Talk:Bounding sphere

"Bouncing Bubble" looks very much like [Wikipedia:SELFPUB] (nor does the animation look like it's O(n)). My apologies if I'm mistaken, but this doesn't feel right to me. I'm writing an expanded section on Welzl's Algorithm since it's a) simple b) a good fit for what I'm doing and c) not self-published. 50.157.249.13 (talk) 21:52, 10 June 2013 (UTC)

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Ritter's algorithm misunderstood

I found the description on Ritter's algorithm here a bit confusing, so I did a little search and found this:

https://www.researchgate.net/publication/242453691_An_Efficient_Bounding_Sphere

It'd seem to me, that the principle has not been understood very well: According to the paper the first run selects three pairs of points that represent the maximum and minimum coordinates in three directions. Obviously some of the points may be the same ones, though that is not pointed out in the paper. Then the pair, that has the greatest distance between them, is selected to form the initial candidate for the sphere. On the second run the sphere is expanded every time, that a point outside the sphere is found. In the process both the radius and the center point get updated in the same step.

Peteihis (talk) 15:30, 1 April 2019 (UTC)

I totally agree, and I could not find a single source describing steps 1 and 2 as they are in this article. I implemented it the way Ritter described it and it works much better. I easily improved it by looking for the extrema along the diagonals, as well as along the axes as described in the original article, and obtained even better results.

Steps 1 and 2 should be replaced by step 1 from Ritter's paper:

Make one (quick) pass through the N points. Find these six points: - The point with minimum x, the point with maximum x, - The point with minimum y, the point with maximum y, - The point with minimum z, the point with maximum z. This gives three pairs of points. Each pair has the maximum span for its dimension. Pick the pair with the maximum point-to-point separation (which could be greater than the maximum dimensional span). Calculate the initial sphere, using this pair of points as a diameter.

And it can be improved by adding these four pairs of points: - The point with minimum x+y+z, the point with maximum x+y+z, - The point with minimum x+y-z, the point with maximum x+y-z, - The point with minimum x-y+z, the point with maximum x-y+z, - The point with minimum x-y-z, the point with maximum x-y-z. Fredyd (talk) 02:25, 15 June 2019 (UTC)