 
Summary: Mathematics and Computers in Simulation 00 (2010) 126
An O(m+n) measure of penetration depth between convex
polyhedral bodies for rigid multibody dynamics$
Gary D. Harta
, Mihai Anitescub
a University of Pittsburgh at Greensburg, Division of Natural Sciences,
150 Finoli Drive, Greensburg, PA 15601, email gdhart@pitt.edu
bMathematics and Computer Science Division, Argonne National Laboratory,
9700 S. Cass Avenue, Argonne, IL 60439, email anitescu@mcs.anl.gov
Abstract
In this work, we define a new metric of the distance and depth of penetration between two
convex polyhedral bodies. The metric is computed by means of a linear program with three
variables and m + n constraints, where m and n are the number of facets of the two polyhedral
bodies. As a result, this metric can be computed with O(m + n) algorithmic complexity, superior
to the best algorithms known for calculating Euclidean penetration depth. Moreover, our metric
is equivalent to the signed Euclidean distance and thus results in the same dynamics when used
in the simulation of rigidbody dynamics in the limit of the time step going to 0. We demonstrate
the use of this new metric in timestepping methods for rigid body dynamics with contact and
friction.
Keywords: rigid body, contact dynamics, friction, measure differential inclusion,
