Create mesh around more than one shape

I am trying to create an autonomous meshing code to create a 2D mesh around certain shapes that are created by the MATLAB contour function via the generateMesh function.

I am building the geometry from the contour coordinate data. This is used to create a polygon shape to be defined in the geometry description matrix, then the MATLAB decsg function is used.

I have succesfully got this working for a domain rectangle with one contour shape deducted from it. However, when I have more than one shape removed from the rectangle it fails, I get the following error displayed:

Output argument "dl1" (and maybe others) not assigned during call to "decsg".

If I instead try to add the domain and the contours together in the Set Formula, then again, it works for the domain plus one contour shape, but for multiple shapes I recieve the following error:

Meshing failed to create initial discretization.

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.

Below is how I autonomously create a character string for the Set Formula and Name-Space matrix.

% Set formula
dr = 'R1';
sf = [dr,'-',cf_i(1,:)];            % set formula for when removing contours from domain
% sf = [dr,'+',cf_i(1,:)];          % set formula for when adding contours to domain
for i = 2:n_contours
   sf = [sf,'-',cf_i(i,:)];         % set formula for when removing contours from domain
%    sf = [sf,'+',cf_i(i,:)];       % set formula for when adding contours to domain
end

% Name geometry
ns = char([dr]);
for i = 1:n_contours
   ns = char([ns;cf_i(i,:)]);
end

% Invoke decsg
g = decsg(gdm,sf,ns');

Below is an image of the meshed domain with one shape successfully removed (left) and the same domain and contour shape but added together (right):

Any insight to why this is not working for more than one shape is greatly appriciated.

Thank you.

Full code attached.

Answer 1

[Elliot Bontoft]

To any others facing this problem in the future, I believe I found the solution:

The MATLAB contours function creates coordinate data that (when the shape is closed) has a coordinate point that starts and ends on the same point. The decsg function, however, only asks for the coordinate point at the beginning point of the edge for a polygon, this was causing problems when run iteratively - but was fine when run for one contour line (as I mentioned in the question above).

Removing the final point from the contour line data resolved the problem:

for i = 1:n_contours
    x = A{1,i}(1,:);
    y = A{1,i}(2,:);
    
    % Contour geometry description
    S(i+1,1) = 2;
    S(i+1,2) = numel(x(1,:))-1;     %introduced this -1
    k = 2;
    for ii = 1:(numel(x(1,:)))-1    %introduced this -1
        k = k+1;
        S(i+1,k) = x(1,ii);
    end
    k = numel(x(1,:)) + 1;          %this is now +1 rather than +2
    for jj = 1:(numel(y(1,:)))-1    %introduced this -1
        k = k+1;
        S(i+1,k) = y(1,jj);
    end
    
    % Names each contour formula iteratively
    cf_i(i,:) = ['S',num2str(i)];
end