CareerCup

How many dimensions?

This question sounds very vague to me.

What do you mean by convex hull? As far as I know, "convex hull" is more of an operator rather than an object, i.e., convex hull of a set is the smallest convex set covering the set.

Intersection of two convex sets is also convex. So if you know an algorithm which gives you the points inside a convex set, just apply it to the intersection.

From a computational point of view, lets approximate the convex set using a convex polyhedron, i.e, assume the set is defined as

S = {x | A x <= b} for some A and b.

Now for two different sets you get two different A and b. Say A1 and A2 and b1 and b2.
Then

S1 \cap S2 = {x | A1 x \le b1 and A2x <= b2} = {x | [A1; A2] [x; x] <= [b1; b2]}
 = {x | [A1; A2] [I, 0; I; 0] x \le [b1 b2]}

which is another polyhedron with A = [A1; A2] \times [I, 0; I, 0] and b = [b1; b2].

BTW, unless your polyhedron is trivial, there are infinite points in it.

I work at microsoft so I know the answer always.

Use vertical ray shooting problem with path compression and fractional cascading. Easy.

Basic feasibility convex problem. CVX can solve this.

find x
st
Ax<=b
Cx<=d