# Minkowski Sums of Polyhedra with Holes

## Dan Halperin, School of Computer Science, Tel-Aviv University

## Date and time: 2pm, Friday, December 14, 2018

## Place: CUNY Graduate Center, Rm 4419

The Minkowski sum of two sets $P$ and $Q$ in Euclidean space is
the result of adding every point (position vector) in $P$ to
every point in $Q$. Considering the Minkowski sum of two
polyhedra with holes (voids), we show that one can always fill up
the holes in one of the summand polyhedra and still get the
same Minkowski sum as of the original summands. We present
a simple proof of this observation, improving on (our)
earlier rather involved proof of a more restricted claim.
As we explain, this observation helps in speeding up the
computation of Minkwoski sums in practice. We also review
additional recent results in computing and using Minkowksi
sums.

Joint work with Alon Baram, Efi Fogel, Michael Hemmer, and
Sebastian Morr.