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How to get contour plot and line plot intersection values/ coordinates

Asked by Mahi Nazir on 16 Jul 2013

I am plotting a 3D graph and a contour of the same. Then I plot few lines on the contour plot. I want to know the value of the contour where the line crosses the contour and also the coordinates where intersection happens. Can anyone please help me with this

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Mahi Nazir

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1 Answer

Answer by Kelly Kearney on 16 Jul 2013

I assume by 3D graph with contour, you mean you have 3D data represented in 2D by a contour plot? Or do you mean something like contour3 or isosurface?

Assuming the former, the coordinates of the contour lines generated via

 [c,h] = contour(x,y,z);

are found in the c matrix. There are a few File Exchange functions (like contourcs) that can simplify the task of extracting those coordinates.

If you have the Mapping Toolbox, polyxpoly can calculate the line intersections. Otherwise, there are a bunch of FEX entries to calculate the intersections of two lines/curves (like this one).

3 Comments

Mahi Nazir on 18 Jul 2013

Thanks kelly

I am quite new to matlab. Do I need to add contourcs in my library. I see thats its not already there?

And yes your assumption is right, 3D data represented in 2D by a contour plot.

The polyxpoly function is used for line intersections, does that include the contour as well, I am not sure? Your help would be greatly appreciated

Mahi Nazir on 18 Jul 2013

And yes after I get the intersection coordinates of the line and contour, I require the value of contour (from 3D graph) at those coordinates.

Kelly Kearney on 19 Jul 2013

Yes, to use the contourcs function, you need to download it from the File Exchange, and then either place it in the same folder as where you are working, or add it to your path (You can read up on that under the "Search Path" section of the documentation).

Here's a quick example of how to use those functions to calculate intersections:

    % Some example data
    [x,y,z] = peaks;
    % Calculate the coordinates of the contour lines
    % (here, just the contour line at z = 0)
    C = contourcs(x(1,:),y(:,1),z,[0 0]);
    % Coordinates of the intersecting line
    xln = [0 0];
    yln = [-3 3];
    % Use polyxpoly to find intersections
    for ic = 1:length(C)
        [xint{ic}, yint{ic}] = polyxpoly(xln, yln, C(ic).X, C(ic).Y);
    end
    xint = cat(1, xint{:});
    yint = cat(1, yint{:});
    % Plot the results
    figure;
    contour(x,y,z,[0 0], 'k');
    hold on;
    plot(xln, yln, 'b');
    plot(xint, yint, 'r*');
Kelly Kearney

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