First 3D transition template

[mrbuche]

Is your feature request related to a problem? Please describe.

It seems that templates consisting of transition hexes can be placed sequentially into the dualized mesh.

Describe the solution you'd like

This implements the 3D version of the typical 2D template, which can be seen all over the interior of Livesu et al. (2021).

Describe alternatives you've considered

Piecing together the atomic schemes and connecting centroids seems time inefficient and unnecessary.

Additional context

Implementing this may shed more light on how difficult all this really is.

[mrbuche]

Relevant octree leaves:

Relevant initial hexahedral finite elements:

Drawn together:

[mrbuche]

What are the relative coordinates of the peak for each prism?

[mrbuche]

Seems like some of the transition elements might have bad quality. From Livesu et al. (2021):

Note that the focus of this work is purely on the transition schemes, and this is just a simplistic workflow that offers no guarantees in terms of mesh quality and geometric fidelity. As reported in Section 2 scientific literature offers various alternative choices for octree splitting rules, padding, feature preservation, and robust surface projection. Our approach can be combined with any of the existing techniques to obtain a fully-fledged meshing pipeline.

Mesh from Pitzalis et al. (2021):

MSJ:

AR:

Metrics:

There is an middle extra piece of the 'wine glass' on the transition interior that seems to be the typical culprit in addition to the 2 pieces flanking it:

Template manually constructed seems to be approximately :

As Marco points out, we might just have to employ things in addition to dualization. Smoothing might help, whether Taubin or something like energetic smoothing, but we might also need additional refinement somehow.

[mrbuche]

Maybe it's fine, seems like Sculpt gets even worse hexes when meshing smooth interfaces in microstructures. Or when also doing adaptive hexmeshing: