Talk:Fortune's algorithm

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In https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering, MathML is wrapped unconditionally. --- Cedar101 (talk) 01:35, 26 November 2015 (UTC)Reply

There seem to be several incongruities, or at best missing definitions, in the presented pseudo-code:

1. z appears to denote a point and *(z) an operation on a point yet * is later applied to regions.
2. It is unclear what a "boundary ray" between two sites (points?) is to mean.
3. In the common case one would assume there is exactly one site with minimal y-coordinate, but then there can be no "initial vertical boundary rays".
4. S is not defined...

I will stop there. It also looks like the pseud-code aims to describe a "rotated" version of the animated demo, further adding to the confusion.

More complaints:

1. The operation S - p1 is not defined
2. V is not defined in the reference to *(V)
3. It's just plain gibberish. One would have to understand the algorithm to be able to understand this filth.

104.179.121.40 (talk) 09:19, 22 February 2022 (UTC)Reply

I started reading the original paper by Fortune and the transformation *(z) = (Zx, Zy+d(z)) (where d(x) is the distance from point x to the nearest site) produces regions that are hyperbolas, NOT parabolas. The animated gif at front shows parabolic boundaries BEHIND the sliding line, but the actual paper describes hyperbolic boundaries that extend in FRONT of the sliding line. The animated gif conveys none of this. The original paper doesn't mention the word "beach" anywhere. What algorithm is this article even describing???? The pseudo-code is similiar but much of the original version is left out. 104.179.121.40 (talk) 22:17, 22 February 2022 (UTC)Reply

The algorithm and the terminology are what is described as Fortune's algorithm in Computational Geometry (3rd ed., de Berg, Cheong, van Kreveld, and Overmars, Springer 2008, Section 7.2, pp. 151–159). On page 168 they write: "The plane sweep algorithm that we described is due to Fortune [183]. Fortune’s original description of the algorithm is a little different from ours, which follows the interpretation of the algorithm given by Guibas and Stolfi [203]." Reference [183] is Fortune Algorithmica 1987; reference [203] is Guibas and Stolfi, "Ruler, compass and computer: The design and analysis of geometric algorithms", Theoretical Foundations of Computer Graphics and CAD, 1988. —David Eppstein (talk) 22:49, 22 February 2022 (UTC)Reply