A trivial knot whose spanning disks have exponential size

  • Authors:

  • Jack Snoeyink

  • Affiliations:

  • Department of Computer Science, Stanford University

  • Venue:
  • SCG '90 Proceedings of the sixth annual symposium on Computational geometry
  • Year:
  • 1990

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Abstract

If a closed curve in space is a trivial knot (intuitively, one can untie it without cutting) then it is the boundary of some disk with no self-intersections. In this paper we investigate the minimum number of faces of a polyhedral spanning disk of a polygonal knot with n segments. We exhibit a knot whose minimal spanning disk has exp(cn) faces, for some positive constant c.