**comp.graphics.algorithms**

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

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"?

--

Hans-Bernhard Broeker (broeker@physik.rwth-aachen.de)

Even if all the snow were burnt, ashes would remain.

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