**comp.graphics.algorithms**

## Subject: **Re: Create PolyMesh From PolyLine**

Hans-Bernhard Broeker wrote:

> Peter Laube

>> 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. 45Â°.

>

> 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 "KeilfÃ¶rmige 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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