One idea is to generate samples uniformly over a hypercube and throw out the ones that are outside of the convex hull without actually computing the hull itself. But, since I don't know which points are on the hull apriori without constructing it I'm not sure how to do this either.
You could do that by solving the QP (e.g., using lsqlin)
min d(w) = norm(V.'*w-y).^2
s.t. sum(w)=1
w>=0
where y is the point you want to test for inclusion in the convex hull. If the optimal d(w) is zero, then y is in the hull
You haven't mentioned how big N is so I can't know in advance how practical this would be for you.
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