STL Import 1 — Generating a Geometry from an Imported Mesh

STL Import 2 — Remeshing an Imported Mesh, the second part of this tutorial series, describes the process of preparing a mesh directly by remeshing it, without creating a geometry.

The two tutorials in this series are complementary, and intend to provide a detailed insight into how to work with imported meshes. Apart from arriving at a simulation mesh in two different ways, the tutorials also cover repairing different types of defects, and different ways of visualizing the mesh. Depending on your application and the imported mesh at hand, pick and choose from the tools detailed in the tutorials to arrive at a mesh that suits your needs.

Lastly, it is important to mention that the techniques used in the tutorial series apply to any type of imported surface meshes, such as the formats PLY and 3MF. They also apply when creating a mesh from a or dataset, which you would do when using the results of a simulation as the mesh for a new simulation, for example during a topology optimization study.

Model Definition

Import the STL file of a vertebra geometry shown below.

Follow the instructions in this tutorial to

•

Import the STL file.

•

Identify and fix small defects in the imported STL mesh.

•

Partition the object and create a surrounding volume to be used for simulation.

•

Generate a volume mesh for the geometry.

•

Create a plot to see how close the created surface is to the original STL mesh.

COMSOL_Multiphysics/Meshing_Tutorials/stl_vertebra_import

Modeling Instructions

From the menu, choose .

In the window, click

In the window, click

In the toolbar, click

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file c6_vertebra.stl.

Click

The import of an STL file consists of three steps: the import of the surface mesh from the file, the generation of a surface geometry from the imported mesh, and finally the creation of a solid object. After the import is complete the geometry appears on the screen.

Notice that after the import completes, the reference to the STL file is no longer visible in the window. The source for the geometry import is now , which is where the mesh import can be found. The sequence is added under the node. The output of a mesh import sequence added here can be imported into any geometry sequence in the mph file. The node in the geometry sequence handles the last steps of the process: conversion from mesh to geometry and creation of a solid object.

According to the information in the window, a mixed object was generated by the import. This means that the object contains both solids and surfaces. Some parts of the STL source mesh form a "watertight" shell that can be converted into a solid. The additional faces are not needed in this case, so these must be found and deleted.

Click

to locate the source mesh in the window.

Mesh Part 1

The mesh import automatically partitions the STL mesh into boundaries based on, for example, an angle criteria. By inspecting the boundaries, it is possible to find mesh faces that are not properly connected to others. Do this by opening the window, clicking on each of the boundaries in the list, and checking in the window if the boundary is wanted or not.

From the menu, choose .

In the window, expand the node, then click .

In the window toolbar, click

next to

, then choose .

If there are many boundaries, reimport the mesh with the import setting as this will partition the mesh into as few boundaries as possible. If reimporting the mesh takes a long time, use the operation to join the boundaries manually, as shown below.

Join Entities 1

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Click

Information

This results in an information message that not all selected entities could be joined into one. When joining boundaries, the operation tries to remove the edges between the boundaries. The node is expected due to the extra faces. Use the selection in the to find and delete the faces.

In the window, click .

Expand the node and click on the second node. In the window, you find information that the operation was unable to delete two edges. Make sure both edges are selected in the list.

Click the

button in the toolbar to zoom in on the selected edges. The button is also available next to the list.

Click the

button in the toolbar.

If the selected edges are hidden behind the mesh, zoom out, rotate the geometry, then click the button again to find the area highlighted in the figure below. The part of the mesh with a semi-elliptical shape forms a fold, as seen in the middle of the image below. Rotate the mesh slightly in the window to see how the mesh elements connect.

To get a better view, it may help to turn off transparency again.

Click the

button in the toolbar.

The two edges are located at the fold in the mesh. Open up the again, make sure is selected, and notice that Boundaries 2 and 3 are in the same location as the short edges on the generated geometry. These are isolated boundaries on the outside of the surface mesh and are attached to the mesh only through a single edge.

In the following steps, delete these boundaries from the imported mesh.

Delete Entities 1

In the toolbar, click

Click the

button in the toolbar.

In the window for , locate the section.

