Generalized self-approaching curves

  title={Generalized self-approaching curves},
  author={Oswin Aichholzer and Franz Aurenhammer and Christian Icking and Rolf Klein and Elmar Langetepe and G{\"u}nter Rote},
  journal={Discrete Applied Mathematics},
We consider all planar oriented curves that have the following property depending on a xed 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… CONTINUE READING
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