| Summary: | 碩士 === 國立臺灣海洋大學 === 電機工程學系 === 101 === Recently, a new algorithm to obtain the sub-shortest path in the Euclidean plane based on the concepts of Delaunay triangulation, an improved Dijkstra algorithm and Fermat points was presented. The length of path obtained by this algorithm is the shortest among two other fastest O(n log n) algorithms in the literature. Based on the previous works, a novel O(n log n) sub–shortest path algorithm in the Quadric plane based on the Delaunay triangulation, an improved Dijkstra algorithm and Ridge points is presented in this paper. Compare to the another O(n log n) sub–shortest path approach (Kanai and Suzuki, KS’s algorithm [21]), the average path of the proposed algorithm is 2.81% longer than the KS’ algorithm, but the computation is about 4215 times faster when KS’s SP point is 29. This, however, has only a few path length difference which still give a good result but best computing time. It is worth to notice that the proposed fast algorithm is ideal to be extended to solve the near-shortest path problem on the quadric surface or even the cruise missile mission planning.
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