Given the following code to merge convex hulls including the code for the upper tangent, write the code finding the lower tangent.

Input: Two convex hulls, Hull A and Hull B Output: Merged convex hull

procedure FindUpperTangent$($Hull A$,$ Hull B$)$

Set i $=$ index of the rightmost point of Hull A

Set j $=$ index of the leftmost point of Hull B

while line segment $($Hull A$[$i$],$Hull B$[$j$])$ is not an upper tangent do

if not an upper tangent for Hull A then Move i counterclockwise in Hull A

else if not an upper tangent for Hull B then Move j clockwise in Hull B

return $($Hull A$[$i$],$Hull B$[$j$])$ as the upper tangent

procedure FindLowerTangent$($Hull A$,$ Hull B$)$

procedure MergeHulls$($Hull A$,$ Hull B$)$

upperT angent $$ FindUpperTangent$($Hull A$,$ Hull B$)$ lowerT angent $$ FindLowerTangent$($Hull A$,$ Hull B$)$ Initialize an empty list for the merged hull

Traverse points from upperTangent to lowerTangent on Hull A Traverse points from upperTangent to lowerTangent on Hull B return the merged convex hull