In the list, select (the large face of the vertebra).

Click

This leaves the two small faces in the list of boundaries to be deleted.

Click

After the operation completes, the contains only one boundary for the mesh. The isolated faces are no longer there. However, the small fold in the mesh is still visible. Follow the steps below to repair this defect in the mesh.

Close the window.

Create Edges 1

Sharp irregularities in the mesh, like this fold or pointy spikes, can cause problems when creating a smooth geometric surface. A smooth source mesh is therefore preferred. To remove the fold, start with partitioning the mesh to create a boundary containing the fold, delete this boundary, and finally, generate a new mesh face to cover the resulting hole.

In the toolbar, click

and choose .

Select mesh edges around the fold by clicking them in the , similar to what is shown in the image below. The selection is most easily done with tansparancy off. If there are mesh edges on the opposite side of the view or are located inside a closed mesh face, it is recommended to use a or to hide boundaries in the mesh to reach those mesh edges. The selected edges can differ from the ones selected in the figure, as long as the edges form a closed loop, include the fold, and delimit only a small region around the fold. The last requirement is important when generating a new mesh face that follows the original mesh as close as possible.

In the window for , click

to generate the edges and partition the boundary.

Delete Entities 2

In the toolbar, click

Select Boundary 2 only (the boundary with the fold).

In the window for , click

There is now a hole in the surface mesh, which means that it isn’t possible to create a solid geometry from this mesh. So, before trying to create a geometry again, the hole must be sealed off. Two operations can be used for this purpose: and . The operation is a manual way of generating mesh faces for holes by selecting edge loops. The operation automatically generates mesh faces to cap several holes at once. In the following tutorial, use the operation that generates mesh faces for selected edge loops.

Note that the mesh faces generated by both of these operations will be minimal faces that strive to be as planar as possible.

Create Faces 1

In the toolbar, click

and choose .

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

In the window for , click

The hole is sealed off with a new mesh face that is much smoother.

Join Entities 2

Now, join the two boundaries.

In the toolbar, click

Click in the window and then press Ctrl+A to select both boundaries.

In the window for , click

Click the

button in the toolbar to again see the full mesh.

Mesh Part 1: Length Unit

Before continuing with the geometry, make sure the mesh and geometry have the correct length unit. The meshing sequence in a has a length unit, just as a geometry sequence. Since STL files do not include units, the length unit is set to the default geometry length unit, meter.

In the window, click .

In the window for , locate the section.

Select the check box.

From the list, choose .

Click

and zoom out to verify that the unit on the axes are indeed set to mm.

Geometry 1

Although the length unit of the sequence now has the correct value, you also need to update the length unit of the sequence. One way to avoid to update both is to set the length unit of the geometry sequence before importing the file.

In the window, under click .

In the window for , locate the section.

From the list, choose .

Import 1 (imp1)

A rebuild of the sequence re-imports the geometry from the mesh and updates the length unit.

In the window, under click .

In the window for , click

While waiting for the import to complete, take a look at the settings. For large meshes, it can be time consuming to locate and handle irregularities manually. Then, tuning the parameters can provide an automatic way to simplify the mesh and remove faults to generate smoother geometry faces.

The is a global tolerance relative to the size of the geometry. If this tolerance is decreased, the generated geometry follows the shape of the original mesh more closely. An increased tolerance will remove larger details and give a more smooth face at the cost of not following the shape of the orignal mesh as closely.

The is a local tolerance. An increased removes small irregularities even if they are big relative to the local element size.

At the end of this tutorial, you can find instructions on how to create a mesh plot to see how well the created faces match the source mesh. But first, complete the geometry set up.

The window now reports having imported one solid object, which means that it is time to continue to add a surrounding volume and cut the geometry in half to make use of the symmetry plane. To begin with, modify the orientation of the geometry to improve the visualization.

Rotate 1 (rot1)

In the toolbar, click

and choose .

Select the object only, in other words the object for the imported vertebra.

In the window for , locate the section.

From the list, choose .

In the text field, type 90.

Click

Click the

button in the toolbar. This will make sure the vertebra is once again in view.

