Tips on Mesh Generation in 3D Using Matlab

3D meshes/girds can be made from different type of mesh elements.

1.) Hexahedral Mesh elements.
2.) Tetrahedral Mesh elements.
3.) Pyramid Shape Mesh elements.
4.) Prism Types of Mesh elements.

Now if you can visualize it is always possible to decompose a basic hexahedral element into 3-Pyramid element, 2-Prism elements, 6-Tetra hedral elements and offcourse Hex is there as always.

So this means that it is always possible to create different kind of meshes using a Basic Hex mesh element. In MATLAB it is very easy to make a hex mesh u can follow these simple steps and u will get a Hex mesh.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
x = [0:1/numx:1];
y = [0:1/numy:1];
z = [0:1/numz:1];

%Where numx, numy and numz are the number of basic hex elements u want in x, y and z %Direction.

%then follow the following step

[X Y Z] = meshgrid(x,y,z);

X = X(:);Y=Y(:);Z=Z(:);
%and then to plot the mesh you need following lines of code

node = [X Y Z];

figure(1);

if sloped==1
patch('Vertices',node,'Faces',faces,...
'FaceVertexCData',hsv(1),'FaceColor','none')
else
patch('Vertices',node,'Faces',faces,...
'FaceVertexCData',hsv(1),'FaceColor','none')
end
view(3); axis square

title(['Cartesian Mesh ', num2str(numx,3),'x',num2str(numy,3),'x',num2str(numz,3)])

% Now here one thing which you need to Compute is the Face connectivites which shoud %be fed into the function Patch which basically patches the different faces of the %hex and there by makes a complete Hexa Hedra. Now to get the Face connectivties you %need to use the following piece of code.

function faces = face_connectivity(num_u,num_v,num_w)


numx = num_u;
numy = num_v;
numz = num_w;

nnodex = numx+1;
nnodey = numy+1;
nnodez = numz+1;

face_pattern = [1 2 nnodex+2 nnodex+1]; % This is your face connectivity Pattern

nnx = numx+1 ;
nny = (nnodex)*(nnodey) ;
inc_u = 1;
inc_v = nnx;
inc_w = nny;
node_pattern=[ 1 2 nnx+2 nnx+1 nny+1 nny+2 nny+nnx+2 nny+nnx+1 ]; % Node connectivity
element = zeros(numx*numy*numz,8);
element = make_elem_hexa(node_pattern,numx,numy,numz,inc_u,inc_v,inc_w,nnx);

% ThisFunction gives the element connectivity.

faces = zeros(1,4);
face = zeros(6,4);
face1 = [1 2 3 4];
face2 = [4 3 7 8];
face3 = [5 6 7 8];
face4 = [2 6 7 3];
face5 = [1 5 8 4];
face6 = [1 2 6 5];

[m,n] = size(element);

for i = 1:size(element,1)

face = [element(i,face1);element(i,face2);element(i,face3);element(i,face4);element(i,face5);element(i,face6)];
faces = cat(1,faces,face);
end

faces(1,:) = [];
faces = faces;