Generalized self-approaching curves
O. Aichholzer, F. Aurenhammer, C. Icking, R. Klein, E. Langetepe, and
We consider all planar oriented curves that have the following property
depending on a fixed angle
. For each point
on the curve, the
rest of the curve lies inside a wedge of angle
with apex in
This property restrains the curve's meandering, and for
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
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 curve's length cannot exceed the perimeter of its convex
hull, divided by
Reference: O. Aichholzer, F. Aurenhammer, C. Icking, R. Klein,
E. Langetepe, and G. Rote.
Generalized self-approaching curves.
In Proc. Int. Symp. Algorithms and Computation ISAAC'98, Lecture
Notes in Computer Science, volume 1533, pages 317-326, Taejon, Korea, 1998.