How to import geometry with holes to use with PDE toolbox?

So there are two main options for creating geometry for a PDE model: geometryFromMesh and importGeometry.

The geometry I have is essentially a hollow sphere (i.e. a solid sphere with a smaller spherical cutout inside). I have created an STL file and attempted to use importGeometry. However, I get the error "Assemblies of more than one geometric model are not currently supported"

Now I am looking into using geometryFromMesh. I have two questions: 1. Is this even possible? 2. If so, then how might I create a mesh that has holes in it?

This is the geometry I'm trying to use.

Answer 1

[Alan Weiss]

You could try something like the following series of commands:

[az,el,r] = meshgrid(linspace(0,2*pi-0.01),linspace(-pi,pi-0.01),linspace(0.25,1));
[x,y,z] = sph2cart(az,el,r);
shp = alphaShape(x(:),y(:),z(:),0.05);
[elements,nodes] = boundaryFacets(shp);
nodes = nodes';
elements = elements';
model = createpde();
geometryFromMesh(model,nodes,elements);
pdegplot(model,'FaceLabels','on','FaceAlpha',0.5)

Don't forget to mesh your resulting geometry by using generateMesh.

Alan Weiss

MATLAB mathematical toolbox documentation

[Brian Chen]

Thanks for the answer. Your code does work; however, if I do something similar from importing an STL file, I keep getting this error:

Failed to create geometry, the input does not form a closed volume.
This may be due to missing faces or gaps in the input.

The thing is, I'm sure my geometry is actually closed since I drew these in Autodesk Inventor and exported to STL. I have also tried using Meshlab to make the surfaces "watertight"/closed and still the issue persists.

Another issue I sometimes encounter is Maltab crashing, saying an "internal issue" has occured. This occurs when attempting to generate the mesh.

[Alan Weiss]

I am sorry, but there are limitations in the current STL import. We are certainly working on improving our 3-D geometry handling. However, at present, the geometry creation commands I gave are the only way I know to create a hollow sphere.

Then again, I don't know all the details of our 3-D STL geometry reconstruction, so it is possible that some other way might work. If the commands I gave are unsatisfactory, then perhaps you can try contacting technical support.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation

[Brian Chen]

Thanks Alan,

Would be awesome to see improvement in 3D geometry handling. Right now, I'm not even using a hollow sphere; it's actually a completely solid object.

[Brian Chen]

I can consistently get MATLAB to crash now when using generateMesh.

When I plot using pdegplot, everything looks fine. Checking the FEMesh also seems ok. However for some reason using your version of the code works.

Here is the code I use:

% Make a big sphere
[x,y,z]=sphere(24);
shp = alphaShape(x(:),y(:),z(:), 10);
[faces,vertices] = boundaryFacets(shp);
vertices = vertices.*10e-4;

% Make a small sphere
[x,y,z]=sphere(24);
shp = alphaShape(x(:),y(:),z(:), 10);
[f,v] = boundaryFacets(shp);
v = v.*10e-5;

% Combine the two spheres
fnew = [faces; f + length(vertices)];
vnew = [vertices; v];
faces = fnew;
vertices = vnew;

model = createpde();
gd = geometryFromMesh(model, vertices', faces');
pdegplot(model,'FaceLabels','on','FaceAlpha',0.5);
% the geometry seems plots alright and has 2 faces
% however the next step crashes
generateMesh(model);

I can also consistently get it to crash with STL files that I have sculpted in Meshmixer--and these are not even large STL files.

[Alan Weiss]

I am very sorry that you are having such trouble with geometry creation. But really, you are trying to push the current 3-D geometry beyond what it can do. It is not designed for subdomains, nor for holes or multiple regions. My code is sort of fortuitously workable, but I don't really know why.

If you can afford to wait until the next release in March, then things might be somewhat better, but I cannot promise or even describe anything that is coming up. Sorry.

Alan Weiss

MATLAB mathematical toolbox documentation