The search drone problem

Imagine that a search drone is on the look-out for a submarine that is careful to avoid detection. The controllers of the drone have been given a convex polygonal area on the surface of the sea and told that the drone should search the area inside that polygon. Assume that the drone flies at 150 KM per hour and the polygonal space covers roughly an area of 60,000 Sq. KM. Further assume that the drone flies at a height of 1 KM above the sea and its sensors can detect the submarine if it is inside a circle, 1 KM diameter, with its centre directly beneath the drone.  

Your task is to program a flight pattern for the drone. You can assume the availability of a function in(X, Y) in the control computer, that returns 1 if the drone’s current position (X, Y) is inside the polygon and 0 otherwise.

It is desirable that the drone’s path be relatively unpredictable, and that all places inside the polygon have equal chances of being visited to the extent possible.

Can you write a program that would plot the scan pattern showing how it would fly the drone over the given area? Use any graphical display software to provide a dynamic display.

Assume that the maximum underwater speed of the submarine is 10 KM per hour when it is trying to evade detection. What would be a good strategy for the submarine to avoid detection under these circumstances? Assume that the submarine gets to sense where the drone is, if it gets within 4 KM of horizontal distance. Try programming this strategy and show the path of the submarine on the display in a different color. 

Srinivasan Ramani