CGAL users discussion list

[Efraim Fogel <>]

You can use an extended arrangement, where you extend the cells of the 
arrangement,. For example, extend the face type, and store with each 
face the originating polygon.

Graviton wrote:
> OK, let say if I use arrangement for this purpose, hmm... now as I 
> think about it, it seems that the arrangement is no more used. 
>
> Because now my purpose is to convert the cleaned polygon to mesh, and 
> for each face ( or element) of the mesh, I would need to be able to 
> link it back to the original polygon, I don't think arrangement is 
> useful here. I will think more about how to use constrained 
> triangulation for this purpose, and see how it goes. 
>
> Let me know if you have better suggestion, thanks!
>
> On Tue, Oct 11, 2011 at 5:15 PM, Sebastien Loriot (GeometryFactory) 
> [via cgal-discuss] <[hidden email] 
> </user/SendEmail.jtp?type=node&node=3893318&i=0>> wrote:
>
>     Graviton wrote:
>     > Thanks! But one thing about the constrained delaunay
>     triangulation is
>     > that, I won't be able to mapped the triangulated face back to the
>     > original polygon, am I right? Any idea how to solve this?
>     You can keep the correspondences between polygon vertices and
>     triangulation vertices.
>     Again, it depends on what you want to do with the output,
>     maybe an arrangement is more suitable in this case.
>
>     Sebastien.
>
>     >
>     > On Tue, Oct 11, 2011 at 4:59 PM, Sebastien Loriot
>     (GeometryFactory) [via
>     > cgal-discuss] <[hidden email]
>     > </user/SendEmail.jtp?type=node&node=3893262&i=0>> wrote:
>
>     >
>     >     The first thing to do is to compute snap rounded version of
>     your
>     >     polygons and then process them. You will avoid degenerate cases
>     >     handling.
>     >     I have no idea what is the expected output but your either
>     use a
>     >     Constrained Delaunay Triangulation or an arrangement to
>     compute one.
>     >
>     >     Relevant documentation pages:
>     >
>     >    
>     http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Triangulation_2/Chapter_main.html#Section_36.8
>     >    
>     http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Snap_rounding_2/Chapter_main.html
>     >    
>     http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Arrangement_on_surface_2/Chapter_main.html
>     >
>
>     >     Sebastien.
>     >
>     >     Graviton wrote:
>     >
>     >      > I have a lot of polygons. Ideally, all the polygons must not
>     >     overlap one
>     >      > other, but they can be located adjacent to one another.
>     You can
>     >     assume that
>     >      > these polygons represent countries on a map, and I import
>     these
>     >     polygons
>     >      > from a drawing. Due to rounding errors, I would have to
>     allow for
>     >     slight
>     >      > polygon overlap ( defined by a certain tolerance) because
>     all
>     >     these polygons
>     >      > are obtained from user hand drawing input, which is not as
>     >     machine-precised
>     >      > as I want them to be.
>     >      >
>     >      > My question is how to convert these polygons into mesh (
>     with
>     >     vertexes and
>     >      > faces) and at the same time, one still knows which face it
>     >     belongs to in the
>     >      > original polygon. Any idea how to proceed with this?
>     >      >
>     >      > My current idea is that I would
>     >      >
>     >      > 1. create one arrangement for each polygon ( a country),
>     tag the
>     >     faces in
>     >      > the arrangement, see whether it is an unbounded face, or a
>     >     bounded one. So
>     >      > that each bounded face, I can still keep track it back to
>     the
>     >     original
>     >      > polygon ( a country)
>     >      > 2. overlay all the arrangement together, and obtain an
>     >     arrangement. Inside
>     >      > this arrangement there will be a lot of faces, some of
>     the faces are
>     >      > correctly belonged to the only 1 face, some of the face is a
>     >     result of two
>     >      > polygon slightly overlapped one another.
>     >      > 3. After obtaining the faces, I will use snap rounding to
>     clear
>     >     off all the
>     >      > sliver (http://en.mimi.hu/gis/sliver_polygon.html) and maybe
>     >     eliminate a few
>     >      > of the faces resulting from two polygon overlapped one
>     another.
>     >     This should
>     >      > properly clean up the topology
>     >      > 4. Now all the polygons are in proper topology, i.e, no more
>     >     sliver, no more
>     >      > overlapped polygon, I can then collect the points and the
>     face to
>     >     construct
>     >      > a mesh.
>     >      >
>     >      > What do you think about the above approach? Or is there
>     any other
>     >     more
>     >      > direct way of doing things?
>     >      >
>     >      > This is a SO post, asking about the same thing.
>     >      >
>     http://stackoverflow.com/questions/7495487/convert-polygons-into-mesh
>     >      >
>     >      >
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