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From: "Efi Fogel";

Date: 2013??4??17??(??????) ????4:26

To: "cgal-discuss";

Cc: "cgal-discuss";

Subject: Re: [cgal-discuss] Clip polygon with hole by half-plane, topology

There is another situation where the clipping line contains a single vertex of the hole (and nothing else of the hole) and the interior of the hole resides entirely on the positive (non-clipped) side of the clipping line. It's actually covered by 3rd case above, and so it doesn't deserve special treatment. (you might have thought of it already.) In this case, the hole remains a hole. This is explained in http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Boolean_set_operations_2/Chapter_main.html#Subsection_19.3.1

On Mon, Apr 15, 2013 at 9:16 PM, Ben Supnik <> wrote:

Hi Y'all,

I'm looking at the possible outcomes of clipping a polygon with holes by a half-plane in 2d. I'm hoping someone who knows more about topology than I do can set me straight...

It appears to me that there are three cases for holes:

- If one of the polygon holes is entirely on the positive (non-clipped) side of the clipping line then it will remain unmodified as a hole in the new polygon.

- If one of the polygon holes is entirely on the negative (clipped) side of the clipping line, then it is clipped and can be deleted.

- If one of the polygon holes spans the clipping line then it will no longer be a hole - the remaining boundary after clipping will become part of the outer boundary of the new clipped polygon-with-holes.

Is this third point always true? Did I miss any cases? Naively it seems that a hole is only a hole if it is not connected to the outside of the polygon by a polygon edge, and after clipping in case three it must be connected.

Thanks!
Ben

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