Talk:Pitteway triangulation

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This article definitely doesn't say enough yet. Specifically what is the difference between a Delaunay triangulation and a Pitteway triangulation? Michael Hardy 01:42, 17 July 2007 (UTC)

An edge in PT exists if and only if it crosses the associated Voronoi hyperplane (edge).

OK, here's a guess: it means the edge crosses the boundary between two Voronoi cells, as opposed to crossing the hyperplane spanned by the boundary (e.g., in the plane, the boundary is a line segment, not the whole unbounded line; if the Delaunay edge crosses that segment, as opposed to crossing the line at some point not within the segment, the that edge is also a Pitteway edge, but otherwise it's not). But that's just a guess. The article shouldn't leave us guessing. Michael Hardy 01:46, 17 July 2007 (UTC)

I agree. I see that it has already been corrected by you. ash 02:35, 18 July 2007 (UTC)

Actually I'm not the one who corrected it. Michael Hardy 03:17, 18 July 2007 (UTC)

[edit] Relation to Gabriel graph?

I haven't seen the name "Pitteway triangulation" before, and Google scholar shows no hits for that phrase. But if I read the article correctly it is describing the subgraph of the Delaunay edges that cross their corresponding Voronoi edges. That graph is more commonly known as the Gabriel graph. If this article really is describing what I think it describes, it should be merged. If not, it should be written more clearly so that one can tell how it differs. —David Eppstein 02:55, 17 July 2007 (UTC)

From some further web searching, it appears that a "Pitteway triangulation" is what you get when the Delaunay triangulation and Gabriel graph coincide. Still searching for acceptable references. —David Eppstein 17:33, 17 July 2007 (UTC)

The current description of PT on the page looks fine to me. ash 03:14, 18 July 2007 (UTC)