Interpolate data between two specified contours

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Carola Forlini
Carola Forlini on 28 Aug 2023
Edited: Star Strider on 28 Aug 2023
Hi,
I would like to interpolate the data between two selected contours (blue and violet lines in the attached plot).
How can I do that?
Thank you,
Carola

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Accepted Answer

Star Strider
Star Strider on 28 Aug 2023
Ran in:
I am not certain what result you want. The easiest way is probably to use the contour function itself to interpolate.
Example —
x = linspace(50, 100, 50);
y = linspace(0.2, 0.6, 50);
z = x(:)*y
z = 50×50
10.0000 10.4082 10.8163 11.2245 11.6327 12.0408 12.4490 12.8571 13.2653 13.6735 14.0816 14.4898 14.8980 15.3061 15.7143 16.1224 16.5306 16.9388 17.3469 17.7551 18.1633 18.5714 18.9796 19.3878 19.7959 20.2041 20.6122 21.0204 21.4286 21.8367 10.2041 10.6206 11.0371 11.4536 11.8701 12.2865 12.7030 13.1195 13.5360 13.9525 14.3690 14.7855 15.2020 15.6185 16.0350 16.4515 16.8680 17.2845 17.7010 18.1175 18.5339 18.9504 19.3669 19.7834 20.1999 20.6164 21.0329 21.4494 21.8659 22.2824 10.4082 10.8330 11.2578 11.6826 12.1075 12.5323 12.9571 13.3819 13.8067 14.2316 14.6564 15.0812 15.5060 15.9309 16.3557 16.7805 17.2053 17.6302 18.0550 18.4798 18.9046 19.3294 19.7543 20.1791 20.6039 21.0287 21.4536 21.8784 22.3032 22.7280 10.6122 11.0454 11.4786 11.9117 12.3449 12.7780 13.2112 13.6443 14.0775 14.5106 14.9438 15.3769 15.8101 16.2432 16.6764 17.1095 17.5427 17.9758 18.4090 18.8421 19.2753 19.7085 20.1416 20.5748 21.0079 21.4411 21.8742 22.3074 22.7405 23.1737 10.8163 11.2578 11.6993 12.1408 12.5823 13.0237 13.4652 13.9067 14.3482 14.7897 15.2312 15.6726 16.1141 16.5556 16.9971 17.4386 17.8800 18.3215 18.7630 19.2045 19.6460 20.0875 20.5289 20.9704 21.4119 21.8534 22.2949 22.7364 23.1778 23.6193 11.0204 11.4702 11.9200 12.3698 12.8197 13.2695 13.7193 14.1691 14.6189 15.0687 15.5185 15.9683 16.4182 16.8680 17.3178 17.7676 18.2174 18.6672 19.1170 19.5668 20.0167 20.4665 20.9163 21.3661 21.8159 22.2657 22.7155 23.1653 23.6152 24.0650 11.2245 11.6826 12.1408 12.5989 13.0571 13.5152 13.9733 14.4315 14.8896 15.3478 15.8059 16.2641 16.7222 17.1803 17.6385 18.0966 18.5548 19.0129 19.4711 19.9292 20.3873 20.8455 21.3036 21.7618 22.2199 22.6781 23.1362 23.5943 24.0525 24.5106 11.4286 11.8950 12.3615 12.8280 13.2945 13.7609 14.2274 14.6939 15.1603 15.6268 16.0933 16.5598 17.0262 17.4927 17.9592 18.4257 18.8921 19.3586 19.8251 20.2915 20.7580 21.2245 21.6910 22.1574 22.6239 23.0904 23.5569 24.0233 24.4898 24.9563 11.6327 12.1075 12.5823 13.0571 13.5319 14.0067 14.4815 14.9563 15.4311 15.9059 16.3807 16.8555 17.3303 17.8051 18.2799 18.7547 19.2295 19.7043 20.1791 20.6539 21.1287 21.6035 22.0783 22.5531 23.0279 23.5027 23.9775 24.4523 24.9271 25.4019 11.8367 12.3199 12.8030 13.2861 13.7693 14.2524 14.7355 15.2187 15.7018 16.1849 16.6681 17.1512 17.6343 18.1175 18.6006 19.0837 19.5668 20.0500 20.5331 21.0162 21.4994 21.9825 22.4656 22.9488 23.4319 23.9150 24.3982 24.8813 25.3644 25.8476
figure
[c1,h1] = contour(x, y, z, 'ShowText',1);
colormap(turbo)
% Lvls = h1.LevelList
hold on
[c2,h2] = contour(x, y, z, [1 1]*26.75, '--k', 'ShowText',1); % Draw Contour At Interpolation Level = 27.75
hold off
LevelInterp = array2table(c2(:,2:end).', 'VariableNames',{'X','Y'}) % (X,Y) Coordinates Of The Interpolated Line
