CGAL users discussion list

["Fernando Cacciola" <>]

Hi xiangzhi,

> Hi! Dear Dr.Vaxman,
>
> Thanks very much for your concern. I assume that you are very intersted in
> this topic.
>
> Yes!! I mentioned split event in my materials because I want to discuss
> something else. Please consider that case a little further, and perturb it a
> little, then you will be able to find that straight skeleton is very
> different.
Right.
In fact, it will be precisely as different as the result you see in the first 
example you posted.

Look at it this way: if the two refex wavefronts don't *exactly* collide 
simulatenously, then one goes past the other: that is the blue bisector coming 
out of the split point that your are seeing.

That's why I wanted to see the exact polygon you used: to see if there should be 
a vertex event, or just almost so.

> [1] Oswin Aichholzer, Franz Aurenhammer, David Alberts, and Bernd Gärtner,
> "A Novel Type of Skeleton for Polygons", *Journal of Universal Computer
> Science* <http://www.iicm.edu/jucs> 1(12) <http://www.iicm.edu/jucs_1_12>,
> pp. 752-761, 1995.
>
> [2] Mirela Tanase, Remco C. Veltkamp. Polygon Decomposition based on the
> Straight Line Skeleton. SoCG'03, June 8-10, 2002, San Diego, USA.
FWIW those two papers are also influencial in the package.

> By the way, this is something related to double number round-off in current
> computer system. In this sense, you can never guarantee the straight
> skeleton pieces are always perpendicular to the "collinear", as a result,
> straight skeleton pieces can be various a lot, you can have a try. Besides,
> for engineering application purpose, more often than not, this kind of
> degeneration (there are others) can be harmful.
FWIW this s not a problem with the CGAL implementation as long as you use the 
recommended kernel:

Exact_predicates_inexact_constructions_kernel.

Please see

http://www.cgal.org/philosophy.html

for an overview of how CGAL packages handle roundoff issues.

Best

Fernando Cacciola
GeometryFactory