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.

中文翻译：

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大海捞针

通过比较它们在任何周围圆上的视角函数，凸多边形在分段 $$C^\infty $$ C ∞ 凸域中是可区分的。这是我们主要结果的结果，$$C^\infty $$C ∞ 多曲线中的每个段都可以从给定的任何周围圆的多曲线的掩蔽函数中重建。