Given any compact closed body $S \subset \mathbb{R}^n$, let $K \subset \mathbb{R}^n$ be its convex hull.
Is there any theories regarding the distance between S and K? Also are there any regarding how well does $K$ approximates $S$ e.g. by volume.
Regarding distance, I interested in finding the maximal distance between a boundary point in $S$ and it's corresponding point (closest point) on the boundary of the convex hull $K$.
Please advise.