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Subject: Re: Create PolyMesh From PolyLine



Hans-Bernhard Broeker wrote:
> Peter Laube wrote:
>> Hello Group,
>
>> I have a (closed) Line of Segments running counterclockwise. All
>> Segments are on the x-y-Plane. Now I compute the bisecting Lines between
>> each Segment-Pair and rotate them so that they point into the Polygon
>> which is defined by the closed Line of Segments.
>
> There seems to be some terminology mixup here. First of all, lines
> are infinite and undirected, so they don't "point" in one direction or
> its opposite. Rays would do that, but not lines. Second, there
> cannot really be a need to rotate a bisector computed from two
> Segments such that it points to the inside of the polygon they're
> forming a vertex of.
>
> Formally, two edges form a pair of angles, one inside polygon, one
> outside. The bisecting rays of these two angles form a single line
> going through the vertex. No need to rotate anything --- just pick
> the bisecting ray of the internal angle.
>
>> I also rotate the bisecting Lines downward so that they have specified
>> angle to the x-y-Plane, e.g. 45°.
>
> So now we're in 3D. And your segments aren't really segments, and the
> polygon isn't by nature a polygon, but rather a horizontal cut through
> a 3D hole in the ground with angled walls.
>
>> If there are neighbor bisecting Lines which intersect each other, i need
>> to calculate the common bisecting Line pointing further down which can
>> also intersect the next bisecting Line (or the previous), for which i
>> need again the common bisecting Line. This sounds to me like a problem
>> which perfectly fits to a recursive algorithm.
>
> It appears what you're actually trying to compute is the straight
> skeleton, a.k.a. "medial axis" of your polygon.
>
>> By that algorithm I try to get a closed band of Polygons, and with that
>> i want to intersect these polygons with each other. In the end, i
>> hopefully get a V-Notch of the formerly 2D-Polygon.
>
> And what's a "V-Notch"?
>
Thanks for correcting my Post so far :) I have still problems to
describe the maths in English. I think you can imagine what i have in
mind too.. well V-Notch, i found it by dict.leo.org.. in german i would
call it "Keilförmige Vertiefung". I try to compute the lower part of my
"3D Hole in the ground with angled walls" where the angled walls meet
their opposite walls.

I Hope i make it a little bit clearer.
Peter

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