Hello, Hippo.69, and
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We hope you enjoy editing here and being a Wikipedian! By the way, you can sign your name on talk and vote pages using four tildes, like this: ~~~~. If you have any questions, see the help pages, add a question to the village pump or ask me on my talk page. Again, welcome! -- TRPoD aka The Red Pen of Doom 23:07, 8 December 2012 (UTC)
Hi Hippo.69, thanks for your extensive discussion on the Talk page of the Smallest-circle_problem problem, and your extra explanation on your User page here.
I am bit puzzled though, as to where/what actually would be a reliable pseudo- (or python) implementation of Welzl's algorithm, as I'm needing it for some research I'm doing. The pseudo-code on Wikipedia still looks wrong to me. When you stated that: "The Welzl's algorithm does not work in the form it is stated in the article and here. It was corrected by Matousek, Sharir, Welzl" - is that still the case, is that just due to the misunderstanding at the time of "trivial(R)" in the \card(R) = 3 case?
The specific counter-example to Welzl I believe I have, is suppose points A = (0, 3.9), B = (-1, 0), C = (1, 0) and D = (0, -0.9). Let's suppose that the excluded point was A, and so we have already processed {B, C, D} and the circle is centred at (0,0) and has radius 1, so B, C are on the boundary (and in R), D is an interior point to that circle, and A is outside it, to the above. Then we need to add A, but since {B, C} is our current R, we end up with at best some subset of {A, B, C}. But the bounding circle for the whole set is the circle of radius 2, centred at (0, 1.9), with A and D on the boundary, and B, C in the interior.
Thanks if you can provide any assistance to my understanding of it. Mozzy66 ( talk) 04:50, 2 January 2024 (UTC)
Hello, Hippo.69, and
welcome to Wikipedia. Thank you for
your contributions. I hope you like the place and decide to stay. If you are stuck, and looking for help, please come to the
New contributors' help page, where experienced Wikipedians can answer any queries you have! Or, you can just type {{helpme}}
and your question on this page, and someone will show up shortly to answer. Here are a few good links for newcomers:
We hope you enjoy editing here and being a Wikipedian! By the way, you can sign your name on talk and vote pages using four tildes, like this: ~~~~. If you have any questions, see the help pages, add a question to the village pump or ask me on my talk page. Again, welcome! -- TRPoD aka The Red Pen of Doom 23:07, 8 December 2012 (UTC)
Hi Hippo.69, thanks for your extensive discussion on the Talk page of the Smallest-circle_problem problem, and your extra explanation on your User page here.
I am bit puzzled though, as to where/what actually would be a reliable pseudo- (or python) implementation of Welzl's algorithm, as I'm needing it for some research I'm doing. The pseudo-code on Wikipedia still looks wrong to me. When you stated that: "The Welzl's algorithm does not work in the form it is stated in the article and here. It was corrected by Matousek, Sharir, Welzl" - is that still the case, is that just due to the misunderstanding at the time of "trivial(R)" in the \card(R) = 3 case?
The specific counter-example to Welzl I believe I have, is suppose points A = (0, 3.9), B = (-1, 0), C = (1, 0) and D = (0, -0.9). Let's suppose that the excluded point was A, and so we have already processed {B, C, D} and the circle is centred at (0,0) and has radius 1, so B, C are on the boundary (and in R), D is an interior point to that circle, and A is outside it, to the above. Then we need to add A, but since {B, C} is our current R, we end up with at best some subset of {A, B, C}. But the bounding circle for the whole set is the circle of radius 2, centred at (0, 1.9), with A and D on the boundary, and B, C in the interior.
Thanks if you can provide any assistance to my understanding of it. Mozzy66 ( talk) 04:50, 2 January 2024 (UTC)