Talk:Delaunay triangulation

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The Mactutor biographies list Boris Nikolaevich Delone at [1] without saying anything about triangulations, and Georgy Fedoseevich Voronoy without mentioning Voronoi tesselations. Can someone confirm that that Delone is the same person who is mentioned in this article? Also, is this the same Delaunay whose name is inscribed on the Eifel Tower alongside Fourier and Cauchy and 69 others? Michael Hardy 23:09, 14 Dec 2004 (UTC)

Yes (same Delone), yes (same Voronoy), and maybe (Eiffel Tower). According to V.A.Zalgaller, B.N. himself spelled his last name as Delaunay. Back during the times (pre-WWII) when the Soviet abstracts were published in French as opposed to English, this was the official Soviet publications spelling as well. OTOH, the math genealogy lists him as Delone (probably due to Mactutor). I can point you at least one SCREAMING inaccuracy at Mactutor's wrt another person --- Vinogradov. Mactutor re-published the common Soviet lie (originating in Vinogradov-edited math journals) that V. was the director of the Steklov institute until his death, not mentioning the period when Sobolev was the director. This despite the fact that the same Mactutor mentions the directorship on the Sobolev page! Both bios are signed by the same 2 authors. No wonder they're also inconsistent with respect to transliteration spellings (or am I instilling guilt by association here? caveat emptor...) Whatever the origins, I am proud to have removed the corresponding inaccuracy from the WP. BACbKA 23:38, 14 Dec 2004 (UTC)

BND has his name used both as Delaunay for his triangulation work and Delone for work I'm not familiar with that is closer to statistics -- Ken Clarkson has a talk slide with both transliterations appearing on it. I don't think it's a communist conspiracy. Bhudson 19:19, 8 December 2006 (UTC)

No to Eiffel Tower. It was astronomer Charles-Eugène Delaunay. The rest of BACbKA is agreed, even without Zalgaller, see the reference from Soviet math journal in the article. Mikkalai 00:42, 15 Dec 2004 (UTC)

Sorry about my dumb question about the Eiffel Tower. Since he was not born until after the tower was built, obviously it's not the same person. Someone has suggested in an email that the one on the Eiffel Tower may have been an ancestor of this Delaunay. Michael Hardy 03:05, 15 Dec 2004 (UTC)

[edit] What is sweepline?

"A common way to speed up this method is to sort the vertices by the first coordinate, and add them in that order."

Sorting the vertices by the first coordinate produces a sequence of vertices that would result if a line were swept over them. (Yes, you're probably thinking of Lumines by now.) This sorting method has O(n log n) performance, and so does "sweepline", which the article doesn't describe. So does "sweepline" just refer to one of the incremental algorithms? --Damian Yerrick 20:51, 14 August 2005 (UTC)

[edit] Triangularization?

I've never heard the term "Delone triangularization" before this page, and neither has Google (though there are loads of copies of this wikipedia article. Can someone confirm its existence? It was added in http://en.wikipedia.org/w/index.php?title=Delaunay_triangulation&oldid=7628612 Bhudson 19:31, 8 December 2006 (UTC)

[edit] Duality

The notion of duality this article linked to is a bit weird: Duality (projective geometry). Normally the Voronoi and Delaunay are regarded to be graph duals, rather than geometric duals. To become geometric duals you have to go through the intermediary of some kind of lifting map like the parabolic one described later in the article.

The same comment holds true with regards to the Voronoi article. Bhudson 23:07, 8 December 2006 (UTC)