# ICS 269, Winter 2002: Theory Seminar

## 8 March 2002:

A presentation of results from
"Moving an Angle Around a Region"
by Frank Hoffman, Christian Icking, Rolf Klein, and Klaus Kriegel,
in *Proc SWAT '98*, *Springer Lecture Notes in Computer
Science*, Stockholm, 1998, and
online publication by the *Journal of Discrete & Computational
Geometry*

Javid Hüseynov

Let D be a connected region inside a simple polygon P. Authors
define the angle hull, AH(D), of D to be the set of all points
in P that can see two points of D at a right angle. They further
prove that the perimeter AH(D) is at most twice the perimeter
of the relative convex hull of D. In special case, when P is
the full plane, this bound is given as {/pi}/2. Both bounds are
tight.

The practical application of this topic is found in designing on-line
competitive navigation strategies for autonomous robots in unknown
environments.