# 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. Aug 21 '17 at 18:06
• If your data is too large to post here, please put it on Pastebin. Aug 21 '17 at 18:09
• Edited Anton. Code posted. Aug 21 '17 at 19:13
• We don't have your para_loop_20.dat; you've already been told where to post it. Aug 21 '17 at 19:23
• I've exceed the maximum paste size, J.M. 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. 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. Aug 21 '17 at 20:13
• @Mateus Strongly related: (85212). Aug 21 '17 at 22:35
• Thanks @AlexeyPopkov! Aug 21 '17 at 22:45
• @MarcoB it works! Thanks a lot! Aug 21 '17 at 22:45