A Fast and Practical Algorithm for Generalized Penetration Depth Computation

14 years 7 days ago

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— We present an efﬁcient algorithm to compute the generalized penetration depth (PDg) between rigid models. Given two overlapping objects, our algorithm attempts to compute the minimal translational and rotational motion that separates the two objects. We formulate the PDg computation based on modeldependent distance metrics using displacement vectors. As a result, our formulation is independent of the choice of inertial and body-ﬁxed reference frames, as well as speciﬁc representation of the conﬁguration space. Furthermore, we show that the optimum answer lies on the boundary of the contact space and pose the computation as a constrained optimization problem. We use global approaches to ﬁnd an initial guess and present efﬁcient techniques to compute a local approximation of the contact space for iterative reﬁnement. We highlight the performance of our algorithm on many complex models.

Liangjun Zhang, Young J. Kim, Dinesh Manocha

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