Write a GUI implemented in MATLAB using App Designer that calls the three functions in Tasks $13.$ tasks are based on $$Buffon$$s needle$$ experiment.

for example this is task one :

"function $[$p$,$ crossings$]=$ BuffonStandardPi$($width$,$ length, throws$)$

crossings $=0$;

for n $=1$:throws

$\%$ Randomly place the needle's midpoint and angle

midpoint $=$ width $*$ rand$()$;

angle $=$ pi $*$ rand$()$;

$\%$ Calculate the distance from the midpoint to the nearest line

distance$\_$to$\_$line $=$ min$($midpoint$,$ width $-$ midpoint$)$;

$\%$ Check if the needle crosses a line

if distance$\_$to$\_$line $<($length$/2)*$ sin$($angle$)$

crossings $=$ crossings $+1$;

end

end

$\%$ Estimate pi using the crossings

if crossings $>0$

p $=(2*$ length $*$ throws$)/($width $*$ crossings$)$;

else

p $=$ Inf; $\%$ If no crossings, the estimate of pi goes to infinity

end

end"

The GUI must

$1.$ Allow the user to select which task is run.

$2.$ Allow the user to adjust the number of needles, dropped squares, and parallel planks of wood, from default values. The program should allow

at least $1,000,000$ needles$/$dropped squares and $10$ parallel planks of wood. Note: not all needles need to be displayed if more than $1000$ are

dropped.

$3.$ Before running the simulation allow the user to adjust the sizes of the needles, dropped squares, and parallel planks of wood from default

values.

$4.$ Display the parallel planks of wood.

$5.$ Display the dropped needles$/$squares$.$

$6.$ Highlight in a different colour all needles$/$dropped squares that intersect the cracks between planks.

$7.$ Display the value estimated by the Monte Carlo simulation.

$8.$ Allow the user to customize elements of the displayed value $($e$.$g$.$ font size, colour$).$

$9.$ an additional function to be applied to Task $1$ needle dropping only:

It should allow the user to select a needle by clicking on or near it with the mouse. The needle will then be highlighted in a different colour and The n needles with most similar orientation will then be highlighted in yet another colour. The default value is n $=3,$ and the value of n can

be modified through the GUI.

$10.$ Allow a mixture of different sized needles to be used.

$11.$ Support saving and loading back sets of needles such that previous results can be combined to produce better estimates.