demo11 of Im2mesh package
demo11 - Find node sets at the interface and boundary
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.
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'))
Kumamon
Let's start. Import image kumamon.tif.
im = imread('kumamon.tif');
if size(im,3) == 3; im = rgb2gray( im ); end
imshow( im,'InitialMagnification','fit' );
Generate mesh.
opt = [];
opt.tolerance = 1;
[ vert, tria, tnum, vert2, tria2 ] = im2mesh( im, opt );
plotMeshes( vert, tria, tnum )
Scale node coordinates
% scale
dx = 1;
% node coordinates for linear element
vert = vert * dx;
% node coordinates for quadratic element
vert2 = vert2 * dx;
Represent mesh in an alternative way
We use function getNodeEle to add node numbering and element numbering, and organize elements into cell array.
[ nodecoor_list, nodecoor_cell, ele_cell ] = getNodeEle( vert, tria, tnum );
[ nodecoor_list, nodecoor_cell, ele_cell ] is an alternative way to represent the triangular mesh. This format is useful for importing the mesh into commercial finite element software.
nodecoor_list is node coordinates, N-by-3 array.
nodecoor_list(i,1:3) = [node_numbering, x_coordinate, y_coordinate];
nodecoor_cell is a 1-by-P cell array. nodecoor_cell{i} represents the node numbering and node coordinates in the i-th phase. nodecoor_cell{i} is a M-by-3 array.
nodecoor_cell{i}(j,1:3) = [node_numbering, x_coordinate, y_coordinate];
ele_cell is a 1-by-P cell array. ele_cell{i} represent elements in the i-th phase. ele_cell{i} is a T-by-4 array.
% When the elements are linear
ele_cell{i}(j,1:4) = [ element_numbering, node_numbering_of_node_1, ...
node_numbering_of_node_2, ...
node_numbering_of_node_3 ];
For quadratic elements, we can use the same function.
% vert2, tria2, tnum define a model with quadratic elements
[ nodecoor_list, nodecoor_cell, ele_cell ] = getNodeEle( vert2, tria2, tnum );
Case 1. Node sets at the boundary for each phase
We use function getBCNode to find nodes at the boundary, which can be used to define boundary condition.
[ xmin_node_cell, xmax_node_cell, ...
ymin_node_cell, ymax_node_cell ] = getBCNode( nodecoor_cell );
xmin_node_cell, xmax_node_cell, ymin_node_cell, ymax_node_cell are the node numbering of nodes that located at x min, x max, y min, y max. They are 1-by-p cell array.
For example, xmin_node_cell{i} is the node numbering of nodes in the i-th phase that located at x min. xmin_node_cell{i} is a column vector.
Display nodes
For example, we are interested in the nodes of the 1st phase that located at y max. We can call it ymax_A.
ymax_A is column vector, recording the node numbering.
ymax_A = ymax_node_cell{1};
node_set = ymax_A;
Let plot them.
figure;
hold on;
axis image off;
% -------------------------------------
% show mesh
tvalue = unique( tnum );
num_phase = length( tvalue );
% setup color
if num_phase == 1
col = 0.98;
elseif num_phase > 1
col = 0.3: 0.68/(num_phase-1): 0.98;
else
error('num_phase < 1')
end
for i = 1: num_phase
phasecode = tvalue(i);
patch('faces',tria( tnum==phasecode, 1:3 ),...
'vertices',vert, ...
'facecolor',[ col(i), col(i), col(i) ], ...
'edgecolor',[.1,.1,.1]);
end
% -------------------------------------
% show nodes
for i=1:length( node_set )
idx = node_set(i);
x = nodecoor_list( nodecoor_list(:,1)==idx, 2 );
y = nodecoor_list( nodecoor_list(:,1)==idx, 3 );
plot(x,y,'r.','MarkerSize',15);
end
% -------------------------------------
hold off
Very good!
Case 2. Node sets at the boundary of the entire model
We can also use function getBCNode to find nodes at the boundary of the entire model.
% the input of function getBCNode has to be a cell array
[ xmin_node, xmax_node, ...
ymin_node, ymax_node ] = getBCNode( {nodecoor_list} );
xmin_node = xmin_node{1};
xmax_node = xmax_node{1};
ymin_node = ymin_node{1};
ymax_node = ymax_node{1};
For example, xmin_node are the node numbering of nodes that located at x min.
xmin_node is a column vector.
Display nodes
For example, we are interested in the nodes at y max.
node_set = ymax_node;
Let plot them.
figure;
hold on;
axis image off;
% -------------------------------------
% show mesh
tvalue = unique( tnum );
num_phase = length( tvalue );
% setup color
if num_phase == 1
col = 0.98;
elseif num_phase > 1
col = 0.3: 0.68/(num_phase-1): 0.98;
else
error('num_phase < 1')
end
for i = 1: num_phase
phasecode = tvalue(i);
patch('faces',tria( tnum==phasecode, 1:3 ),...
'vertices',vert, ...
'facecolor',[ col(i), col(i), col(i) ], ...
'edgecolor',[.1,.1,.1]);
end
% -------------------------------------
% show nodes
for i=1:length( node_set )
idx = node_set(i);
x = nodecoor_list( nodecoor_list(:,1)==idx, 2 );
y = nodecoor_list( nodecoor_list(:,1)==idx, 3 );
plot(x,y,'r.','MarkerSize',15);
end
% -------------------------------------
hold off
Very good!
Case 3. Node sets at the interface
We use function getInterf to find nodes at the interface between different phases.
interfnode_cell = getInterf( nodecoor_cell );
interfnode_cell is a N-by-N cell array. interfnode_cell{i,j} stores the interfacial node numbering between the i-th phase and the j-th phase. interfnode_cell{i,j} is column vector.
If the i-th phase and the j-th phase have no contact, interfnode_cell{i,j} would be empty.
Display nodes
For example, we are interested in the nodes at the interface between the 1st phase and the 3rd phase. We can call it interf_AC.
interf_AC is column vector, recording the node numbering.
interf_AC = interfnode_cell{1,3};
node_set = interf_AC;
Let plot them.
figure;
hold on;
axis image off;
% -------------------------------------
% show mesh
tvalue = unique( tnum );
num_phase = length( tvalue );
% setup color
if num_phase == 1
col = 0.98;
elseif num_phase > 1
col = 0.3: 0.68/(num_phase-1): 0.98;
else
error('num_phase < 1')
end
for i = 1: num_phase
phasecode = tvalue(i);
patch('faces',tria( tnum==phasecode, 1:3 ),...
'vertices',vert, ...
'facecolor',[ col(i), col(i), col(i) ], ...
'edgecolor',[.1,.1,.1]);
end
% -------------------------------------
% show nodes
for i=1:length( node_set )
idx = node_set(i);
x = nodecoor_list( nodecoor_list(:,1)==idx, 2 );
y = nodecoor_list( nodecoor_list(:,1)==idx, 3 );
plot(x,y,'r.','MarkerSize',15);
end
% -------------------------------------
hold off
Very good!
% reset image size
set(groot, 'DefaultFigurePosition', 'factory')
% end of demo