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In order to compute the height of the grid, which is represented by AB + AD (Optimized sensor deployment with rectangle-shaped grids), we consider ∆CDSN_3 .
line DSN_3 = rsin(90 – ¥è2) = rcos(¥è2)
Line AD = Line ASN_3 - line DSN_3 = r – rcos(¥è2)
So, lines BA + AD can be represented by lines AB +AD =
2¡î(r^2-〖r^2 k〗^2 ) + r – rcos(¥è2) ¡¦¡¦¡¦¡¦ (13)
Therefore, the area and the diagonal of the grid are computed as follows:
Area of grid = 2rk(2¡î(r^2-〖r^2 k〗^2 ) + r – rcos(¥è2))
Diagonal of grid = ¡î(4〖r^2 k〗^2+ 〖r^2 (2¡î(1-k^2 )+1-cos(¥è_2))〗^2 )
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IEEE/ICACT20210142 Slide.21
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