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[Johnny Bigert <>]

Hi Sebastien,

Thank you for the link and the swift response, it was very helpful. I was trying to read up on CDTs, but the description is a bit abstract. Would you care to explain a few things about the linked example?

1. In simple words, what does a CDT do? I guess it incrementally creates a triangulation as we repeatedly call cdt.insert_constraint(start, end)?
2. I got the impression from Wikipedia (https://en.wikipedia.org/wiki/Constrained_Delaunay_triangulation) that a CDT tries to keep the constrained edges (they mention an example with "breaklines along rivers")? But in the linked example, we use insert_constraint on all the edges of the mesh, and keeping all edges makes no sense, so I must be missing something :)
3. In the linked example, what does the cdt.is_constrained(e) call do exactly? It can't give us back the insert_constraint-inserted edges (although the name seems to suggest it). So I guess it gives us the outer borders?
4. If cdt.is_constrained(e) gives us the outer borders, then why do we iterate over faces, look at neighbors etc, why not iterate over edges directly?

Thank you.

    Best regards, Johnny

On Thu, Jun 30, 2022 at 2:18 PM Sebastien Loriot <> wrote:

Hi,

this thread talks about this topic:

https://github.com/CGAL/cgal/discussions/6472

Sebastien.

On 6/30/22 12:51, Johnny Bigert ( via cgal-discuss
Mailing List) wrote:
> Hi,
>
> I would like to kindly ask for ideas regarding a problem I'm trying to
> solve.
>
> I have a triangulated shape as a Polyhedron_3 with exact constructions.
> The shape is closed and simple and may contain holes.
>
> What I would like to calculate is most easily described like this (and
> takes an input parameter z): if we cut away parts of the shape from Z =
> minus infinity to Z = z, what would the shadow (projection) of the shape
> look like if we shine a flashlight from above, from Z = plus infinity.
>
> The result will consist of multiple polygons since the shadow might have
> disjoint areas (e.g. candelabra) and holes (e.g. drinking glass).
>
> Do you have any ideas how to implement this efficiently? Sweep line
> algorithms? Ray casting? Thanks!
>
>       Best regards, Johnny
>
>
>
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