calculating bitangent of bounded shape

[Christine Keim]

hi all,

i have (maybe it is a newby) question

i have 2 polygons, one is the convex hull of a shape, and the other one
is a sector contained in the convex hull (a bounded area).
the orignal shape is mser_plus_6.bmp
In the enclosed image boundedShape.jpg, i have combined the convex hull
as a mask and the original image, so that a bounded area can be selected
by the wand tool.
so in my code, i have the polygon for the convex hull of the whole shape
(an airfighter)
and the polygon for a bounded area (like in the example, the left bottom
area which has
a yellow selection border).
what i need is the intersection of the borders of both polygon-ROIs,
meaning the bitangent going from the head of the airfighter to its left
wing, (i would just need the starting point and the endpoint)

i tried to go through all the x/y coordinates of the hull
and using the contains() function for the section, but the coordinates
given by the hull are not (!!) nessecarily contained in the section.
either i need to get all the coordinates of the convex hull OR i need
some sort of intersect of the borders only. maybe someone can point me
in the right direction

these are the convex hull coordinates i have:
[0] = 135/0
[1] = 0/29
[2] = 0/31
[3] = 96/114
[4] = 101/116
[5] = 109/118
[6] = 114/119
[7] = 120/120
[8] = 125/120
[9] = 157/106
[10] = 159/104
[11] = 184/76
[12] = 184/73
[13] = 182/37
[14] = 164/6
[15] = 160/4
[16] = 148/1
[17] = 143/0