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. For
on the curve, the rest of the curve lies inside a wedge of
with apex in
is fixed. This
property restrains the curve's meandering. we provide an upper bound
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,
Reference: O. Aichholzer, F. Aurenhammer, C. Icking, R. Klein,
E. Langetepe, and G. Rote.
Generalized self-approaching curves.
In Proc. European Workshop on Computational Geometry CG '98,
pages 15-18, Barcelona, Spain, 1998.