Finding Needles in a Haystack

Convex polygons are distinguishable among the piecewise $$C^\infty $$ C ∞ convex domains by comparing their visual angle functions on any surrounding circle. This is a consequence of our main result, that every segment in a $$C^\infty $$ C ∞ multicurve can be reconstructed from the masking function of the multicurve given on any surrounding circle.