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DGCI

2005

Springer

2005

Springer

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.

Added |
26 Jun 2010 |

Updated |
26 Jun 2010 |

Type |
Conference |

Year |
2005 |

Where |
DGCI |

Authors |
Fajie Li, Reinhard Klette |

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