I begin by defining an interpolation of some data I have stored at this link for brevity. The interpolating function is a function of two variables, x
and y
S = (*data*)
f = Interpolation[S]
Plot3D[f[x, y], {x, -5, 4}, {y, -5, 4}]

I then want to define a one-dimensional surface by when this interpolated function intersects zero
R = ImplicitRegion[f[x, y] == 0.0]
RegionPlot[R, PlotRange -> {{-5, 4}, {-5, 4}}

This looks like it has worked quite well, but now when I try to calculate ArcLength[R]
, I don't get an answer, even when I try restricting the domain of the implicit region
R = ImplicitRegion[f[x, y] == 0.0, {{x, -5, 4}, {y, -5, 4}}]
The ellipse looks pretty well-defined, is there a way of getting its arc Length?
S = Import["https://gist.github.com/jhwilson/10467024a973e3b8cf0acf4990a1a21d", "Data"][[1, 2]] // ToExpression
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