**7. Conclusion**

In this chapter, an *O*(*n*log *n*) time near-shortest path planning based on the Delaunay triangulation, the Ahuja-Dijkstra algorithm, and ridge points on the quadric surface are introduced. Although the length of path obtained by Delaunay triangulation-based algorithm is 0.28% longer than another *O*(*n*log *n*) time KS's algorithm, the average computation time is 31.71 times faster. Furthermore, when the KS's Steiner point is 29, which means that the shortest path in the NP-hard problem will be obtained, the Delaunay triangulation-based algorithm has at most a 2.81% difference on the path searching, but the computation time is 4216 times faster approximately. Therefore, the Delaunay triangulation-based algorithm presents a good near-shortest path searching solution in the quadric surface with a very short amount of computation time.

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