Reversing the search for a convex hull

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In the wikipedia article on convex hulls, there is an image showing a rubber band shrinking down to form a polygon around a set of points in a plane.

I have a set of data with a region with no points and I want to be able to expand outward to create a polygon that encloses the empty region. The empty region will have points but I need to be able to select because their value needs to be set to zero.

Are there algorithms or methods to do this?