LevelInterp = 83×2 table
X Y ______ _______ 58.438 0.6 58.782 0.59184 59.134 0.58367 59.184 0.58254 59.493 0.57551 59.86 0.56735 60.204 0.55986 60.235 0.55918 60.618 0.55102 61.01 0.54286 61.224 0.53845 61.41 0.53469 61.819 0.52653 62.237 0.51837 62.245 0.51822 62.665 0.5102
Your data seem to be contonuous (only one contour at each level of interest) so this approach should work both to draw the contour and return the (x,y) coordinates of that contour if that is what you want to do. You can do this more than once for more interpolated levels, or get more than one interpolated contour in one call to contour (however that then requires a bit of straightforward — although nontrivial — coding to extract the (x,y) coordinates of each contour).
.
  2 Comments
Carola Forlini
Carola Forlini on 28 Aug 2023
Thank you for your reply. I am looking for interpolating between two levels and then take probasly the mean between all the values.
From your example: what if I want to interpolate continuously between levels 25 and 30? How can I extract the (x,y) coodinates?
Star Strider
Star Strider on 28 Aug 2023
Edited: Star Strider on 28 Aug 2023
Ran in:
My pleasure!
Extracting all those values would not necessarily require using contour once you decided on the levels.
That might be simply something like this —
X = linspace(50, 100, 50);
Y = linspace(0.2, 0.6, 50);
Z = X(:)*Y
Z = 50×50
10.0000 10.4082 10.8163 11.2245 11.6327 12.0408 12.4490 12.8571 13.2653 13.6735 14.0816 14.4898 14.8980 15.3061 15.7143 16.1224 16.5306 16.9388 17.3469 17.7551 18.1633 18.5714 18.9796 19.3878 19.7959 20.2041 20.6122 21.0204 21.4286 21.8367 10.2041 10.6206 11.0371 11.4536 11.8701 12.2865 12.7030 13.1195 13.5360 13.9525 14.3690 14.7855 15.2020 15.6185 16.0350 16.4515 16.8680 17.2845 17.7010 18.1175 18.5339 18.9504 19.3669 19.7834 20.1999 20.6164 21.0329 21.4494 21.8659 22.2824 10.4082 10.8330 11.2578 11.6826 12.1075 12.5323 12.9571 13.3819 13.8067 14.2316 14.6564 15.0812 15.5060 15.9309 16.3557 16.7805 17.2053 17.6302 18.0550 18.4798 18.9046 19.3294 19.7543 20.1791 20.6039 21.0287 21.4536 21.8784 22.3032 22.7280 10.6122 11.0454 11.4786 11.9117 12.3449 12.7780 13.2112 13.6443 14.0775 14.5106 14.9438 15.3769 15.8101 16.2432 16.6764 17.1095 17.5427 17.9758 18.4090 18.8421 19.2753 19.7085 20.1416 20.5748 21.0079 21.4411 21.8742 22.3074 22.7405 23.1737 10.8163 11.2578 11.6993 12.1408 12.5823 13.0237 13.4652 13.9067 14.3482 14.7897 15.2312 15.6726 16.1141 16.5556 16.9971 17.4386 17.8800 18.3215 18.7630 19.2045 19.6460 20.0875 20.5289 20.9704 21.4119 21.8534 22.2949 22.7364 23.1778 23.6193 11.0204 11.4702 11.9200 12.3698 12.8197 13.2695 13.7193 14.1691 14.6189 15.0687 15.5185 15.9683 16.4182 16.8680 17.3178 17.7676 18.2174 18.6672 19.1170 19.5668 20.0167 20.4665 20.9163 21.3661 21.8159 22.2657 22.7155 23.1653 23.6152 24.0650 11.2245 11.6826 12.1408 12.5989 13.0571 13.5152 13.9733 14.4315 14.8896 15.3478 15.8059 16.2641 16.7222 17.1803 17.6385 18.0966 18.5548 19.0129 19.4711 19.9292 20.3873 20.8455 21.3036 21.7618 22.2199 22.6781 23.1362 23.5943 24.0525 24.5106 11.4286 11.8950 12.3615 12.8280 13.2945 13.7609 14.2274 14.6939 15.1603 15.6268 16.0933 16.5598 17.0262 17.4927 17.9592 18.4257 18.8921 19.3586 19.8251 20.2915 20.7580 21.2245 21.6910 22.1574 22.6239 23.0904 23.5569 24.0233 24.4898 24.9563 11.6327 12.1075 12.5823 13.0571 13.5319 14.0067 14.4815 14.9563 15.4311 15.9059 16.3807 16.8555 17.3303 17.8051 18.2799 18.7547 19.2295 19.7043 20.1791 20.6539 21.1287 21.6035 22.0783 22.5531 23.0279 23.5027 23.9775 24.4523 24.9271 25.4019 11.8367 12.3199 12.8030 13.2861 13.7693 14.2524 14.7355 15.2187 15.7018 16.1849 16.6681 17.1512 17.6343 18.1175 18.6006 19.0837 19.5668 20.0500 20.5331 21.0162 21.4994 21.9825 22.4656 22.9488 23.4319 23.9150 24.3982 24.8813 25.3644 25.8476
