Meshing a 2D contour plot

I am looking to create a mesh within the lines of a 2D contour plot.

For example, with the code:

f = peaks;
contour(f,[2 2])

You achieve the following plot:

I would like to be able to generate a mesh inside and outside of the contour lines (within a domain of say 50x50 for this example).

Could someone suggest the best way to achieve this?

Thank you in advance.

[Ameer Hamza]

Are you trying to create a mesh plot? If you want to plot both inside and outside the contour lines, isn't it the same as a regular mesh plot? Can you show an example image of what is your intended output?

[Elliot Bontoft]

I am trying to develop a finite element mesh, both inside and outside the contour lines, where the nodes align on the contours themselves.

Something like:

but with the inside of the shape meshed too.

Where the shape would be defined by the contour lines from the contour(f,[2 2]) function.

Thanks

Answer 1

[darova]

Use initmesh

clc,clear

x1 = [0 5 5 0];                                 % rectangle
y1 = [0 0 3 3]; 
[x2,y2] = pol2cart(0:.3:2*pi,1);                % circle
gd2 = [2;length(x2);x2(:)+1.5;y2(:)+1.5];       % circle geometry
gd1 = gd2*0;
gd11 = [2;length(x1);x1(:);y1(:)];              % rectangle geometry
gd1(1:length(gd11)) = gd11;
dl = decsg([gd1 gd2],'P1-P2',char('P1','P2')'); % decomposition geometry
[p,e,t] = initmesh(dl);                         % build a mesh

pdemesh(p,e,t)                                  % display mesh

dl2 = decsg(gd2);                               % decomposition of circle
[p,e,t] = initmesh(dl2);                        % build a mesh
hold on
pdemesh(p,e,t)                                  % display emsh
hold off

[Elliot Bontoft]

Hi Darova,

This is very useful, I have been trying to use this (except with the generateMesh function rather than initmesh - as I believe initmesh is a legacy method https://uk.mathworks.com/help/pde/ug/initmesh.html)

I have used the coordinate data of the contours to build the geometry description matrix for the decsg function. This has been effective for when I have only one contour inside the domain rectangle. However, for more than one contour this creates an error - I have posted this in another forum question as I believe it is a seperate question (https://uk.mathworks.com/matlabcentral/answers/526595-create-mesh-around-more-than-one-shape).

Below is the algorithm I am using to build the geometry description matrix from the contour data:

% Domain rectangle
DR = [3,4,x_dom(1),x_dom(2),x_dom(2),x_dom(1),y_dom(2),y_dom(2),y_dom(1),y_dom(1)]';
S(1,:) = DR(:,1)';

% Contours from contour plot
for i = 1:n_contours
    x = A{1,i}(1,:);                                % extract x data
    y = A{1,i}(2,:);                                % extract y data
    % Contour geometry description
    S(i+1,1) = 2;
    S(i+1,2) = numel(x(1,:));
    k = 2;
    for ii = 1:(numel(x(1,:)))
        k = k+1;
        S(i+1,k) = x(1,ii);
    end
    k = numel(x(1,:)) + 2;
    for jj = 1:(numel(y(1,:)))
        k = k+1;
        S(i+1,k) = y(1,jj);
    end
    % Names each contour formula iteratively
    cf_i(i,:) = ['S',num2str(i)];
end
gdm = S';   % geometry description matrix

where, n_contours is the total number of contours produced by the MATLAB contour function, and A is the cell array that hold all the contour data sets. See below the mesh successfully created for a domain with one contour.

To my knowledge this is the best way to achieve this.

Thank you for your help.

Full code attached.

[darova]

What about brute force?

x1 = [5 5 0 0 5];                % rectangle
y1 = [0 3 3 0 0]; 
[x2,y2] = pol2cart(0:.2:2*pi,1); % circle
gd = [2;length(x2)+length(x1)
    x2(:)+1.5;x1(:)
    y2(:)+1.5;y1(:)];            
dl = decsg(gd);
[p,e,t] = initmesh(dl);          % build a mesh
pdemesh(p,e,t)                   % display mesh
axis equal

[darova]

Can be connected closer

[Elliot Bontoft]

Hi Darova,

I see what you've done there, very clever work around. However, I will be using this meshed model to run a simulation on, and the boundaries will influence the behaviour of the response.

Thank you for the suggestions

Answer 2

[Jiexian Ma]

As far as I know, there are two ways to do this.

• Method 1. Create geometry through Constructive Solid Geometry and obtain mesh via PDE toolbox. darova's answer used this method.
• Method 2. Create geometry via polyshape and generate mesh via Im2mesh package.

Personally, I perfer method 2 because you can edit polyshape object easily.

Matlab code

You could check demo14 to demo17 in Im2mesh package. I provide a few examples.