# Interpolate contour line

I have a list of data points. From this list I generate a plot using ListCountourPlot. Mathematica interpolates multiple Countour lines.

I want to extract the points $(d,b)$ for a specific line which is the line $\omega_i = 0$ (red line).

How can I do that? Mathematica code:

j132 = Import["/home/mateus/Desktop/LaminarSeparationBubble/para_loop_20.dat"];

newStyle[x_] := x /. l_Line :> Sequence[Opacity, Thick, Red, l]

lista131 =
Table[{j132[[i, 2]], j132[[i, 1]], j132[[i, 9]]}, {i, 1,
Length[j132]}];

ListContourPlot[lista131, PlotLegends -> Automatic, Contours -> 30,
FrameLabel -> {"b", "d", "ωi"}, PlotRange -> All,
ImageSize -> 400] /. Tooltip[x_, 0] :> Tooltip[newStyle[x], 0]

• Please post the Mathematica code you used to produce this plot. – Anton Antonov Aug 21 '17 at 18:06
• If your data is too large to post here, please put it on Pastebin. – J. M. will be back soon Aug 21 '17 at 18:09
• Edited Anton. Code posted. – Mateus Aug 21 '17 at 19:13
• We don't have your para_loop_20.dat; you've already been told where to post it. – J. M. will be back soon Aug 21 '17 at 19:23
• I've exceed the maximum paste size, J.M. – Mateus Aug 21 '17 at 19:31

I am not sure that I understand, but it seems to me that you already have a method to isolate the Line element corresponding to that contour line. In fact, you do that in your newStyle function.

Try:

Cases[
Normal@ListContourPlot[lista131, Contours -> {{0}}],
Tooltip[x_, 0] :> Cases[x, l_Line :> l[]], Infinity
]

• My objective in fact is draw a tangent line (derivate = 0) at this curve (wi = 0). So my plan is get these coordinates (d,b) for wi = 0, interpolate and get the point when derivate is = 0. – Mateus Aug 21 '17 at 20:08
• @Mateus OK. Could you specify whether the method I proposed works to extract the (d, b) pairs at least? Also, if you need help with the rest of the problem, you should really include that in your original question. – MarcoB Aug 21 '17 at 20:13
• @Mateus Strongly related: (85212). – Alexey Popkov Aug 21 '17 at 22:35
• Thanks @AlexeyPopkov! – Mateus Aug 21 '17 at 22:45
• @MarcoB it works! Thanks a lot! – Mateus Aug 21 '17 at 22:45