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Subject: Re: Fast determination of the link-condition in a triangular mesh



Hans-Bernhard Broeker wrote:
> Fernando Cacciola wrote:
>
>>Hi people,
>
>
>>In the realm of triangulated surface mesh simplification there is a
>>technique known as edge-collapse which uses a so-called "link-condition".
>>That condition is a necessary (but not sufficient AFAICT) to preserve
>>the topological validity of the mesh after the collapse.
>
>
>>If the edge 'pq' is given by the vertices 'p' and 'q' (the orientation
>>of the edge is unimportant), the link condition is as follows:
>
>
>>link(p) .intersection. link(q) == link(pq)
>
>
>>The link of a vertex is the cycle of edges _around_ the vertex and
>>likewise the link of an edge is the cycle of edges around the edge.
>
>
>>Now, the above is what you can find in any paper on the subject.. but
>>what I can't find is the optimal algorithm to determine the
>>link-condition.
>
>
> Optimality can't be discussed without knowing the implementation
> platform.

Ya OK. Forget about that...
I was actually disguising the real question which is: have I understood
the link condition correctly and the determination procedure is
basically what I've outlined in that pseudo code?

>>Yet, it seems TO ME that this determination is actually
>>quite simple at least in the case where the input mesh is known to be a
>>valid 2-manifold (that is, a triangulation).
>
>
> NB: not all triangulations are 2-manifolds. Not even if the surface
> that was triangulated was a manifold.
>
Yes I know, to simplify my life I was focusing on this ideal case first.

TIA

Fenando Cacciola

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