm is straightforward. The dynamics equations, though slightly more complex due to the reduced coordinate formulation, can be integrated easily using explicit integrators without the need for constraint stabilization. The use of reduced coordinates also confines integration errors to lie within the constraint manifold which is preferable for visualization. Our algorithm is suitable for piecewise parametric or parameterizable surfaces with polygonal domain boundaries. Because a contact will not always remain in the same patch, we demonstrate how a contact can be evolved across patch boundaries. We also address the issue of non-regular parameterizations occurring in Loop subdivision surfaces through surface replacement with n sided S-patch surfaces. Three simulations show our results. We partially verify our technique first with a frictionless system and then with a blob sliding and rolling inside a bowl. Our third simulation shows that our formulation correctly predicts the spin reversal of a rattleback top. We also present timings of the various components of the algorithm.

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