Generalized Self-Approaching Curves

Abstract. We consider all planar oriented curves that have the following property depending on a fixed 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 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 curve's length cannot exceed the perimeter of its convex hull, divided by 1 + cos .

• Type: Conference
• Year: 1998
• Where: ISAAC
• Authors: Oswin Aichholzer, Franz Aurenhammer, Christian Icking, Rolf Klein, Elmar Langetepe, Günter Rote
• Keywords: Algorithms, Curve's Meandering, Fixed Angle, ISAAC 1998, Planar Oriented Curves