Drawing nice projections of objects in space

  • Prosenjit Bose
  • Pedro Ramos
  • Francisco Gomez
  • Godfried Toussaint
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1027)

Abstract

Our results on regular and minimum-crossing projections of line segments have immediate corollaries for polygonal chains, polygons, trees and more general geometric graphs in 3-D since these are all special cases of sets of line segments. Our results also have application to graph drawing for knot-theorists. Let K be a knot with n vertices. To study the knot's combinatorial properties, knot theorists obtain a planar graph G called the diagram of K by a regular projection of K. Many of their algorithms are applied to G and therefore their time complexity depends on the space complexity of G. By combining our algorithms we can obtain regular projections with the minimum number of crossings thereby minimizing the time complexity of their algorithms.

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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Prosenjit Bose
    • 1
  • Pedro Ramos
    • 2
  • Francisco Gomez
    • 2
  • Godfried Toussaint
    • 3
  1. 1.University of British ColumbiaVancouverCanada
  2. 2.Universidad Politecnica de MadridMadridSpain
  3. 3.McGill UniversityMontrealCanada

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