# Refine delaunay triangulation mesh

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Bruno Neto on 22 Jun 2022
Commented: Kevin Moerman on 22 Jun 2022
I have the code wich generates this delaunay triangulation. I need to add more triangles inside this object to get it as uniform as possible. I wanted to refine my mesh in order to remove those chunky triangles inside and get a larger number of triangles.
Note that my object has 3 holes inside it, and obviously, I dont want to fill them with triangles
How do I get a refined delaunay triangulation mesh? Without using the alphashape command

Kevin Holly on 22 Jun 2022
Edited: Kevin Holly on 22 Jun 2022
I was able to increase the density using the subtri() function upload by Kevin Moerman to the File Exchange.
ImgClosed=im2bw(ImgClosed);
[B,L,N,A] = bwboundaries(ImgClosed);
figure
imshow(ImgClosed)
hold on;
for k = 1:N
% Boundary k is the parent of a hole if the k-th column of the adjacency matrix A contains a non-zero element
if (nnz(A(:,k)) > 0)
boundary = B{k};
redline = plot(boundary(:,2),boundary(:,1),'r','LineWidth',2);
% Loop through the children of boundary k
for l = find(A(:,k))'
boundary = B{l};
greenline(l,:) = plot(boundary(:,2),boundary(:,1),'g','LineWidth',2);
end
end
end
figure
axes
plot(redline.XData,redline.YData,'r','LineWidth',2)
hold on
x=redline.XData;
y=redline.YData;
c = [(1:length(x)-1).' (2:length(x)).'];
for jj = 1:size(greenline,1)
try
plot(greenline(jj).XData,greenline(jj).YData,'g','LineWidth',2);
x_start = length(x);
x=[x greenline(jj).XData];
y=[y greenline(jj).YData];
c = [c;(x_start+(1:length(greenline(jj).XData)-1)).' (x_start+(2:length(greenline(jj).XData))).'];
catch
end
end
DT = delaunayTriangulation(x',y',c);
Warning: Duplicate data points have been detected and removed.
The Triangulation indices and constraints are defined with respect to the unique set of points in delaunayTriangulation.
triplot(DT)
figure
DT = delaunayTriangulation(x',y',c);
Warning: Duplicate data points have been detected and removed.
The Triangulation indices and constraints are defined with respect to the unique set of points in delaunayTriangulation.
IO = isInterior(DT);
triplot(DT(IO, :),DT.Points(:,1), DT.Points(:,2),'LineWidth', 2)
h=trimesh(DT(IO, :),DT.Points(:,1), DT.Points(:,2),zeros(size(DT.Points(:,2))),'LineWidth', 2);
[Fs,Vs]=subtri(h.Faces,h.Vertices,2);% Note, you can increase the density by increase the value of the last input
figure
subplot(1,2,1);patch('Faces',h.Faces,'Vertices',h.Vertices,'FaceAlpha',0.5,'EdgeColor','k','LineWidth',2);
hold on;
subplot(1,2,2);patch('Faces',Fs,'Vertices',Vs,'FaceAlpha',0.5,'EdgeColor','k','LineWidth',2);
Kevin Moerman on 22 Jun 2022
@Kevin Holly @Bruno Neto thanks for checking out subtri, note the latest version of it is part of my GIBBON project (see also: https://www.mathworks.com/matlabcentral/fileexchange/48208-gibboncode-gibbon and https://github.com/gibbonCode/GIBBON/blob/master/lib/subtri.m).
@Bruno Neto if you want it as uniform as possible subtri is not great in this case. It would be better to use: https://www.gibboncode.org/html/HELP_regionTriMesh2D.html. You'd first need the boundary edges using https://www.gibboncode.org/html/HELP_patchBoundary.html then group each to get your inner edges and outer edges e.g. https://www.gibboncode.org/html/HELP_tesgroup.html then convert each edge list to a curve using https://www.gibboncode.org/html/HELP_edgeListToCurve.html .
If you use GIBBON for research, please cite it using: https://doi.org/10.21105/joss.00506
Let me know if you have questions: kevin.moerman@nuigalway.ie

R2021b

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