**6. The shortest path application on the quadric surface**

This section explains an application that benefits from the Delaunay triangulation-based algorithm. Actually, it can be applied to shortest path planning for Mars rover and mission planning for cruise missiles in the quadric surface. For cruise missile mission planning, we steady up with the angle *θ*<sup>1</sup> at source point and down with the angle *θ*<sup>2</sup> at destination point, respectively. Furthermore, the z-coordinate is limited by the *l* altitude units to avoid the radar's scan as well as crash prevention, where *l* is a constant, as shown in **Figure 6(a)**. To verify the correctness and performance, we assume a cruise missile needs to move from the source position *S* to the destination position *D*, as shown in **Figure 6(b)**. In order to keep the safety margin between the cruise missile and quadric surface, virtual *l* altitude units are added up to the graph *G*′ (e.g. 20 meters above the *G*). Once the virtual altitude and thresholds are applied, a shortest path is obtained. Apparently, **Figure 6** shows that this shortest path algorithm can be also applied to intelligently guide the cruise missile to pass a narrow passage and avoid radar's scan.

**Figure 6.** An illustration of the shortest path for planning a cruise missile on the landscape. (a) Cruise missile planning;

Path Planning on Quadric Surfaces and Its Application http://dx.doi.org/10.5772/intechopen.72573 101

(b) land scope (top view); (c) result (aerial view 1) and (d) result (aerial view 2).

**6. The shortest path application on the quadric surface**

infinity. (a) Average computation time and (b) average length difference.

steady up with the angle *θ*<sup>1</sup>

100 Advanced Path Planning for Mobile Entities

added up to the graph *G*′

passage and avoid radar's scan.

This section explains an application that benefits from the Delaunay triangulation-based algorithm. Actually, it can be applied to shortest path planning for Mars rover and mission planning for cruise missiles in the quadric surface. For cruise missile mission planning, we

**Figure 5.** The prediction of the average computation time and length difference if the number of KS's Steiner points is

respectively. Furthermore, the z-coordinate is limited by the *l* altitude units to avoid the radar's scan as well as crash prevention, where *l* is a constant, as shown in **Figure 6(a)**. To verify the correctness and performance, we assume a cruise missile needs to move from the source position *S* to the destination position *D*, as shown in **Figure 6(b)**. In order to keep the safety margin between the cruise missile and quadric surface, virtual *l* altitude units are

olds are applied, a shortest path is obtained. Apparently, **Figure 6** shows that this shortest path algorithm can be also applied to intelligently guide the cruise missile to pass a narrow

at source point and down with the angle *θ*<sup>2</sup>

(e.g. 20 meters above the *G*). Once the virtual altitude and thresh-

at destination point,

**Figure 6.** An illustration of the shortest path for planning a cruise missile on the landscape. (a) Cruise missile planning; (b) land scope (top view); (c) result (aerial view 1) and (d) result (aerial view 2).
