Alternative to Shewchuk's triangle

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Alternative to Shewchuk's triangle

Zohar
I'm currently using Shewchuk's triangle to triangulate a given .poly file. It
fails sometimes (out of memory crash), and I thought to try something else.
I was wondering if CGAL constrained triangulation can offer similar
function. These are the lists of switches:

http://www.cs.cmu.edu/afs/cs/Web/People/quake/triangle.switch.html

What's important to me:
- Constrain edges.
- Limit minimal angle.
- Don't add Steiner points on the boundary.
- Limit the number of Steiner points.

My guess it that suppressing point insertion on the border is the problem:

http://cgal-discuss.949826.n4.nabble.com/Option-to-suppress-insertion-of-points-on-border-when-meshing-td4663895.html




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Re: Alternative to Shewchuk's triangle

chrism
Hi,

I can't speak to the Steiner points as I've never had to limit them (the edge triangles have always been good for me), but the other two I can.

You can impose constraint edges via

And you can use either a default or custom Criteria

to impose other criteria on the inserted triangles as per the example here, such inner angles

Section 2.2 here has more details


Cheers
Chris

On Sun, Mar 17, 2019 at 5:01 PM Zohar <[hidden email]> wrote:
I'm currently using Shewchuk's triangle to triangulate a given .poly file. It
fails sometimes (out of memory crash), and I thought to try something else.
I was wondering if CGAL constrained triangulation can offer similar
function. These are the lists of switches:

http://www.cs.cmu.edu/afs/cs/Web/People/quake/triangle.switch.html

What's important to me:
- Constrain edges.
- Limit minimal angle.
- Don't add Steiner points on the boundary.
- Limit the number of Steiner points.

My guess it that suppressing point insertion on the border is the problem:

http://cgal-discuss.949826.n4.nabble.com/Option-to-suppress-insertion-of-points-on-border-when-meshing-td4663895.html




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Re: Alternative to Shewchuk's triangle

Laurent Rineau (CGAL/GeometryFactory)
In reply to this post by Zohar
On Monday, March 18, 2019 12:01:16 AM CET Zohar wrote:

> I'm currently using Shewchuk's triangle to triangulate a given .poly file.
> It fails sometimes (out of memory crash), and I thought to try something
> else. I was wondering if CGAL constrained triangulation can offer similar
> function. These are the lists of switches:
>
> http://www.cs.cmu.edu/afs/cs/Web/People/quake/triangle.switch.html
>
> What's important to me:
> - Constrain edges.
> - Limit minimal angle.
> - Don't add Steiner points on the boundary.
> - Limit the number of Steiner points.
>
> My guess it that suppressing point insertion on the border is the problem:
>
> http://cgal-discuss.949826.n4.nabble.com/Option-to-suppress-insertion-of-poi
> nts-on-border-when-meshing-td4663895.html

There is already an undocumented header that allows to do that:

  <CGAL/Delaunay_mesher_no_edge_refinement_2.h>

Its API is similar to
 
  <CGAL/Delaunay_mesher_2.h>

but it does not insert any Steiner points on constrained edges (and that
sacrifices the mesh quality).


I plan to document it. What could be a good use-case to document? I am
concerned about the degraded mesh quality.

--
Laurent Rineau, PhD
R&D Engineer at GeometryFactory           http://www.geometryfactory.com/
Release Manager of the CGAL Project       http://www.cgal.org/




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Re: Alternative to Shewchuk's triangle

Zohar
Thanks, I'll check that.

Motivation: Mapping to a given boundary that can't change. Generating the
map usually involves discretizing the interior, i.e. a triangulation without
Steiner points on the boundary.

An example:
[Weber14 "Locally Injective Parametrization with Arbitrary Fixed
Boundaries"]
In Fig. 16, the mesh is cut and mapped to a non-convex (planar polygonal)
boundary. If I want to triangulate (remesh) this polygon and glue it back to
a surface, the twin seam edges need to correspond. Adding Steiner points
haphazardly on them may compromise that.

A 3D example:
[Levi15 "Smooth Rotation Enhanced As-Rigid-As-Possible Mesh Animation"]
In Fig. 1, the 4th cylinder is a surface deformation done with discretizing
the interior and deforming the tets. This without changing the given
surface. TetGen was used for the task instead of CGAL for a similar reason.




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