Write a GUI implemented in MATLAB using App Designer that calls the three functions in Tasks

$1$

$$

$3.$

$$ 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.