demo05 of Im2mesh package

demo05 - Parameter tf_avoid_sharp_corner
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.
Table of Contents
Note Setup Circle Avoid sharp corner

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')
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'))

Circle

Let's start demo. Import image Circle.tif.
im = imread('Circle.tif');
if size(im,3) == 3; im = rgb2gray( im ); end
imshow( im,'InitialMagnification','fit' );
Generate mesh.
opt = []; % reset opt
opt.tf_avoid_sharp_corner = false;
opt.threshold_num_turning = 10;
opt.threshold_num_vert_Smo = 20;
opt.threshold_num_vert_Sim = 20;
[ vert, tria, tnum ] = im2mesh( im, opt );
Refine triangulation... ------------------------------------------------------- |ITER.| |CDT1(X)| |CDT2(X)| ------------------------------------------------------- 4 356 424 10 388 896 13 388 940 Refine triangulation... ------------------------------------------------------- |ITER.| |CDT1(X)| |CDT2(X)| ------------------------------------------------------- 7 511 424 10 531 1808 20 547 2865 29 552 2947 Smooth triangulation... ------------------------------------------------------- |ITER.| |MOVE(X)| |DTRI(X)| ------------------------------------------------------- 4 704 2929 8 179 2929 12 22 2929 16 0 2929
plotMeshes( vert, tria, tnum )
You can see the mesh is very dense in some region. That is induced by the sharp corner between polygonal boundaries. Let's zoom in to confirm that.
plotMeshes( vert, tria, tnum )
xlim([53.4 65.8])
ylim([30.8 42.9])

Avoid sharp corner

We can set parameter tf_avoid_sharp_corner to true. It may help.
opt = []; % reset opt
opt.tf_avoid_sharp_corner = true;
opt.threshold_num_turning = 10;
opt.threshold_num_vert_Smo = 20;
opt.threshold_num_vert_Sim = 20;
[ vert, tria, tnum ] = im2mesh( im, opt );
Refine triangulation... ------------------------------------------------------- |ITER.| |CDT1(X)| |CDT2(X)| ------------------------------------------------------- 5 352 444 10 383 806 13 384 887 Refine triangulation... ------------------------------------------------------- |ITER.| |CDT1(X)| |CDT2(X)| ------------------------------------------------------- 7 502 444 10 522 1685 20 529 2541 23 530 2556 Smooth triangulation... ------------------------------------------------------- |ITER.| |MOVE(X)| |DTRI(X)| ------------------------------------------------------- 4 549 2534 8 164 2534 12 2 2534 16 2 2534
plotMeshes( vert, tria, tnum )
Zoom in
plotMeshes( vert, tria, tnum )
xlim([53.4 65.8])
ylim([30.8 42.9])
Yes, it helps.
% reset image size
set(groot, 'DefaultFigurePosition', 'factory')
% end of demo