Merry, Bruce and Perkins, Simon James and Marais, Patrick and Gain, James
(2012)
*Proof of Field D*'s Case Separation for Arbitrary Simplices*, CS12-07-00, Department of Computer Science, University of Cape Town.

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## Abstract

In their development of the Field D* algorithm, Ferguson et. al. prove that a path through a unit length right-angled triangle originating from an interpolated edge, and travelling to the opposite vertex must either be a direct or indirect case. A combination of the two is not optimal. Later work, proves this for arbitrary, but non-degenerate triangles. In this technical report, we prove the same for non-degenerate simplices, which are generalisations of triangles to higher dimensions.

Item Type: | Technical report |
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Uncontrolled Keywords: | computational geometry mathematical proof |

Subjects: | Computing methodologies > Artificial intelligence |

Date Deposited: | 25 Sep 2012 |

Last Modified: | 10 Oct 2019 15:33 |

URI: | http://pubs.cs.uct.ac.za/id/eprint/785 |

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