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Minimum-Length Polygons in Simple Cube-Curves

  • Reinhard Klette
  • Thomas Bülow
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1953)

Abstract

Simple cube-curves in a 3D orthogonal grid are polyhedrally bounded sets which model digitized curves or arcs in three-dimensional euclidean space. The length of such a simple digital curve is defined to be the length of the minimum-length polygonal curve fully contained and complete in the tube of this digital curve. A critical edge is a grid edge contained in three consecutive cubes of a simple cube-curve. This paper shows that critical edges are the only possible locations of vertices of the minimum-length polygonal curve fully contained and complete in the tube of this digital curve.

Keywords

Line Segment Straight Line Segment Polygonal Curve Critical Edge Polygonal Chain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Reinhard Klette
    • 1
  • Thomas Bülow
    • 2
  1. 1.CITRUniversity of AucklandAucklandNew Zealand
  2. 2.GRASP LaboratoryUniversity of PennsylvaniaPhiladelphiaUSA

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