Cohen$-$Sutherland Line Clipping Algorithm

In this problem, you are provided with a clipping window $($which defines the

"viewport"$)$ and a sample line. You are required to execute the steps of the line

clipping algorithm that was recently covered in class.

Input: The viewport is defined by $x_{\text{m}\text{i}\text{n}}=2,x_{\text{m}\text{a}\text{x}}=10,y_{\text{m}\text{i}\text{n}}=3,y_{\text{m}\text{a}\text{x}}=8.$

The line is defined by points $P=(1,5)$ and $Q=(11,1).$

$($a$)$ Identify the coordinates of all intersecting points $($e$.$g$.,$ intersection points

with the top boundary, bottom boundary, etc.$).$

$($b$)$ Calculate the new clipped points $P^{\text{'}}$ and $Q^{\text{'}}$ for the line.

Q$.$

Apply the above problem in Cyrus$-$Beck line clipping algorithm, calculate the

values of $\text{'}t\text{'}$ for all boundaries, labeling them as $t_E$ or $t_L.$ Then, determine the

maximum and minimum values among them accordingly.

Give mathematical solutions and working details $,$ do not use codes.