demo06 of Im2mesh package

demo06 - Parameter hmax and grad_limit in mesh generation
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
Jiexian Ma, mjx0799@gmail.com Project website List of demo
Table of Contents
Note Initialize Import image hmax = 8 hmax = 500 grad_limit = 0.5 grad_limit = 0.25

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. No need to install any MATLAB toolboxes when running this demo.

Initialize

Before we start, please set folder "Im2mesh_Matlab" as your current folder of MATLAB.
clearvars
Set default image size (optional).
x = 250; y = 250; width = 250; height = 250;
set(groot, 'DefaultFigurePosition', [x,y,width,height])
% To reset:
% set(groot, 'DefaultFigurePosition', 'factory')
Function im2mesh use a mesh generator called MESH2D (developed by Darren Engwirda). We can use the following command to add the folder 'mesh2d-master' to the path of MATLAB.
addpath(genpath('mesh2d-master'))

Import image

im = imread('Transition.tif');
if size(im,3) == 3; im = rgb2gray( im ); end
imshow( im,'InitialMagnification','fit' );

hmax = 8

opt = []; % reset opt
opt.grad_limit = 0.25;
opt.hmax = 8;
[ vert, tria, tnum ] = im2mesh( im, opt );
Refine triangulation... ------------------------------------------------------- |ITER.| |CDT1(X)| |CDT2(X)| ------------------------------------------------------- 4 163 290 10 202 870 13 203 964 Refine triangulation... ------------------------------------------------------- |ITER.| |CDT1(X)| |CDT2(X)| ------------------------------------------------------- 10 365 290 13 377 290 20 381 3861 27 381 4499 Smooth triangulation... ------------------------------------------------------- |ITER.| |MOVE(X)| |DTRI(X)| ------------------------------------------------------- 10 176 4461
plotMeshes( vert, tria, tnum )
We can see that the max mesh size is limited by the parameter hmax.

hmax = 500

Let's use a much larger hmax to see how things are changing.
opt = []; % reset opt
opt.grad_limit = 0.25;
opt.hmax = 500;
[ vert, tria, tnum ] = im2mesh( im, opt );
Refine triangulation... ------------------------------------------------------- |ITER.| |CDT1(X)| |CDT2(X)| ------------------------------------------------------- 4 163 290 10 202 870 13 203 964 Refine triangulation... ------------------------------------------------------- |ITER.| |CDT1(X)| |CDT2(X)| ------------------------------------------------------- 7 335 290 10 337 1849 20 339 4111 21 339 4115 Smooth triangulation... ------------------------------------------------------- |ITER.| |MOVE(X)| |DTRI(X)| ------------------------------------------------------- 10 197 4081
plotMeshes( vert, tria, tnum )
Now, the max mesh size is much larger. Note that hmax is a upper bound for the max mesh size. There exists boundary edge contraints and gradient-limt, so the max mesh size in the generated mesh can not reach hmax.

grad_limit = 0.5

opt = []; % reset opt
opt.grad_limit = 0.5;
opt.hmax = 500;
[ vert, tria, tnum ] = im2mesh( im, opt );
Refine triangulation... ------------------------------------------------------- |ITER.| |CDT1(X)| |CDT2(X)| ------------------------------------------------------- 4 163 290 10 202 870 13 203 964 Refine triangulation... ------------------------------------------------------- |ITER.| |CDT1(X)| |CDT2(X)| ------------------------------------------------------- 4 283 290 10 300 2162 20 306 2518 20 306 2518 Smooth triangulation... ------------------------------------------------------- |ITER.| |MOVE(X)| |DTRI(X)| ------------------------------------------------------- 10 42 2470 20 8 2470 30 8 2470
plotMeshes( vert, tria, tnum )
We can evaluate the mesh quality.
tricost( vert, tria );

grad_limit = 0.25

Let's use a smaller grad_limit to see how things are changing.
opt = []; % reset opt
opt.grad_limit = 0.25;
opt.hmax = 500;
[ vert, tria, tnum ] = im2mesh( im, opt );
Refine triangulation... ------------------------------------------------------- |ITER.| |CDT1(X)| |CDT2(X)| ------------------------------------------------------- 4 163 290 10 202 870 13 203 964 Refine triangulation... ------------------------------------------------------- |ITER.| |CDT1(X)| |CDT2(X)| ------------------------------------------------------- 7 335 290 10 337 1849 20 339 4111 21 339 4115 Smooth triangulation... ------------------------------------------------------- |ITER.| |MOVE(X)| |DTRI(X)| ------------------------------------------------------- 10 197 4081
plotMeshes( vert, tria, tnum )
We can evaluate the mesh quality again.
tricost( vert, tria );
Very good!
% reset image size
set(groot, 'DefaultFigurePosition', 'factory')
% end of demo