Extend the GUI with an additional function to be applied to Task $1$ needle dropping:

$1.$ 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.

$2.$ 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.

this the code for task $1$ code:

"function $[$p$,$ crossings, allLines, allvertices$\_$counters$]=$ BuffonStandardPiPlot$($width$,$ length, throws, floorboards$)$

crossings $=0$;

allLines $=$ cell$($throws$,1)$; $\%$ Initialize the cell array

allvertices$\_$counters $=$ cell$($throws$,1)$;

for i$=1$:throws

vertex$\_$counter $=0$;

centerX $=$ rand$()*$ width $*$floorboards;

centerY $=($rand$()*($width$))*$floorboards ;

rotationAngle $=$ rand$()*($pi$/2)$;

$\%$ Genereating vertices of the lines

lineVertices $=[$centerX $+($length$/2)*$ cos$($rotationAngle$),$ centerY $+($length$/2)*$ sin$($rotationAngle$)$;

centerX $-($length$/2)*$ cos$($rotationAngle$),$ centerY $-($length$/2)*$ sin$($rotationAngle$)$; $]$;

allLines$\{$i$,1\}=$ lineVertices; $\%$ Store the generated line vertices

leftside $=$ floor$($centerX$/$width$)*$ width;

rightside $=$ leftside $+$ width;

$\%$Check every vertex whether crossed the vertical line or not

vertex$\_$counter $=$ sum$($lineVertices$($:$,1)>=$ rightside $|$ lineVertices$($: leftside$)+$ vertex$\_$counter;

allvertices$\_$counters$\{$i$\}=$ vertex$\_$counter;

crossings $=$ crossings $+$ sum$($vertex$\_$counter ~$=0)$;

end

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

disp$([\text{'}$Estimated p: $\text{'},$ num$2$str$($p$)])$;

disp$([\text{'}$Number of needles that crossed a crack: $\text{'},$ num$2$str$($crossings$)])$

end

$"$

and this is the GUI code