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[Graviton <>]

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]> 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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