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)


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.


Line Segment Straight Line Segment Polygonal Curve Critical Edge Polygonal Chain 
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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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