Paper Info
Title
Generalized self-approaching curves
Abstract
We consider all planar oriented curves that have the following property depending on a fixed angle ϕ . For each point B on the curve, the rest of the curve lies inside a wedge of angle ϕ with apex in B . This property restrains the curve's meandering, and for ϕ ⩽π/2 this means that a point running along the curve always gets closer to all points on the remaining part. For all ϕ <π, we provide an upper bound c ( ϕ ) 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 ϕ .
Year
DOI
Venue
2001
10.1016/S0166-218X(00)00233-X
International Symposium on Algorithms and Computation
Keywords
Field
DocType
convex hull,self-approaching curves,detour,generalized self-approaching curve,arc length,upper bound
Osculating curve,Curve orientation,Upper and lower bounds,Wedge (mechanical device),Vertical line test,Arc length,Geometry,Track transition curve,Mathematics,Osculating circle
Journal
Volume
Issue
ISSN
109
1-2
Discrete Applied Mathematics
ISBN
Citations 
PageRank 
3-540-65385-6
10
1.38
References 
Authors
5
6
Name
Order
Citations
PageRank
Oswin Aichholzer185296.04
Franz Aurenhammer22060202.90
Christian Icking336433.17
Rolf Klein423719.69
Elmar Langetepe519925.87
Günter Rote61181129.29