STL Import 2 — Remeshing an Imported Mesh

Import 1

In the toolbar, click

In the window for , locate the section.

Browse to the model’s Application Libraries folder and double-click the file c2_vertebra.stl.

Notice that the check box is selected. Domains are needed before you can generate a tetrahedral mesh. The import checks if the imported surface mesh forms any watertight regions, and if so, it forms domains.

From the list, choose .

This setting is suitable when importing mesh files that have no obvious boundary partitioning, for example, meshes generated by medical imaging techniques. After the import, the mesh will usually consist of only one boundary that you can partition as needed, using the available tools. Use the or settings when importing meshes that contain planar faces and fillets, which can then be detected to partition the mesh accordingly.

An information message appears stating that no domains were created for the face of the vertebra.

In the window, click .

Expand the node and click on the subnode for more details.

This information message indicates that the mesh of the vertebra does not form a watertight component. The edges that appear in the selection for the node are exterior edges that are adjacent to one or several holes in the mesh. Disable the rendering of the mesh to see them more clearly in the window.

The larger hole at the lower-left is a triangular hole that seems to be caused by a missing mesh element. The two additional holes located in the upper half of the image are both slit-like holes with zero or almost zero areas, as will be clear later when zooming in on the individual holes. Such slits usually result when the vertices of the imported mesh triangles do not match within the specified import tolerance.

button in the toolbar. Zoom in to see the exact view below.

There are three holes, all located on the same side of the vertebra. You can verify this by going through the list of edges or by turning on to make sure there are no other edges hiding behind the faces of the vertebra. If you do, remember to turn off before continuing.

Use two different techniques to repair the holes as they require different kinds of treatment. Of the three holes in the image above, first repair the one in the upper right corner of the image. Then, continue with the small hole in the upper-left corner and, lastly, fill in the triangular hole in the lower-left corner.

If more than three edges are listed in the , go back to the node and make sure that the setting is , then reimport the mesh.

In the window, expand the node, then click .

In the window for , locate the section.

In the list, select (the edge located in the upper right corner of the previous image).

button in the toolbar.

The selected edge is next to a very narrow slit that has the same number of edge elements on both sides. Zoom in further on the upper center of the image above, a bit down from the end of the slit where the shorter edge elements are located.

button in the toolbar.

The corners of the triangular elements do not match since the corresponding mesh vertices were not merged during the import. To fix this, reimport the file using a larger tolerance.

Import 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

In the text field, type 1e-4[mm].

Also, under the section, notice that a selection of the surfaces of the vertebra has been automatically created during the import. We will use this selection later to easily select the surface of the vertebra in operations and size attributes. Rename it to something more descriptive.

Locate the section. In the table, enter the following settings:


Name	SOLID section in file
Vertebra boundary	COMSOL mesh mesh1

Locate the section. Click

The mesh vertices are now merged, thereby eliminating the hole and the edge adjacent to it. You can easily verify this by inspecting the number of edges listed in the node or by turning off the mesh rendering temporarily.

button in the toolbar.

Transform 1

Before repairing the rest of the holes, move the mesh to the origin. You can easily move, rotate, and scale an imported mesh by adding a subnode to an node. Add several subnodes to rotate an imported mesh around more than one axis.

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type -10[mm].

In the text field, type -90[mm].

In the text field, type -10[mm].

In the window, expand the node, then click .

In the window for , locate the section.

Next, repair the other slit in the mesh, which is the smaller of the two remaining holes.

to zoom in on the two remaining holes.

In the list, select .

Zoom out a bit to see the triangle elements on both sides of the slit, as shown below.

On one side of the slit (on the left side of the green edge in the figure), there is one triangle element, whereas on the other side there are two elements. Since the import functionality cannot partition elements or add new ones, the mesh edges on the two sides of the slit could not be merged even with the larger tolerance.

Fill Holes 1

To repair the slit, we will use the operation, which can introduce new mesh edges in order to merge edges. The operation searches for holes within a selection of boundaries and will automatically fill all holes smaller than a specified tolerance. We can therefore use this operation to also repair the third hole.

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose (the boundary of the vertebra).

Notice that the check box is automatically selected, which means that once all holes are filled and the surface mesh forms a watertight boundary, a domain will be created.

The slit has been repaired by introducing a mesh edge on the left side of the slit, merging the two sides of the hole, and removing the edge.

