CGAL users discussion list

["Fernando Cacciola" <>]

Dear Xiangzhi,

> I am sorry, I did not  save it,
OK, that's what I imagined.
In that case you just drawn the polygon right there in the demo program, but 
then, the edges V1V2 and V5V6 *are not exactly* along the same line, just almost 
so.
Thus, the generated straight skeleton is correct for the given input.
That is, what you are seeing is not a bug in the program, not even an undesired 
effect of the choosen algorithm, is the way a straight skeleton is, by 
definition, and any correct implementation of any algorithm will produce the 
same output.

If you use a polygon where the edges are truly aligned you'll see the vertex 
event that you expected. For that you need to define the polygons in a text file 
so you can define the coordinates exactly. Then you can load the polygon in the 
demo (via File->Load Polygon)

I'm attaching here some examples from my internal test-suite so you can see 
vertex events:

pseudo_split_0.poly
is the classic "eppstein" example

pseudo_split_11.poly
is the essentially equivalent to your test case (but upwards)

pseudo_split_6.poly
pseudo_split_8.poly
pseudo_split_13.poly
are just some additional examples for you to see


> but you can also  do some experiment on
> "Straight_Skeleton_2"  with some polygons alike. If you want to further
> discuss those degeneration cases, please refer to the attached file. In
> fact, I hope some one can explain them in a mathematical way.

The fact that a vertex event radically changes the resulting straight skeleton 
is simply an avoidable consequence of the topological changes that ocurr when 
edges collide.
The vertex event is like a singularity in the sense that two split events are 
ocurring simultaneously and corresponding topological change is not the same as 
one split after the other (that's why the algorithm *must* handle this 
explicitely)

> And how to avoid those cases.
What exactly do you want to avoid? if you want the structure of the skeleton not 
to be so sensitive to the exact coordinates of the input vertices then I you are 
just out of luck... it is like wanting water not to boil when it reaches 100º 
becasue it doesn't when it is at 99.99º

HTH

Fernando Cacciola
GeometryFactory

Attachment: pseudo_split_0.poly
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Attachment: pseudo_split_6.poly
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Attachment: pseudo_split_8.poly
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Attachment: pseudo_split_11.poly
Description: Binary data

Attachment: pseudo_split_13.poly
Description: Binary data