Model-based Probing Strategies for Convex Polygons

We prove that n + 4 finger probes are sufficient to determine the shape of a convex n-gon from a finite collection of models, improving the previous result of 2n + 1. Further, we show that n − 1 are necessary, proving this is optimal to within an additive constant. For line probes, we show that 2n + 4 probes are sufficient and 2n − 3 necessary. The difference between these results is particularly interesting in light of the duality relationship between finger and line probes.