Dakota Charles Baker

The Kernel Deficit Dominates Twice the Hull Deficit

For a simple polygon F in the plane, the kernel K(F) is the set of points that see all of F, and the convex hull C(F) measures how far F is from being convex. We prove that the two associated losses are linked by a sharp factor of two: area(F)(area(F) − area(K)) ≥ 2·area(K)(area(...

The Kernel Deficit Dominates Twice the Hull Deficit

For a simple polygon F in the plane, the kernel K(F) is the set of points that see all of F, and the convex hull C(F) measures how far F is from being convex. We prove that the two associated losses are linked by a sharp factor of two: area(F)(area(F) − area(K)) ≥ 2·area(K)(area(...