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

Jiexian Ma, mjx0799@gmail.com. Project website.

Table of Contents

Note Setup Overview Import image Get boundries from image Create 3d pde model object Generate mesh Find elements in different phases Plot mesh Change view angle Evaluate mesh quality Extract mesh data

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 = 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'))

Overview

There are 3 methods to generate tetrahedral or hexahedral mesh based on a 2D image.

Method 1. Use MATLAB built-in function generateMesh to create tetrahedral mesh. We will demostrate this method in demo18.

Method 2. CAD file. Import the dxf file created by Im2mesh into finite element software.

Method 3. Gmsh. Modify the geo file created by Im2mesh and then generate 3D mesh via Gmsh.

To run demo18, you need to have MATLAB Partial Differential Equation Toolbox.

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 2d polygonal boundaries

plotBounds( bounds );

Create 3d pde model object

We can use function bounds2pde3d to create Matlab 3d pde model object.

'height' is the extrusion height in the Z direction.

'scale_factor' is the scale factor for the node coordinites. We can set it as the physical dimensions of a pixel in the image.

height = 50;
scale_factor = 1;
model3d = bounds2pde3d( bounds, height, scale_factor )
model3d = 
  PDEModel with properties:

           PDESystemSize: 1
         IsTimeDependent: 0
                Geometry: [1×1 DiscreteGeometry]
    EquationCoefficients: []
      BoundaryConditions: []
       InitialConditions: []
                    Mesh: []
           SolverOptions: [1×1 pde.PDESolverOptions]

We can visualize the geometry.

pdegplot(model3d)

Awesome!

Generate mesh

We can use Matlab built-in function generateMesh to generate tetrahedral mesh.

generateMesh( model3d, 'Hmax',500, 'Hmin', 5, 'Hgrad', 1.2, 'GeometricOrder', 'quadratic' )
ans = 
  FEMesh with properties:

             Nodes: [3×22776 double]
          Elements: [10×14642 double]
    MaxElementSize: 500
    MinElementSize: 5
     MeshGradation: 1.2000
    GeometricOrder: 'quadratic'

Find elements in different phases

Before plotting the mesh, we need to find elements in different phases, also known as cells or parts.

numCell = model3d.Geometry.NumCells;
elementIDsCell = cell( [1, numCell] );
for i = 1: numCell
    elementIDsCell{i} = findElements( model3d.Mesh, "region", Cell=i );
end

Plot mesh

Now we can plot the mesh. Different phases are labelled with different colors.

figure

colors = lines(numCell); % colormap

for i = 1: numCell

pdemesh( model3d.Mesh.Nodes, ...

model3d.Mesh.Elements(:,elementIDsCell{i}), ...

'FaceColor', colors(i,:))

hold on

end

hold off

Awesome! We saw 3 phases in the mesh.

Change view angle

figure

colors = lines(numCell); % colormap

for i = 1: numCell

pdemesh(model3d.Mesh.Nodes, ...

model3d.Mesh.Elements(:,elementIDsCell{i}), ...

'FaceColor', colors(i,:))

hold on

end

view([-0 90])

hold off

Please check the following link about mesh refinement.

https://www.mathworks.com/help/pde/ug/pde.pdemodel.generatemesh.html

Evaluate mesh quality

We use Matlab built-in function meshQuality to check mesh qualtiy.

Q = meshQuality( model3d.Mesh );
mean(Q)
ans = 0.8509
min(Q)
ans = 0.1072

We can plot the histogram of mesh qualtiy.

figure

histogram(Q)

xlabel( "Element Shape Quality", "fontweight", "b" )

ylabel( "Number of Elements", "fontweight", "b" )

Extract mesh data

We can use the following code to extract mesh data from the pde model object for other purposes.

vert = model3d.Mesh.Nodes';
ele = model3d.Mesh.Elements';
numCell = model3d.Geometry.NumCells;
tnum = zeros( size(ele,1), 1 );
for i = 1: numCell
    index = findElements( model3d.Mesh, "region", Cell=i );
    tnum(index) = i;
end

We got 3 variables: vert, ele, tnum

vert: Mesh nodes. It’s a Nn-by-3 matrix, where Nn is the number of nodes in the mesh. Each row of vert contains the x, y, z coordinates for that mesh node.

ele: Mesh elements. Each row in tria contains the indices of the nodes for that mesh element.

tnum: Label of phase. Ne-by-1 array, where Ne is the number of elements.

tnum(j,1) = k; means the j-th element belongs to the k-th phase.

% reset image size
set(groot, 'DefaultFigurePosition', 'factory')
% end of demo