Another information message indicates that there is still a hole in the surface mesh as no domain could be created. Zoom in on the hole by following the steps below.

In the window, expand the node, then click .

In the window for , locate the section.

In the list, select .

The original triangular hole remains since it is larger than the automatically determined tolerance for . Measure the perimeter of the remaining hole to obtain an estimate for the tolerance value to use with the feature. The edge should already be selected, but select it again if needed.

In the toolbar, click

The length of the edge is reported in the window. It is about 2.2 mm long.

Next, go back to the window for .

Fill Holes 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

In the text field, type 2.3[mm]. The value you enter here should be slightly larger than the measured hole perimeter.

This concludes the repair of the imported mesh and the window reports that there is now one domain. Continue with the steps below to learn how to combine the imported mesh with a block created in the same component, intersect the mesh with a plane to delete a portion of the mesh, and generate a volume mesh both inside and outside the vertebra. The mesh of the block could just as well be imported from file, if available.

Geometry 1

Block 1 (blk1)

In the toolbar, click

In the dialog box, , you get the question if you want to combine this geometry with the mesh in . If you don’t want to do this or don’t want to decide at this point, you can just click and decide what to do with the geometry at a later stage. In this tutorial, we want to combine the geometry of the block with the mesh of the vertebra, so let us look at the options of how to do this.

Add an node to . This will import a surface mesh of the geometry to the meshing sequence, where the two will be combined. This is what we intend to do in this tutorial and the option we will use.

Add a new meshing sequence which is conforming to the geometry and an node in where the mesh of the geometry is imported. Use this option if you want full control over the mesh you import into .

Click to confirm the first option.

Look to verify that an node has been added last in the sequence. However, before going there, finish building the geometry by choosing the size and position of the block such that it will contain the vertebra mesh.

In the window for , locate the section.

In the text field, type 30[mm].

In the text field, type 20[mm].

In the text field, type 25[mm].

Locate the section. From the list, choose .

button in the toolbar.

Now, go back to and import a surface mesh of the built block into the meshing sequence.

Import 2

The settings are already set up to import a surface mesh of the finalized geometry in . The mesh will be built by the operation of, in this case, size, but there is also the option to import a visualization mesh of the geometry. The option will decrease the mesh size where the boundaries are close to a narrow region, similar to what the boundary mesh would look like if you generate a domain mesh. For the block, there are no narrow regions, so you will just get a triangle mesh with similar size on all boundaries.

In the window, under right-click and choose to import a sized surface mesh of the block.

Continue with intersecting the mesh of the block and vertebra with an assumed symmetry plane.

button in the toolbar, to see the vertebra inside the block.

Rotate the mesh in the window to check that the vertebra is fully contained in the block, the two meshes should not intersect. Click the button.

You can also use mesh to check that only triangle elements were imported for the block.

In the window, right-click and choose .

The state that this is a mesh with unmeshed domains, and it only lists , , and . If the meshes intersect, check and make sure that the settings for are correct, then reimport the mesh of the block.

In the window for , locate the section.

From the list, choose .

In the window, we can now also see that the of the surface mesh is rather low (about 1.7e-4). Furthermore, the reveals that a large portion of the elements have low quality. You will remesh the vertebra further ahead to get a higher element quality.

Intersect with Plane 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

The is set to 0.01 mm by default, which is the value we will use here. The setting uses a higher tolerance (0.09 mm), which is something you can see if you first build the operation with the setting, and then switch to .

Intersecting a mesh can introduce small and sliver mesh elements. The cleanup part of the operation collapses these, but in doing so, it may change the shape of the mesh that is intersected to ensure a planar intersection face. A lower tolerance will preserve the original shape of the mesh better, but will also keep more of the small and sliver elements introduced by the intersection. Here, the lower tolerance helps to keep the original shape better and avoid some small faces. The small faces result when parts of the vertebra that are very close to the intersecting plane are collapsed onto the plane.

You should now see in the window that the mesh of the vertebra and the block have been partitioned by the plane. New mesh surfaces that connect the vertebra and the block along the plane have also been created inside the block. This is controlled by the check box. When selected, the operation creates planar faces inside closed edge loops generated by the intersection.

Delete Entities 1

Next, delete half of the mesh to make use of the symmetry plane that was introduced above.

In the toolbar, click

Go to the tab.

In the toolbar, click

and choose .

Keep the open as you will use it throughout the tutorial.

Selection List

Go to the window.

In the list, choose and .

