Define a function, temperature$\_$at$\_$nearest$\_$edge$($x$,$ y$,$ length, edge, cnr$\_$temps$),$ which returns the temperature that is closest to point $($x$,$y$)$ near edge. The edge parameter is an integer $(0,$ South; $1,$ East; $2,$ North; $3,$ West$).$ The temperatures at the corners of the square are supplied as a dictionary with keys as the compass points: $$sw$,$se$,$ne$$ and $$nw$,$ and the values are the temperatures at those corners. For example: cnr$\_$temps $=\{\text{'}$sw$\text{'}=600\mathrm{.}0,\text{'}$se$\text{'}=700\mathrm{.}0,\text{'}$ne$\text{'}=1000\mathrm{.}0,\text{'}$nw$\text{'}=850\mathrm{.}0\}.$ The temperature at the nearest point on the edge will need to be linearly interpolated $,$ for example if the nearest point is at x $=0\mathrm{.}6$ on the $[0]$ edge. This means we need to interpolate the temperature value from the known values at the south$-$west corner $(600\mathrm{.}0$ K$)$ and the south$-$east corner $(700\mathrm{.}0$ K$).$ We can compute the fractional distance along the edge, f $($with $0<=$ f $<=1),$

and then use that to weight the contribution from each corner. This gives us a linear interpolation of the value:

Tedge $=(1$ f$)$ X TSW $+$ f X TSE