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The Class of Simple Cube-Curves Whose MLPs Cannot Have Vertices at Grid Points

  • Fajie Li
  • Reinhard Klette
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3429)

Abstract

We consider simple cube-curves in the orthogonal 3D grid of cells. The union of all cells contained in such a curve (also called the tube of this curve) is a polyhedrally bounded set. The curve’s length is defined to be that of the minimum-length polygonal curve (MLP) fully contained and complete in the tube of the curve. So far only one general algorithm called rubber-band algorithm was known for the approximative calculation of such a MLP. There is an open problem which is related to the design of algorithms for calculation a 3D MLP of a cube-curve: Is there a simple cube-curve such that none of the vertices of its 3D MLP is a grid vertex? This paper constructs an example of such a simple cube-curve. We also characterize this class of cube-curves.

Keywords

Critical Line Parallel Projection Simple Cube Grid Plane Robot Motion Planning 
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 2005

Authors and Affiliations

  • Fajie Li
    • 1
  • Reinhard Klette
    • 1
  1. 1.CITRUniversity of AucklandAucklandNew Zealand

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