[Algorithms] Virtual vertices in Butterfly scheme

[Pierre T. <p.t...@wa...>]

Hi,

Here I go again with a question about the virtual vertices in the modified
Butterfly scheme. Here's an excerpt from Sig'96 paper:

"Edges which are not on the boundary but which have a vertex which is on the
boundary are subdivided as before while any vertices in the stencil which
would be on the other side of the boundary are replaced with "virtual"
vertices."

Let's examine two cases. In all of them we are in the situation described
above.

1) The boundary vertex has a valence of 4:

How many virtual vertices am I supposed to create? Until now, I've alwayd
blindly created enough virtual vertices to transform the vertex into a
regular one (valence = 6), but this is not explicitely written in Zorin's
paper.

What if I just use the extraordinary scheme for valence = 4, without
creating virtual vertices?

2) The boundary vertex has a valence of more than 6, say 7:

Here's the case I'm having a lot of trouble with. Actually that's why I'm
suddenly writing this message. I recently found that one is a particular
mesh, and my code crashed. Because, of course, I tried to create enough
virtual vertices to reach valence 6, ie "-1" vertex. Err... What ?!

Here, the only correct behaviour looks like using the standard extraordinary
scheme for valence = 7, without creating virtual vertices. But if this is
the case, why shouldn't I just do the same in 1)....? And if this is not the
correct behaviour, what is it? Am I supposed to create virtual vertices in
that case? How many and how ?


Puzzled again.


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