Lm = Z>=25 & Z<=30 % Logical Matrix Of Values Meeting Criteria
Lm = 50×50 logical array
Columns 1 through 49 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Ze = Z.*Lm;
for kc = 1:size(Ze,2)
Zm{:,kc} = Ze(Ze(:,kc)~=0,kc);
end
Zmnzc = cellfun(@(x)any(x~=0,1), Zm, 'Unif',0); % Logical Index Of Non-Zero Entries
Zmnz = Zm([Zmnzc{:}]) % Cell Array Of Noin-Zero Entries
Zmnz = 1×43 cell array
Columns 1 through 11 {3×1 double} {6×1 double} {9×1 double} {12×1 double} {14×1 double} {16×1 double} {16×1 double} {16×1 double} {16×1 double} {14×1 double} {14×1 double} Columns 12 through 22 {14×1 double} {14×1 double} {13×1 double} {14×1 double} {13×1 double} {12×1 double} {13×1 double} {12×1 double} {12×1 double} {11×1 double} {11×1 double} Columns 23 through 33 {11×1 double} {11×1 double} {10×1 double} {10×1 double} {10×1 double} {10×1 double} {10×1 double} {10×1 double} {10×1 double} {9×1 double} {8×1 double} Columns 34 through 43 {7×1 double} {6×1 double} {6×1 double} {5×1 double} {4×1 double} {3×1 double} {3×1 double} {2×1 double} {[29.5918]} {[30]}
Column_Means = cellfun(@mean, Zmnz)
Column_Means = 1×43
25.4519 25.8538 26.2307 26.5827 27.0575 27.5156 27.6447 27.4198 27.4740 27.4948 27.4823 27.4365 27.3574 27.4302 27.4781 27.5010 27.4990 27.4719 27.4198 27.5531 27.4552 27.5510 27.6302 27.6926 27.5073 27.5323 27.5406 27.5323 27.5073 27.4656
This finds all the values for ‘Z’ meeting the criteria, and then (since there might be different numbers of elements in each row or column) isolates the columns with at least one non-zero value and then takes the mean of each column. The grand mean would then be the means off all those, in this instance:
GrandMean = mean(Column_Means)
EDIT — (28 Aug 2023 at 22:21)
Another option of course is to just do —
GrandMean = mean(Z(Lm))
GrandMean = 27.5002
.

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More Answers (1)

Matt J
Matt J on 28 Aug 2023
Edited: Matt J on 28 Aug 2023
We don't know in what form your input data exists. Most of the contour plotting functions allow you to specify the isocontour level that you want computed. To interpolate, you would just choose a level that lies between the levels of the blue and violet lines.
  2 Comments
Carola Forlini
Carola Forlini on 28 Aug 2023
My input data are organzed as follow:
Time = 1XN
Frequency = 1XM
Z = MxN
I am using the contour plot in order to visualize the different levels of my data based on a specified colormap. I would like to interpolate and plot the data between two specified levels (there will be nans).
Matt J
Matt J on 28 Aug 2023
Edited: Matt J on 28 Aug 2023
One possibility would be to use contourc
C = contourc(Time,Frequency,Z,target_level)
You can extract x,y coordinates from the contour matrix C using getContourLineCoordinates from this FEX download,
https://www.mathworks.com/matlabcentral/fileexchange/74010-getcontourlinecoordinates?s_tid=srchtitle
contourTable = getContourLineCoordinates(C)

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