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.