How does CGAL mesh isosurfaces defined as gray levels in 3D images?

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How does CGAL mesh isosurfaces defined as gray levels in 3D images?

yellowbed
Hello everyone,
 
I'm using CGAL to mesh isosurfaces defined as gray levels in 3D images. It produces nice results. However, I don't have a clue how the underlying algorithm works. Can someone explain to me on a high-level what the algorithm does?
 
The cited paper "Jean-Daniel Boissonnat and Steve Oudot. Provably good sampling and meshing of surfaces. Graphical Models, 67:405–451, 2005." goes to much into detail. I can not really follow it, due to missing background.
 
Kind regards 
 
Jacky
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Re: How does CGAL mesh isosurfaces defined as gray levels in 3D images?

Laurent Rineau (CGAL/GeometryFactory)
On Saturday, February 23, 2019 10:11:24 AM CET [hidden email] wrote:
> Hello everyone,
>  
> I'm using CGAL to mesh isosurfaces defined as gray levels in 3D images. It
> produces nice results. However, I don't have a clue how the underlying
> algorithm works. Can someone explain to me on a high-level what the
> algorithm does?
> The cited paper "Jean-Daniel Boissonnat and Steve Oudot. Provably good
> sampling and meshing of surfaces. Graphical Models, 67:405–451, 2005." goes
> to much into detail. I can not really follow it, due to missing background.

Hi, the two tools to understand are :

  - the "Delaunay refinement" algorithm,
  - and "restricted Delaunay triangulations".

You can search for introduction materials on the web. Most of them are
scientific articles, and presentation slides, but you can also find teaching
notes (for master degrees), and a few videos.

--
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: How does CGAL mesh isosurfaces defined as gray levels in 3D images?

yellowbed
Thank you Laurent.

Do I get the simplified idea of CGAL's meshing procedure correctly?

1. Our oracle gives us some points in the isosurface

2. A restricted Delaunay triangulation is computed for these points and
gives us already a good approximation

3. In the resulting triangulation skinny triangles below some limit are
eliminated by applying Delaunay refinement


On 25.02.2019 09:59, Laurent Rineau (CGAL/GeometryFactory) wrote:

> On Saturday, February 23, 2019 10:11:24 AM CET [hidden email] wrote:
>> Hello everyone,
>>
>> I'm using CGAL to mesh isosurfaces defined as gray levels in 3D images. It
>> produces nice results. However, I don't have a clue how the underlying
>> algorithm works. Can someone explain to me on a high-level what the
>> algorithm does?
>> The cited paper "Jean-Daniel Boissonnat and Steve Oudot. Provably good
>> sampling and meshing of surfaces. Graphical Models, 67:405–451, 2005." goes
>> to much into detail. I can not really follow it, due to missing background.
> Hi, the two tools to understand are :
>
>   - the "Delaunay refinement" algorithm,
>   - and "restricted Delaunay triangulations".
>
> You can search for introduction materials on the web. Most of them are
> scientific articles, and presentation slides, but you can also find teaching
> notes (for master degrees), and a few videos.
>


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Re: How does CGAL mesh isosurfaces defined as gray levels in 3D images?

Laurent Rineau (CGAL/GeometryFactory)
On Monday, February 25, 2019 11:13:01 AM CET YB wrote:

> Thank you Laurent.
>
> Do I get the simplified idea of CGAL's meshing procedure correctly?
>
> 1. Our oracle gives us some points in the isosurface
>
> 2. A restricted Delaunay triangulation is computed for these points and
> gives us already a good approximation
>
> 3. In the resulting triangulation skinny triangles below some limit are
> eliminated by applying Delaunay refinement

Yes. That's roughly that. Here is brief summary of the algo

https://www-sop.inria.fr/geometrica/software/cgalmesh/restrictedDT.html

--
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: How does CGAL mesh isosurfaces defined as gray levels in 3D images?

yellowbed
Perfect. Thank you for the brief summary. It helps a lot for my
understanding.

On 25.02.2019 17:01, Laurent Rineau (CGAL/GeometryFactory) wrote:

> On Monday, February 25, 2019 11:13:01 AM CET YB wrote:
>> Thank you Laurent.
>>
>> Do I get the simplified idea of CGAL's meshing procedure correctly?
>>
>> 1. Our oracle gives us some points in the isosurface
>>
>> 2. A restricted Delaunay triangulation is computed for these points and
>> gives us already a good approximation
>>
>> 3. In the resulting triangulation skinny triangles below some limit are
>> eliminated by applying Delaunay refinement
> Yes. That's roughly that. Here is brief summary of the algo
>
> https://www-sop.inria.fr/geometrica/software/cgalmesh/restrictedDT.html
>


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