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Summary: Discrete Applied Mathematics 109 (2001) 324
Generalized self-approaching curves
Oswin Aichholzera; 2
, Franz Aurenhammera;2
, Christian Ickingb; 1
,
Rolf Kleinb;1
, Elmar Langetepeb; ; 1
, Gunter Rotec;2
aFernUniversitat Hagen, Praktische Informatik VI, D-58084 Hagen, Germany
bTechnische Universitat Graz, A-8010 Graz, Austria
cFreie Universitat Berlin, Institut fur Informatik, D-14195 Berlin, Germany
Received 1 September 1998; revised 6 September 1999; accepted 9 February 2000
Abstract
We consider all planar oriented curves that have the following property depending on a ÿxed
angle '. For each point B on the curve, the rest of the curve lies inside a wedge of angle '
with apex in B. This property restrains the curve's meandering, and for '6 =2 this means that
a point running along the curve always gets closer to all points on the remaining part. For all
'¡ , we provide an upper bound c(') for the length of such a curve, divided by the distance
between its endpoints, and prove this bound to be tight. A main step is in proving that the
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