Creating modified cavities in 3D models.

Hi, I wish to create cavities in a cubic model (discrete geometry) similar to that found here.

The only difference is I wish to have more control over the size of the cube and sphere, possibly add multiple, and control the location of the sphere within the 3D space, is any/all of this possible?

[darova]

Can you make a simple sketch of desired result? Did you try sphere?

[Luke Benham]

Yeah my current idea was to use sphere as used in the mathworks code in the previously supplied hyperlink. The attached shows an idea as a pdegplot that i wish to generate using code. (The figure was created using an imported .stl file however)

[Nathan Welch]

I'm having a similar issue that I posted here

However, I wish to mesh the internal cavity and include it in my model. So the cavity mesh must match up with the body mesh, i.e. same nodes and same faces at the interface surface.

Is this possible in MATLAB? The example that you reference above does something close but it isn't very good as the 'mesh' that is used to model the spherical cavity is just a set of terrible tetrahedrals not a delaunay type mesh.

I know about other meshing softwares, GMSH etc, but I want something in MATLAB (even if I have to write it myself) as I need to do a lot of optimisation and solving PDEs, whilst updating meshes and carrying out incremental alterations - rather than entirely recreating them. My BIG stumbling block is just getting even a basic, terribly performing discretization method for an arbitrary geometry.

Answer 1

[ADSW121365]

All of this is definitely possible, but the inbuilt CAD capabilities/geometry design in MATLAB aren't its strongest point.

From experience complicated geometries generally fall into two catagories for use in the toolbox:

• Direct Geometry Design Inside an external mesh generator: See a question I asked for nested cubes on stackexchange here. GMSH is free, robust, has inbuilt optimisation and isn't too hard to learn, though finding anything in the documentation is long. There are many other mesh generators, but GMSH also has a direct export to a .m file for MATLAB.
• CAD Design & Creation of an STL/BREP/STEP file depending on the geometry, subsequent external meshing then importing to MATLAB. Some questions I've answered on this forum which maybe helpful to this approach can be found here and here

Edit: The approach via alphashapes mentioned in the comments is actually really good for this type of problem and worth considering.

[Luke Benham]

Thanks for the reply, does this mean it isn't possible/feasible to create the geometry using functions such as sphere and multicuboid, or even more complicated processes using meshgrid, alphashape, alphaTriangulation and geometryFromMesh? such as;

%% Create Cavity Cube

[xg, yg, zg] = meshgrid(-2:0.25:2);

Pcube = [xg(:) yg(:), zg(:)];

Pcavitycube = Pcube(vecnorm(Pcube') > 1,:);

[x1,y1,z1] = sphere(24);

Psphere = [x1(:) y1(:) z1(:)];

Psphere = unique(Psphere,'rows');

Pcombined = [Pcavitycube;Psphere];

shpCubeWithSphericalCavity = alphaShape(Pcombined(:,1), ...

Pcombined(:,2), ...

Pcombined(:,3));

[tri,loc] = alphaTriangulation(shpCubeWithSphericalCavity);

model = createpde;

[sensor,mshCube] = geometryFromMesh(model,loc',tri');

figure

pdegplot(model,'FaceLabels','on','FaceAlpha',0.5);

title('PDEModel: Cube with Spherical Cavity');

[ADSW121365]

My recommended route is via geometryfrommesh, that way you can design everything in CAD seperately.

It is almost certainly possible to setup the same thing with alphashapes, but you mentioned a need for flexibility - more cavities, moving the cavities, maybe different shaped cavities would be a feasible extension and my experience suggests in the long run using CAD will probably save you time and give you access to boolean operators and the like which give you much more flexibility in your geometry design.

So my current work for example looks at a nested 3D domain which contains 20 internal subdomains (some with their own internal divisions), the toolbox can handle this happily when using geometryfrommesh, but I haven't found another approach which supports subdomains in the same way (though the addFaces feature released in 2020a probably helps).

[Luke Benham]

Thank you, this is very helpful and support the answer seen here.

[ADSW121365]

The approach suggested is actually really good - I'm thinking too generally, the CAD approach allows a drag-and-drop type approach to geometry design which is probably more beneficial when you wish to consider complicated embedded stuctures.