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<p><b>Abstract</b>—We present a fast algorithm to estimate the penetration depth between convex polytopes in 3D. The algorithm incrementally seeks a "locally optimal solution” by walking on the surface of the Minkowski sums. The surface of the Minkowski sums is computed <tmath>implicitly</tmath> by constructing a local dual mapping on the Gauss map. We also present three heuristic techniques that are used to estimate the initial features used by the walking algorithm. We have implemented the algorithm and compared its performance with earlier approaches. In our experiments, the algorithm is able to estimate the penetration depth in about a milli-second on an 1 GHz Pentium PC. Moreover, its performance is almost independent of model complexity in environments with high coherence between successive instances.</p>
Penetration depth, Minkowski sums, Gauss map, incremental algorithm, haptic rendering.

M. C. Lin, D. Manocha and Y. J. Kim, "Incremental Penetration Depth Estimation between Convex Polytopes Using Dual-Space Expansion," in IEEE Transactions on Visualization & Computer Graphics, vol. 10, no. , pp. 152-163, 2004.
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