Maybe i miss something import but "a" intersects "b" if and only if
the intersection of internal areas is not empty. One has to solve the
following LP problem (feasibility test):

min z=0
s.t.
x >= 1
x <= 3
y >= 2
y <= 3
x >= 2
x <= 4
y >= 1
y <= 4

If the question would be that how to compute the convex hull of the
red area in the general case, that is an other question but not the
original one.

Of course one has to decide how to handle the degenerate cases e.g. if
the intersection is a line segment, etc.

Do i misunderstand something?

Ali


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