Click in the window toolbar.

Delete Entities 1

In the window, click .

In the window for , click

to delete the part of the vertebra and block on one side of the symmetry plane.

After intersecting a mesh with a plane, remeshing is usually needed to eliminate small elements that often result on the faces intersected by the plane. Also, the mesh on intersection faces is always generated as coarsely as possible and will typically need to be refined. Remeshing the faces will result in mesh elements of more uniform size, and will also result in triangles that are closer to the wanted equilateral shape.

button in the toolbar.

In the window toolbar, click

next to

, then choose .

In the , confirm that you have the expected nine boundaries; six for the block and three for the vertebra. If there are more than nine boundaries in the list, check the tolerance setting for the operation.

button in the toolbar, as this makes it easier to see the mesh on the outside of the block. Also, if you have turned off earlier, turn it on again.

In the window, click .

Hide boundaries 2,6, and 8 by clicking on them in the graphics to arrive at the image below.

button in the toolbar.

The mesh on the far end of the block (Boundary 1) has not been modified, and is of good quality. Therefore, there is no need to remesh it.

button in the toolbar again to deactivate the functionality and avoid hiding more boundaries.

Next, you will remesh the faces with the operation to generate a finer mesh and improve element quality. This may be needed when the quality of an imported mesh is not suitable for the simulation at hand or, as discussed earlier, to improve the mesh on the intersection faces and close to the intersection edges.

Free Triangular 1

In the toolbar, click

and choose .

Select Boundaries 2–9 only. This is most easily done from the , as some of the boundaries are hidden.

In the window for , click to expand the section.

In the text field, type 0.001. The lowered tolerance allows for a closer representation of the curved parts of the vertebra faces with a smaller radius.

Size 1

In the window, right-click and choose .

This adds a size attribute, , to the operation. Use it to set a smaller element size on the boundary of the vertebra. The first subnode specifies the default element size for the operation, which applies to all boundaries, unless it is overridden by other size settings.

In the window for , locate the section.

From the list, choose to set a finer mesh size on the face of the vertebra.

Locate the section. From the list, choose .

It is possible to change the individual mesh size parameters to customize the mesh size even further. This is described in the meshing tutorial Adjusting the Element Size for the Unstructured Mesh Generator, available in the Application Libraries.

The mesh now consists of approximately 6500 triangles.

When generating a new mesh with the operation, smooth surfaces are first created in the background, based on the original mesh. These surfaces are then used when the new mesh is generated. See the discussion in the section Comparing the Meshed Geometry with the STL Mesh in the tutorial STL Import 1 — Generating a Geometry from an Imported Mesh for more information on how the influences the shape of the faces to remesh.

Another alternative is to modify the mesh using the operation with an absolute size expression. For an imported linear mesh, the operation places new or moved mesh vertices on a curved representation of the mesh, where the curvature is derived from the linear mesh.

On the toolbar, click the button.

In the window, you can verify that the Minimum element quality is now much improved (0.4) and the high average quality (0.8) indicates that most of the triangle elements have good quality.

Free Tetrahedral 1

Now, fill the domains with a volume mesh.

In the toolbar, click

In the window for , click

The window reports that the mesh now contains domain (tetrahedral) elements. If you check the window, you can also see that the two domains listed there are marked as ’(selected, meshed)’ and no unmeshed domains are left. This means that the mesh is now ready and can be used to set up materials and physics for a 3D simulation in the software.

Before concluding the tutorial, let us take a closer look at how to create and customize a mesh plot for a visual inspection of the mesh.

In the toolbar, click

The default mesh plot shows the quality of the mesh elements. The light green color indicates a good quality mesh (quality close to 1).

Results

Follow the steps below to create a plot of the volume elements colored according to the domain they belong to and apply filtering to see the elements inside the block and vertebra.

In the window for , locate the section.

From the list, choose to color the mesh elements white.

Click to expand the section. Select the check box.

In the text field, type x>1[mm] to visualize elements with at least one vertex with x-coordinate higher than 1 mm.

In the toolbar, click

Next, add a to the plot node and select the vertebra domain.

Selection 1

Right-click and choose .

Select Domain 2 only (the domain of the vertebra).

In the toolbar, click

Now, duplicate the plot node and make some changes to color the surrounding elements in a light blue color.

Mesh 2

Right-click and choose .

Selection 1

In the window, expand the node, then click .

In the window for , locate the section.