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5

Since your figure is a closed loop, its parametric curves $x(t)$ and $y(t)$ must be periodic functions. This suggests one way to generate such figures, by constructing random smooth periodic functions $x(t)$ and $y(t)$ via summation of sinusoids/harmonics with randomized amplitude and phase. Unfortunately, it would be difficult to guarantee such a figure ...


2

I am going to assume that we have arrays of the edges representing the top and bottom curves for the winding polygon with edges going from left to right. Also make $n$ as the total number of edges in this polygon. Now consider the following visualization of the geometry where we construct some point using the two "sides" of the concave polygon: It ...


2

I'm sure there are better solutions than this, but since no one else has answered to this point, I'll throw out a this-is-what-I'd-do answer. Triangulate the polygon If your polygon doesn't have too many points, a simple $\mathcal{O}(N^2)$ ear-clipping method could be viable. For large polygons, this might be an inefficient solution. It's important to the ...


2

You could use a medial axis transform if the transform is discretized, each point in the transform indicates the radius from that point to the nearest two edges. Doubling this gives the width. To deal with noise, you could take something like the 95th+ percentile of such points and then average. You could also look into rotating caliper methods: though I ...


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