demo05 of Im2mesh package

demo05 - Avoid sharp corners
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.thresh_turn = 10;
opt.thresh_vert_smooth = 20;
opt.thresh_vert_simplify = 20;
[ vert, tria, tnum ] = im2mesh( im, opt );
Refine triangulation... ------------------------------------------------------- |ITER.| |CDT1(X)| |CDT2(X)| -------------------------------------------------------
Warning: Edge constraints have been split by a coincident point.
4 356 424 10 388 896 13 388 940 Refine triangulation... ------------------------------------------------------- |ITER.| |CDT1(X)| |CDT2(X)| -------------------------------------------------------
Warning: Edge constraints have been split by a coincident point.
7 511 424 10 531 1808 20 547 2865 29 552 2947 Smooth triangulation... ------------------------------------------------------- |ITER.| |MOVE(X)| |DTRI(X)| ------------------------------------------------------- 10 49 2929
plotMeshes( vert, tria, tnum )
Let's zoom in.
plotMeshes( vert, tria, tnum )
xlim([55.4 62.3])
ylim([33.7 40.3])
We can see a sharp corner between polygonal boundaries.
In some applications, we don't like these sharp corners.

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.thresh_turn = 10;
opt.thresh_vert_smooth = 20;
opt.thresh_vert_simplify = 20;
[ vert, tria, tnum ] = im2mesh( im, opt );
Refine triangulation... ------------------------------------------------------- |ITER.| |CDT1(X)| |CDT2(X)| -------------------------------------------------------
Warning: Edge constraints have been split by a coincident point.
5 366 440 10 395 876 13 395 974 Refine triangulation... ------------------------------------------------------- |ITER.| |CDT1(X)| |CDT2(X)| -------------------------------------------------------
Warning: Edge constraints have been split by a coincident point.
7 516 440 10 521 1767 20 527 2657 20 527 2657 Smooth triangulation... ------------------------------------------------------- |ITER.| |MOVE(X)| |DTRI(X)| ------------------------------------------------------- 10 88 2639
plotMeshes( vert, tria, tnum )
Zoom in
plotMeshes( vert, tria, tnum )
xlim([55.4 62.3])
ylim([33.7 40.3])
Yes, it helps.
% reset image size
set(groot, 'DefaultFigurePosition', 'factory')
% end of demo