  This paper deals with the accomplishment of total area coverage of an
arbitrary region using sensors with a finite sensing radius of rs. For a given
region, we aim to obtain a deterministic placement of sensors which, apart from
ensuring that the entire region comes under the purview of at least a single
sensor, minimises the number of sensors utilised. We begin by considering
regions devoid of obstacles and thus having every location amenable for
placement. Herein, we formalise the popular notion that sensors at the centres
of the hexagons of a hexagonal tessellation provide the most optimal placement.
We then move on to regions which may comprise obstacles of arbitrary size at
arbitrary locations. We recognise two distinct classes of obstacles, namely
transparent and opaque obstacles, which are distinguished by their ability (or
the lack of it) to permit sensing radiation through them. In the real world,
transparent obstacles model lakes, ponds and swamps, while the opaque ones
stand for, inter alia, hills, trees and walls.We propose a polynomial-time
algorithm for achieving optimal placement in the aforesaid scenarios and we
prove its convergence.
