$($a$)$ Describe in detail an algorithm that returns the minimum distance from a point

to a line segment in two dimensions. Ensure that you include all of your

assumptions and all necessary mathematical calculations.

$($b$)$ A quadratic Bezier curve is defined by three points, $P_1,P_2,P_3,$ and a

parameter, $t$ :

$P(t)=(1-t{)}^2{P}_1+2t(1-t)P_2+t2P_3$;$0t1$

$($b$)$Describe an algorithm that draws the quadratic Bezier curve, using straight

lines only, to within a tolerance $.$ You may use the algorithm from part $($a$)$

and you may assume that you already have an algorithm for drawing a straight

line.