Sibley's Guard-Point Convexity Measure: A Perimeter Counterexample and a Dominance Bound

Masahito Nakano

For a simple polygonal region $F$, let $K(F)$ be its polygon kernel, or Sibley's guard-point set, and let $C=\mathrm{conv}(F)$. The associated guard-point, exterior, and peri…