![](bg6.png)
Table 1: Maximum, minimum, and median volumes and
aspect ratios (higher is better) of the meshes shown on the
left hand sides (before) and right hand sides (after) of Fig. 3
(hole fill) and Fig. 4 (erosion).
Volume Aspect Ratio
Edit Op. Max. Min. Med. Max. Min. Med.
Before Hole Fill 3.3e-10 1.4e-11 1.1e-10 .3333 .0803 .2737
After Hole Fill 2.4e-9 1.4e-11 1.1e-10 .3333 .0456 .2736
Before Erosion 1.6e-10 5.4e-12 4.9e-11 .3333 .0872 .2688
After Erosion 1.6e-10 1.0e-12 4.9e-11 .3333 .0004 .2689
tion with six iterations of subsequent quality preserv-
ing surface smoothing did not introduce inverted ele-
ments or infinitesimally small volume tetrahedra. The
resulting tetrahedra exhibit sufficient aspect ratios. As
a result, both mesh editing operations succeed at pro-
ducing meshes suitable for the FEM, as we have also
validated in our experiments.
5 CONCLUSIONS
In summary, we have introduced a novel tetrahedral
mesh editor with immediate simulation feedback. By
directly operating on CAE meshes, modifications can
be performed and simulated, while avoiding switch-
ing to a CAD tool and remeshing the entire domain.
As 3D printing can support and often only supports
discrete triangular surfaces, this approach avoids hav-
ing to feed back the results into a CAD tool com-
pletely. While the current set of editing operations
is somewhat limited, our prototype demonstrates how
the iterative product design loop can be shortened for
individualized versions of mass-produced parts.
The use of a GPU-accelerated FEA solver ensures
short iteration times, while the distributed architec-
ture minimizes user hardware requirements. Due to
the use of Unity (Unity, 2020) and WebSockets, the
front end can be deployed directly as a web applica-
tion. Bandwidth requirements are low due to the use
of surface meshes only between the front end and the
modeling service (the modeling and simulation ser-
vice should reside in the same data center, as they ex-
change volumetric meshes).
As the implemented editing operations preserve
the correspondence between individual boundary tri-
angles and their originating CAD surface IDs (or a
newly created contiguous surface ID), the user can in-
teract at a significantly higher level of abstraction than
individual surface triangles. Furthermore, this allows
automatic remapping of surface-based boundary con-
ditions for simulation. Additionally, mesh optimiza-
tion ensures mesh quality is preserved.
5.1 Future Work
Besides the extension to further editing operations, it-
eration times could be further reduced in the future by
performing geometry processing on the GPU, as done
by Mueller-Roemer et al. (Mueller-Roemer et al.,
2017). While our local, topological erosion works
well for the removal of fin- or plate-like structures,
the addition of geometric morphological operations,
such as the opening and closing operations on trian-
gle meshes recently shown by Sell
´
an et al. (Sell
´
an
et al., 2020), could greatly improve the flexibility of
the editor. Furthermore, hole filling could be extended
to non-planar holes by reparametrization of the loop
into 2D space and subsequent determination of inte-
rior point positions in 3D by solving a Laplacian.
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