Meshing a 2D contour plot

Question

Elliot Bontoft 2020-5-14

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/525473-meshing-a-2d-contour-plot

回答： Jiexian Ma 2025-4-6

采纳的回答： darova

在 MATLAB Online 中打开

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.

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Ameer Hamza 2020-5-14

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 2020-5-14

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

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Answer 1

darova 2020-5-14

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https://ww2.mathworks.cn/matlabcentral/answers/525473-meshing-a-2d-contour-plot#answer_432523

在 MATLAB Online 中打开

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

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Elliot Bontoft 2020-5-19

编辑：Elliot Bontoft 2020-5-19

在 MATLAB Online 中打开

generateMesh_V9.m

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 2020-5-19

Can be connected closer

Elliot Bontoft 2020-5-20

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

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Answer 2

Jiexian Ma 2025-4-6

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https://ww2.mathworks.cn/matlabcentral/answers/525473-meshing-a-2d-contour-plot#answer_1563214

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.

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