Abstract:
The generalized penetration depth PD of two overlapping bodies X and Y is the distance between the given colliding position of X and the closest collisionfree Euclidean copy X" to X according to a distance metric. We present geometric optimization algorithms for the computation of PD with respect to an objectoriented metric S which takes the mass distribution of the moving body X into consideration. We use a kinematic mapping which maps rigid body displacements to points of a 6dimensional manifold M6 in the 12dimensional space R12 of affine mappings equipped with S. We formulate PD as the solution of the constrained minimization problem of finding the closest point on the boundary of the set of all points of M6 which correspond to colliding configurations. Based on the theory of gliding motions, the closest point with respect to the metric S () PDS) can be computed with an adapted projected gradient algorithm. We also present an algorithm for the computation of the closest point with respect to the geodesic metric G of M6 induced by S () PDG). Moreover we introduce two methods for the computation of a collisionfree initial guess and give a physical interpretation of PDS and PDG.Bibtex:
@article{nawratil2009gpdckg,
author = "G. Nawratil and H. Pottmann and and B. Ravani",
title = "Generalized Penetration Depth Computation based on Kinematical Geometry",
journal = {Computer Aided Geometric Design},
year = 2009,
volume = 26,
number = 4,
pages = "425443",
url = "http://www.geometrie.tuwien.ac.at/nawratil/gpdcbokg.pdf",
doi = "http://dx.doi.org/doi:10.1016/j.cagd.2009.01.001",
}

