Geometry Fillets?

[Earl Fairall]

Does anyone know if I can do concave fillets like the image below? I would also like to do convex fillets. Would shifting a node and playing with edge curvature accomplish this task? I built a previous script in C# to generate geometries like this, but I was never able to crack the fillet code...

Maybe I could create a triangle from the tooth and hypershell vectors, then set the edge curvature property along the fillet? This might get messy though, because the hypershell vector will change as the mesh is refined. I am not sure this would work for convex fillets either.

Thanks for any guidance you can provide.

Sincerely,

Earl

[Wolfgang Bangerth]

Earl,
the picture you attached does not appear to be available any more. Can
you send it again as an attachment to your email, rather than inlined?
Best
W.

> Sincerely,
>
> Earl
>
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[Earl Fairall]

Hmmm, that is unusual....please see the attached image.

Earl Fairall
p. 815.419.8690
efai...@gmail.com

On Mon, Jun 4, 2018 at 12:12 PM, Wolfgang Bangerth <bang...@colostate.edu> wrote:

Earl,
the picture you attached does not appear to be available any more. Can you send it again as an attachment to your email, rather than inlined?
Best
 W.

On 06/03/2018 09:47 PM, Earl Fairall wrote:

Does anyone know if I can do concave fillets like the image below? I would also like to do convex fillets. Would shifting a node and playing with edge curvature accomplish this task? I built a previous script in C# to generate geometries like this, but I was never able to crack the fillet code...

Maybe I could create a triangle from the tooth and hypershell vectors, then set the edge curvature property along the fillet? This might get messy though, because the hypershell vector will change as the mesh is refined. I am not sure this would work for convex fillets either.

Thanks for any guidance you can provide.



Sincerely,

Earl

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[Jean-Paul Pelteret]

Dear Earl,

If I understand correctly then what you wish to do here is project a small portion of the boundary to this fillet curve... Although I have no familiarity with the class (so I stand to be corrected), I think that you might be able to do this with the help of a ChartManifold. I would suggest that you look at the documentation for that class and its various OpenCascade derivatives, as well step-53 and step-54 for application examples.

I hope that this gets you going in the right direction.

Regards,

Jean-Paul

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<fillet.png>

[Wolfgang Bangerth]

On 06/05/2018 08:55 AM, Jean-Paul Pelteret wrote:
> If I understand correctly then what you wish to do here is project a small
> portion of the boundary to this fillet curve...

That has the disadvantage that it bends open the corner, leading to degenerate
quads. Better to attach a triangle with a curved boundary, and subdivide the
triangle into three quads. That should be easy to do by hand, but you could
probably also use GridGenerator::simplex() for it and then shift, rotate,
transform the resulting cells.

Best
W.

[Earl Fairall]

Wolfgang,

What do you mean by attach and subdivide a triangle "by hand"? Is there an alternative method to simplex?

This morning I was able to attach a triangle using simplex, but there seems to be a boundary/manifold issue. I should be able to resolve this issue and get the shape I need with a better understanding of the boundaries as Jean Paul suggested.

Earl

[Wolfgang Bangerth]

Earl,

> What do you mean by attach and subdivide a triangle "by hand"? Is there an
> alternative method to simplex?

You can create a Triangulation "by hand" using
Triangulation::create_triangulation() in the way step-14 does, i.e. by
specifying where vertices are located and how they are connected to cells.
Internally, that is of course exactly how the functions in GridGenerator do
their work.

If you do this for the geometry of the fillet, you can then use
GridGenerator::merge_triangulations() to attach it to the rest of the geometry
you already have.

> This morning I was able to attach a triangle using simplex, but there seems to
> be a boundary/manifold issue. I should be able to resolve this issue and get
> the shape I need with a better understanding of the boundaries as Jean Paul
> suggested.

Yes. Take a look at the example programs that talk about geometry ("manifold")
descriptions.