I finally got AC !
All colinear points should be present in the convex hull.
I finally used Graham's algorithm, just as mentionned above, and then added a piece of code to add ignored colinear points, because modifying the basis algorithm to include colinear points revealed to be a real pain.
But if anybody has another idea (I'm sure there's much better things to do, I'm not as good as I'd like to be), please say !!!