Abstract: In certain embodiments, path determination includes receiving terrain elevation data comprising elevation values for locations of an area, where each elevation value indicates an elevation at a location. One or more gradient matrices are calculated from the elevation values. Each gradient matrix comprises gradient values corresponding to the locations. Traversable segments are determined from the gradient matrices, and a path is determined from the traversable segments.

Abstract: In certain embodiments, determining maritime paths includes accessing a feasibility matrix comprising feasibility values for locations of an area. A feasibility value indicates navigability at a location. One or more non-navigable locations represent one or more barriers. Waypoints around the barriers are determined. A cost matrix comprising cost values is calculated. A cost value indicates a distance between two points of a set of points, where the set of points comprises one or more start points, one or more end points, and the waypoints. Dijkstra's technique is applied to a selected start point and a selected end point to yield a shortest length path between the selected start point and the selected end point.

Abstract: According to certain embodiments, paths are identified from path data. One or more sensors are assigned to each path. The following are performed: at least one sensor is moved to a path intersection and excess sensors are removed. An excess sensor is a sensor that is not required to satisfy the desired number of sensors of one or more paths. According to certain embodiments, a combined array comprising combined entries is accessed. Each combined entry represents a location and has a value indicating a number of paths at the location. The following are performed to yield a sensor arrangement: a maximum value of the combined array is identified, a sensor is assigned to a location associated with the maximum value, and the paths are removed from the combined array. A result associated with the sensor arrangement is reported.

Abstract: In certain embodiments, path determination includes receiving terrain elevation data comprising elevation values for locations of an area, where each elevation value indicates an elevation at a location. One or more gradient matrices are calculated from the elevation values. Each gradient matrix comprises gradient values corresponding to the locations. Traversable segments are determined from the gradient matrices, and a path is determined from the traversable segments.

Abstract: In certain embodiments, determining maritime paths includes accessing a feasibility matrix comprising feasibility values for locations of an area. A feasibility value indicates navigability at a location. One or more non-navigable locations represent one or more barriers. Waypoints around the barriers are determined. A cost matrix comprising cost values is calculated. A cost value indicates a distance between two points of a set of points, where the set of points comprises one or more start points, one or more end points, and the waypoints. Dijkstra's technique is applied to a selected start point and a selected end point to yield a shortest length path between the selected start point and the selected end point.

Abstract: According to certain embodiments, paths are identified from path data. One or more sensors are assigned to each path. The following are performed: at least one sensor is moved to a path intersection and excess sensors are removed. An excess sensor is a sensor that is not required to satisfy the desired number of sensors of one or more paths. According to certain embodiments, a combined array comprising combined entries is accessed. Each combined entry represents a location and has a value indicating a number of paths at the location. The following are performed to yield a sensor arrangement: a maximum value of the combined array is identified, a sensor is assigned to a location associated with the maximum value, and the paths are removed from the combined array. A result associated with the sensor arrangement is reported.