Rotate 2 (rot2)

In the toolbar, click

and choose .

Select the object only.

In the window for , locate the section.

In the text field, type -90.

Click

Click the

button in the toolbar.

Block 1 (blk1)

In the following section, create a block, combine it with the imported vertebra geometry to create a domain outside of the vertebra, and to cut the geometry in half.

In the toolbar, click

In the window for , locate the section.

In the text field, type 23[mm].

In the text field, type 15[mm].

Locate the section. In the text field, type -22[mm].

In the text field, type -11.1[mm].

In the text field, type 60[mm].

Click

Partition Objects 1 (par1)

In the toolbar, click

and choose .

Select the object only (the block).

In the window for , locate the section.

Find the subsection. Click to select the

toggle button.

Select the object only (the vertebra).

Click

Click the

button in the toolbar.

Click the

button in the toolbar.

The resulting object now contains two domains, inside and outside the imported geometry. Using a transparent view can help to see the parts inside the block. Continue with finalizing the geometry and creating a mesh.

Form Union (fin)

In the window, click .

In the window for , click

Mesh 1

In the window, under right-click and choose .

This builds a tetrahedral mesh on the domains. If this mesh is good enough for the application at hand, it is possible to start setting up the physics at this point. However, many geometries created from mesh require more fine-tuned mesh settings. For example, a specific mesh size setting may cause problems due to the representation of the created face. Then, it often helps to premesh the face with a triangular mesh, restricting the size of the triangles to a more narrow interval. This results in triangles of more similar size and more control over the generated surface mesh. Follow the steps below to generate such a mesh by editing the physics-induced mesh.

In the window for , locate the section.

From the list, choose .

Size

In the window, under right-click and choose .

Building a feature node in the sequence of operations will make sure that any further operation that is added will be placed directly after the built one.

Free Triangular 1

In the toolbar, click

and choose .

Select Boundary 6 only (the large face of the vertebra).

Size 1

Right-click and choose .

In the window for , locate the section.

Click the button.

Locate the section. Select the check box.

In the associated text field, type 0.7[mm].

Select the check box.

In the associated text field, type 0.5[mm].

This will lower the maximum element size the triangles are allowed to take down to 0.7 mm. In the same way, it will increase the minimum element size allowed to 0.5 mm. The rest of the settings are still taken from the settings of the first node in the sequence.

Free Tetrahedral 1

In the window, under right-click and choose to once again build the mesh on the domains.

Hide some boundaries and turn off transparency to better see the mesh on the boundaries of the vertebra.

Click the

button in the toolbar.

In the window for , locate the section.

Click to clear the

toggle button.

In the window toolbar, click

next to

, then choose .

Click the

button in the toolbar.

In the , click to hide Boundaries 1, 2, and 4, to get the view in the image below.

The mesh is now ready for simulation.

Comparing the Meshed Geometry with the STL Mesh

In order to see how close the meshed geometry follows the source STL mesh, create a plot with both meshes. In this final part of the tutorial you will do this in a new component in the model, and also test the effect of the when generating the geometry.

Mesh Part 1

In the window, under click .

Right-click and choose to reimport the vertebra into a new Component.

Mesh 2

Next, generate a triangular mesh for the vertebra. As the purpose of this part of the tutorial is to check the shape of the face generated by the import, there is no need for a tetrahedral mesh.

Free Triangular 1

In the toolbar, click

and choose .

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

In the window for , click

Refine 1

Add a operation to further refine the mesh and make sure any curvature is resolved.

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Click

In the toolbar, click

to automatically create a dataset and add a under .

Results

Mesh 2

Use the option for the to plot only half of the mesh. This will make it easier to compare the two meshes.

In the window for , click to expand the section.

Select the check box.

In the text field, type x>11[mm].

This means that only mesh elements that are located at x coordinates larger than 11 mm will be included in the plot.

In the toolbar, click

The generated geometry face is smooth and has a corresponding to the discretization of the physics in the model. In practice, this means that the is most often quadratic, unless solving a CFD problem, where linear discretization is used. To plot the curved elements on the boundary, change the corresponding setting on the dataset.

Mesh 2