How to access the data of contourf function to decides whether the interior of the contour is filled or not?

How can I access the contourf function data that could inform me on whether the internal data of the contour (that has a filled colour) is greater or lesser than the value the contour is designated to 'cut' the surface function at.

I.e.

p = peaks;
figure
k = contourf(p, [2 2]);

The 'cut' of the surface function, p, occurs at a defined value (or you could think of it as a height) of 2. This would give a plot as follows:

To restate my question; how/where can I access the data that dictates if the internal value of the contour is greater or lesser than the cut off value (in this case, 2). In this case it is clear that the internal value is greater than the cut off value, but I would like to access this information so that can create an algorithm to do this autonomously for any contourf plot. I am confident this information should be availible as the contourf function knows whether to colour fill the interior of the contour or not.

Thank you for any advice in advance.

Answer 1

[darova]

You can access to each contour separately

[C,h] = contourf(p, [2 2]);
h1 = get(h,'children');
for i = 1:length(h1)
    x = get(h1(i),'xdata');
    y = get(h1(i),'ydata');
end

[Elliot Bontoft]

Thanks Darova, This will get me the X and Y data of the coordinate points along the contour. However, I would like to determine whether the interior enclosed by the contour is greater or lesser than the contour cut-off value.

[darova]

You want to calculate area. Is it correct?

[Elliot Bontoft]

No, I would like to determine whether the values of the function inside the closed contour are greater or lesser than the value the contour is imposed at.

[darova]

I extracted data of each contour and get value at the center

Use interp2 to get value for specific point

[X,Y,Z] = peaks(30);
surf(X,Y,Z,'edgecolor','none')
alpha(0.3)
hold on
val = 3;
[C,h] = contour3(X,Y,Z,val*[1 1],'b');
hold off

% h1 = get(h,'children');
for i = 1:length(h)
    x = get(h(i),'xdata');                  % extract data
    y = get(h(i),'ydata');
    z = interp2(X,Y,Z,mean(x),mean(y));     % value at center of contour
    if z > val
        patch(x,y,x*0+val,'r')
    else
        patch(x,y,x*0+val,'b')
    end
end
axis vis3d

Results

[Elliot Bontoft]

Hi Darova,

I have been through your response, it is effective for cases such as Peaks.

However, I am trying to develop a technique that will work for all functions. If I could present another case for which finding the centre point will not work.

%% Case: Closed contour within another
x = [-4 4];                                     % x limits
y = [-4 4];                                     % y limits
xlin = linspace(min(x),max(x),100);
ylin = linspace(min(y),max(y),100);
[X,Y] = meshgrid(xlin,ylin);
Z = (X.^2 + Y.^2) - 0.1*(X.^4 + Y.^4);          % equation of surface function

%% Figure begins
figure()
surf(X,Y,Z,'edgecolor','none');
alpha(0.3);
hold on
val = 2;                                        % value at which contours are extracted
[C,h] = contour3(X,Y,Z,(val*[1 1]),'b');

%% Isolating all contours to seperate data files via the contour matrix, C
length = numel(C(1,:));
index_i = C(2,1);
index_t_old = index_i + 1;
n_contours = 1;
A{n_contours} = C(:,2:index_t_old);
while index_t_old < length
    n_contours = n_contours + 1;
    index_i = C(2,index_t_old+1);
    index_t_new = index_t_old + index_i + 1;
    A{n_contours} = C(: , index_t_old + 2 : index_t_new);
    index_t_old = index_t_new;
end

%% Adding Patches to closed contours -> blue = NEG / red = POS
for i = 1:n_contours
    x = A{1,i}(1,:);                            % extract data
    y = A{1,i}(2,:);
    z = interp2(X,Y,Z,mean(x),mean(y));         % value at center of contour
    if z > val
        patch(x,y,(x*0+val),'r')
    else
        patch(x,y,(x*0+val),'b')
    end
end

axis vis3d

This will provide the surface presented below. Where if the internal value of the contours is taken, they will both return as less than the contour cut off value (z<val).

I wonder if there is any data availible built into the MATLAB function contourf. As it is clear that the function is able to identify the internal values of the contours, for example:

Z = peaks;
contourf(Z)

alone provides the figure below. Which tells me that maybe somewhere in the contourf property data there is information on the internal values of the contour (with respect to other internal contours), in order to know what colour to use; however, I have not been able to find/understand this.

Thank you for your help.

[darova]

I understand. Here is another idea:

• Get value inside contour close to boundary

I used cross product to calculate direction of a curve. Because i don't know how MATLAB get points of a contour (they can be clockwise or anticlockwise)

Another problem is rendering. Which contour should be lower or higher?

I just add 1/numel(x) to z value (small contour will be a little higher)

Also i noticed that you use variable name of already existing function. It's a bad practice

See attached script

[Elliot Bontoft]

Hi Darova,

Thank you for your response, it has been very valuable.

However, I have noticed something when experimenting with the algorithm. This set up is dependant on the starting coordinates on the contour i.e where the step 'into' the contour starts from. Please see below:

In this case, the method works effectively. I have introduced a for loop to create a step into the contour and check of the interpolated function value every 1/4 of the number of coordinates in the contour data set. Please not that I have enlarged the step size for visual purposes - I am not working with it at this size.

However, if i am to use a difficult function, this does not work, as the starting position of the contour can create a vector with a direction pointing outside of the contour. Please see below:

Where some of the contours that should be a hole/void (represented by a blue patch), are coming back with a red patch - i.e. value greater than the contour (z1>val). This can be visualised with the figures below:

I thought maybe to take the majority of the points, and trust they are correct, however you can see from the left figure above, that the majority could actually be incorrect. I have attached the code.

Thanks for your support so far, any insight in how to progress from here is appriciated.

[darova]

Sorry fot the late response. Didn't see you answered

What about inpolygon? It can check if point is inside a contour

[Elliot Bontoft]

Hi @darova,

Thanks for getting back to this post.

Yes, in the end I used the first three points, calculated the angle between the vector from point 2-1, and 2-3. Then took a small step in the vector of half that angle in either direction (thus, one must be inside and one outside).

Knowing this, I used inpolygon to check which one was internal.

Thanks for your help, this is working well and is quite robust.

Code attached.