Probing convex polygons with X-rays

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 necesssary 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.