demo18 of Im2mesh package
demo18 - Create tetrahedral mesh based on 2d image
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.
To run demo18, you need to have MATLAB Partial Differential Equation Toolbox.
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 = 400; height = 400;
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'))
Import image
im = imread('logo.tif');
if size(im,3) == 3; im = rgb2gray( im ); end
imshow( im,'InitialMagnification','fit' );
Get boundries from image
We have demostrate how to do this in example3 of demo01.mlx
opt = []; % reset opt
opt.tolerance = 1;
opt.tf_mesh = false;
bounds = im2mesh( im, opt );
% bounds is the simplified polygonal boundaries
plotBounds( bounds );
Generate 2d mesh
hmax = 500;
grad_limit = 1;
opt = [];
opt.disp = inf; % silence verbosity
[vert,tria,tnum,vert2,tria2] = bounds2mesh( bounds, hmax, grad_limit, opt );
Plot mesh.
plotMeshes(vert,tria,tnum);
Create 2d PDE model
We can use the following command to create 2d PDE model object (for Matlab PDE toolbox).
% Create matlab pde model object
model2d = createpde(); % qudratic model
geometryFromMesh( model2d, vert2', tria2', tnum' );
g = model2d.Geometry;
pdegplot( g, "FaceLabels", "on" )
Extrude 2d geometry
height = 35;
extrude( g, height );
pdegplot( g, "FaceLabels", "on", "FaceAlpha", 0.5 )
Create 3d PDE model
model3d = createpde;
model3d.Geometry = g;
Generate Mesh
generateMesh( model3d, 'Hmax',500, 'Hmin', 5, 'Hgrad', 1.2 )
Plot mesh
pdemesh(model3d)
pdegplot(model3d, 'CellLabels','on', 'FaceAlpha',0.5);
Find elements in different regions
numCell = model3d.Geometry.NumCells;
elementIDsCell = cell( [1, numCell] );
for i = 1: numCell
elementIDsCell{i} = findElements( model3d.Mesh, "region", Cell=i );
end
Plot mesh
colors = lines(numCell);
figure
for i = 1: numCell
pdemesh( model3d.Mesh.Nodes, ...
model3d.Mesh.Elements(:,elementIDsCell{i}), ...
'FaceColor', colors(i,:))
hold on
end
hold off
Change view angle
colors = lines(numCell);
figure
for i = 1: numCell
pdemesh(model3d.Mesh.Nodes, ...
model3d.Mesh.Elements(:,elementIDsCell{i}), ...
'FaceColor', colors(i,:))
hold on
end
view([-0 90])
hold off
Note
The input image has 3 phases. However, the generated tetrahedral mesh has 4 phases. This does not meet our objective.
I may fix this issue in the next update of Im2mesh.
An alternative approach is to use Gmsh.
Evaluate mesh quality
Q = meshQuality( model3d.Mesh );
mean(Q)
ans = 0.8555
min(Q)
ans = 0.2720
figure
histogram(Q)
xlabel( "Element Shape Quality", "fontweight", "b" )
ylabel( "Number of Elements", "fontweight", "b" )
% reset image size
set(groot, 'DefaultFigurePosition', 'factory')
% end of demo