Between Shapes, Using the Hausdorff Distance

Marc van Kreveld, Tillmann Miltzow, Tim Ophelders +2

Given two shapes $A$ and $B$ in the plane with Hausdorff distance $1$, is there a shape $S$ with Hausdorff distance $1/2$ to and from $A$ and $B$? The answer is always yes, and dep…