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.

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.

Transform 1

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. Here, we will move the mesh to the origin.

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].

This operation is needed before you can generate a tetrahedral mesh. It checks if the imported surface mesh forms any watertight regions, and if so, it forms domains.

Create Domains 1

In the toolbar, click

and choose .

In the window for , click

Warning

A warning appears stating that the operation failed to create a domain for the face of the vertebra.

In the window, click .

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

Warning

This 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 in the bottom left is a triangular hole that seems to be caused by a missing mesh element. The two additional holes located on the upper half of the image are both slit like holes that have zero or almost zero area, as we will see soon when we zoom 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, which are 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.

We will use two techniques to repair the holes as they require different kind of treatment. Of the three holes in the image above, first we will repair the one in the upper right corner of the image, we will continue with the small hole in the upper left. Lastly, fill in the triangular hole in the bottom left.

From the menu, choose .

If there are more than 3 edges listed in the , go back to the node and make sure that the setting is set to , then reimport the mesh.

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

Selection List

Go to the window.

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 at 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, expand the node, then click .

In the window for , locate the section.

From the list, choose .

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

The mesh vertices are now merged, thereby eliminating the hole and the edge adjacent to it. You can easily verify this by hovering over the location of the hole with the pointer: no edge becomes highlighted.

Next, repair the other slit in the mesh.

Selection List

Go to the window.

In the list, select .

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

button in the toolbar.

On one side of the slit (on the left side of the red 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 elements, the mesh edges on the two sides of the slit could not be merged even with the larger tolerance. 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 that are smaller than a specified tolerance. We can therefore use this operation to also repair the third hole.

Select Boundary 1 only (the boundary of the vertebra).

Fill Holes 1

In the toolbar, click

and choose .

In the window, note that the node is inserted after the node in the model tree, since the was the current node. The current node is indicated by a frame around its icon, either green (node is built) or yellow (node is not built). It is desired to insert operations that fix the holes before creating a domain, so leave the node unbuilt for now.

In the window for , click

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. Now, let’s find out if the third hole is also repaired.

button in the toolbar.

Select Edge 1 only (the edge of the triangular hole).

button in the toolbar, to check if any edges remain. You can zoom in a bit to see the exact view as in the image below.

The original triangular hole (bottom left corner in the above image) 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.

In the window toolbar, click

next to

, then choose .

In the toolbar, click

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

Go back to 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, which now forms a watertight boundary. Continue with the steps below to learn how to combine the imported mesh with a block created in the same component, how to 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

Choose 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 .

Continue to generate a mesh for the block using default mesh size settings.

button in the toolbar.

Mesh 2

A second mesh () was automatically added when the block was added to the geometry sequence. is conforming with while defines its own geometric model with its own set of entities (domains, boundaries, edges, and points). The frame around the icon indicates that any physics that you will add to the Component will be defined on Mesh 1. In the window for the node, you can easily switch so that the physics will be defined on instead. There is no need for that here as we are interested in analyzing the vertebra.

Size

In the window, expand the node.

Right-click and choose .

This will automatically add a operation to as the block is a solid object.

button in the toolbar.

You only need to import the surface mesh for the block to the meshing sequence of the vertebra, as overlapping volume elements are not supported.

Import 2

In the window, expand the node.

Right-click and choose . Make sure the node is added after in the model tree.

In the window for , locate the section.

From the list, choose . This will automatically suggest to import , which is the mesh of the block.

Clear the check box.

Click .

As both boundary meshes are imported and do not contain any holes, build the node.

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.

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

In the window, right-click and select .

The mesh should not contain any domain elements. This means that the first part of the section should only list , , and . If tetrahedra are present, or if the meshes intersect, check and make sure that the settings for and are correct, then reimport the mesh of the block.

In the window, we can 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.

Create Domains 1

In the window, right-click and choose .

Check the window. Two domains were created; one for the vertebra and one for the domain of the surrounding block.

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

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).

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 better keep the original shape 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 be able to see in the window that the mesh of the vertebra and the block have been partitioned by the plane. A new mesh face that connects the vertebra and the block along the plane has also been created inside the block. This is controlled by the check box. When it is selected, the operation creates planar faces inside closed edge loops generated by the intersection.

Delete Entities 1

In the toolbar, click

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 from the intersection. 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 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.

Select Boundary 5 only 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 software creates a smooth surface in the background, which is used to place new or moved mesh vertices when adapting the mesh.

On the toolbar, click the button.

In the window, you can verify that the Minimum element quality is now much improved (0.32) and the high average quality (0.80) indicates that most of the triangle elements have a good quality.

Now, fill the domains with a volume mesh.

Free Tetrahedral 1

In the toolbar, click

In the window for , click

The window reports that the two domains contain about 53 000 domain elements. If you check the window, you can also see that the two domains listed there are marked as ’(meshed)’ and that there are no unmeshed domains 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’s 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 filtering applied 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.