Probing Convex Polygons with X-rays
Herbert Edelsbrunner, Steven Skiena · SIAM Journal on Computing · 1988
An X-ray probe through a polygon measures the length of intersection between a line and the polygon. This paper considers the properties of various classes of X-ray probes, and shows how they interact to give finite strategies for completely describing convex n-gons. It is shown that $({{3n} / 2}) + 6$ probes are sufficient to verify a specified n-gon, while for determining convex polygons ${{(3n - 1)} / 2}$ X-ray probes are necessary and $5n + O(1)$ sufficient, with $3n + O(1)$ sufficient given that a lower bound on the size of the smallest edge of P is known.