Polygon enclosing a set of points

Question

I have a set S of points (2D : defined by x and y) and I want to find P, the smallest (meaning : with the smallest number of points) polygon enclosing all the points of the

Answer 1

You probably mean you want the smallest area, which is the convex hull.

If you really do want the fewest points, you can just make a triangle with super-large vertex positions so that all your points are enclosed.