demo13 of Im2mesh package
demo13 - How to use Gmsh as mesh generator in Im2mesh package
Cite as: Ma, J., & Li, Y. (2025). Im2mesh: A MATLAB/Octave package for generating finite element mesh based on 2D multi-phase image (2.1.5). Zenodo. https://doi.org/10.5281/zenodo.14847059
Table of Contents
Note
I suggest familiarizing yourself with Im2mesh_GUI before learning Im2mesh package. With graphical user interface, Im2mesh_GUI will help you better understand the workflow and parameters of Im2mesh package.
Im2mesh_GUI: https://www.mathworks.com/matlabcentral/fileexchange/179684-im2mesh_gui-2d-image-to-finite-element-mesh
If you are using Im2mesh package in MATLAB, you need to install MATLAB Image Processing Toolbox and Mapping Toolbox because Im2mesh package use a few functions in these toolboxes.
Setup
Before we start, please set folder "Im2mesh_Matlab" as your current folder of MATLAB.
clearvars
Set default image size.
x = 250; y = 250; width = 250; height = 250;
set(groot, 'DefaultFigurePosition', [x,y,width,height])
% To reset:
% set(groot, 'DefaultFigurePosition', 'factory')
We add the folder 'mesh2d-master' to the path of MATLAB.
addpath(genpath('mesh2d-master'))
We need to know the location of gmesh.exe
% for example
path_to_gmsh = 'C:\Users\Jason\Downloads\gmsh-4.13.1-Windows64\gmsh.exe';
Get boundries from image
We have demostrate how to do this in example3 of demo01.mlx
im = imread('Shape.tif');
if size(im,3) == 3; im = rgb2gray( im ); end
opt = []; % reset opt
opt.threshold_num_turning = 0;
opt.threshold_num_vert_Smo = 0;
opt.tolerance = 0.3;
opt.threshold_num_vert_Sim = 0;
opt.tf_mesh = false;
bounds = im2mesh( im, opt );
% bounds is the simplified polygonal boundaries
plotBounds( bounds );
Phase selection before meshing
Suppose we don't need the background.
select_phase = [2 3 4];
bounds = bounds( select_phase );
plotBounds( bounds );
Print geo file for Gmsh
Before printing geo file, we need to obtain surface loops from polygonal boundaries since Gmsh use loops to define suface.
We use function bound2SurfaceLoop to convert polygonal boundaries to surface loops.
[ phaseLoops, vertex, edge ] = bound2SurfaceLoop( bounds );
% rename variables to be consistent with gmsh
point = vertex;
line = edge;
geo file is the input file for Gmsh. We use function printGeo to print surface loops to geo file. We will see a geo file 'gmshTemp.geo' in the current working folder of MATLAB.
Please refer to 'Im2mesh_GUI Tutorial.pdf' and Gmsh manual about how to choose meshing parameters.
% setup parameters
opt = []; % reset
opt.sizeMin = 0.1;
opt.sizeMax = 6;
opt.algthm = 6;
opt.recombAll = 0;
opt.recombAlgthm = 3;
opt.eleOrder = 1;
path_to_geo = 'gmshTemp.geo';
printGeo( phaseLoops, point, line, opt, path_to_geo );
Generate mesh via Gmsh
We use the following command to send the geo file to Gmsh. Gmsh will generate a m file 'gmshTemp.m'.
path_to_m = 'gmshTemp.m';
verbosity = 3;
str=sprintf('"%s" "%s" -o "%s" -v %i -save', ...
path_to_gmsh, path_to_geo, path_to_m, verbosity );
system(str);
When we run the m file, we will see a struct variable 'msh' in the workspace of MATLAB.
% run m file
run(path_to_m)
msh
Plot mesh
Before ploting the mesh, we need to do some processing to the mesh data.
vert = msh.POS(:,1:2);
ele = msh.TRIANGLES(:,1:end-1);
tnum = msh.TRIANGLES(:,end);
% flip for correct signs
area = triarea( vert, ele );
ele(area<0.,:) = ele( area<0., [1,3,2] );
Now we can plot the mesh
plotMeshes( vert, ele, tnum )
We can use function tricost to check the mesh quality. Function tricost is written by by Darren Engwirda.
tricost( vert, ele, tnum );
Note
If the mesh is quadratic trangular, the processing is slightly different.
vert = msh.POS(:,1:2);
ele = msh.TRIANGLES6(:,1:end-1);
tnum = msh.TRIANGLES6(:,end);
% flip for correct signs
area = triarea( vert, ele );
ele(area<0.,:) = ele( area<0., [1,3,2,6,5,4] );
plotMeshes( vert, ele, tnum )
After we got the mesh, we can use Gmsh or the functions in demo03 to export it.
Export mesh via Gmsh
Suppose we want to export as stl file 'gmshExport.stl'.
path_to_file = 'gmshExport.stl';
verbosity = 3;
str=sprintf('"%s" "%s" -o "%s" -v %i -save', ...
path_to_gmsh, path_to_geo, path_to_file, verbosity );
system(str);
We should be able to see a file 'gmshExport.stl' in current working folder of Matlab.
Unstructured quadrilateral mesh
We can use Gmsh to generate unstructured quadrilateral mesh. The method is similar. Please refer to 'Im2mesh_GUI Tutorial.pdf' and Gmsh manual about how to choose meshing parameters.
% setup parameters
opt = []; % reset
opt.sizeMin = 0.1;
opt.sizeMax = 6;
opt.algthm = 8;
opt.recombAll = 1;
opt.recombAlgthm = 3;
opt.eleOrder = 1;
path_to_geo = 'gmshTemp.geo';
printGeo( phaseLoops, point, line, opt, path_to_geo );
path_to_m = 'gmshTemp.m';
verbosity = 3;
str=sprintf('"%s" "%s" -o "%s" -v %i -save', ...
path_to_gmsh, path_to_geo, path_to_m, verbosity );
system(str);
Gmsh will generate a m file. When we run the m file, we will see a struct variable 'msh' in the workspace of MATLAB.
% run m file
run(path_to_m)
msh
Before ploting the mesh, we need to do some processing to the mesh data.
vert = msh.POS(:,1:2);
ele = msh.QUADS(:,1:end-1);
tnum = msh.QUADS(:,end);
% flip for correct signs
area = quadarea( vert, ele );
ele(area<0.,:) = ele( area<0., [1,4,3,2] );
Plot mesh.
plotMeshes( vert, ele, tnum )
Awesome!
We can use function MeshQualityQuads (written by Allan Peter Engsig-Karup) to evaluate mesh quality.
[q,theta] = MeshQualityQuads( ele, vert(:,1), vert(:,2) );
q_mean = mean(q)
q_mean = 0.6407
Plot histogram of q
histogram( q, 'BinWidth', 0.02, 'BinLimits', [0,1], ...
'EdgeColor', 'none');
xlabel('Q','FontSize',10,'FontWeight','bold');
pbaspect([2 0.6 1]);
After we got the mesh, we can use Gmsh or the functions in demo03 to export it.
Note
If the mesh is quadratic quadrilateral, the processing is slightly different.
vert = msh.POS(:,1:2);
ele = msh.QUADS9(:,1:end-1);
tnum = msh.QUADS9(:,end);
% flip for correct signs
area = quadarea( vert, ele );
ele(area<0.,:) = ele( area<0., [1,4,3,2,8,7,6,5] );
plotMeshes( vert, ele, tnum );
% reset image size
set(groot, 'DefaultFigurePosition', 'factory')
% end of demo