A set S is convex if, for any two points in S, the line segment connecting them is also in S. Given a set of points P, we define their convex hull as the smallest convex set that contains P.

Sometimes, we want to shrink the convex hull of a set of points in a non-uniform manner. This gives rise to the more general concept of a “reduced convex hull.” Such objects originated in binary classification problems in machine learning, and have been studied further in the field of computational geometry. We will explore various properties of reduced convex hulls, and how these properties behave as the number of points in our set gets large.

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