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Let a planar region $R$ be defined by the vertical range bounded by a polynomial $f(x) \pm c$ with $c>0$ a constant, and with $x$ varying between the smallest and largest roots of $f(x)$. For ...

I have a need to find a polynomial of minimal degree that connects two points and stays within a given "corridor," by which I mean an $x$-monotone polygon. Here is an example:       &...