I came across this same problem when designing my IEC fusor.
@Ruktiet
2 ай бұрын
This is utter bullshit. 1: you dó use calculus. You use goniometric functions. I don’t think you even know what calculus means. 2: you just experimentally derived data to find a more optimal, but nowhere near global optimal solution, for the cases you chose. 3: the handshake problem has nothing to do with this and is a counting problem in the field of graph theory. 4: you sell this as if you are the first person who found this way to space points on a sphere (“my algorithm”). It shows terrible grandiosity syndrome. I hope you improved yourself in the past 7 years. You’re the reason why pattents exist, you thief.
@HappyMathDad
3 ай бұрын
Google must have started using a new method for efficiently spacing points on a sphere, for video recommendations.
@thelocalsage
3 ай бұрын
How does this fair for numerical analysis like approximating surface integrals of spherical functions? currently lebedev quadrature is the norm in non-periodic quantum computational chemistry but those are preset numbers of points. my favorite exchange correlation functionals are sensitive to the integration grid so it’d be cool to find out in very applications what the coarsest grid you can get away with is.
@TashiRogo
3 ай бұрын
Ah, the confident infallibility of youth.
@rainytreecat3992
3 ай бұрын
Use it to unfold it into a generally polygonal or circular map that isn't stretched or squished
@TheAlison1456
3 ай бұрын
1:48 J J Thomson discovered the electron? The first time I ever hear of him is right here in a maths video totally unrelated to that.
@alexwang982
3 ай бұрын
this solves my chem problems
@thederpydude2088
3 ай бұрын
Does this algorithm not find a better way to space 5 points?
@DavidZMediaisAwesome
3 ай бұрын
here’s my solution: put them all on the same point. they will all be 0 units apart and will therefore be the same distance apart.
@theevilcottonball
3 ай бұрын
Genius! My sphere has radius 0, so any configuration will do.
@dizzypear
3 ай бұрын
The engineer's solution
@HyperDevv
3 ай бұрын
"computationally efficient" also shows the laggiest simulation ive ever seen (no hate, i love the math and video)
@locallyringedspace3190
3 ай бұрын
As a proud user of SpherePoints[n_] (I have implemented this same function in 3 other programming languages since joining industry). I salute you, sir. As a fellow computational explorer, I salute you. Excellent work!!
@CNLohr
3 ай бұрын
A major benefit of this would be for compressing uniform vectors, i.e. one could dedicate "10 bits" worth of data, and out of that 10 bits, it could get an 3-vector, approximated to the closest vector. I have needed this before and compromised. Now, the real question is can you generalize this to ℝ4, then you could compress quaternions quickly/efficiently.
@VeteranVandal
3 ай бұрын
#blessed_by_the_algorithm
@MetaBuddha
3 ай бұрын
tbh.. Solid Work, man 🎉
@ONRIPRESENCE
3 ай бұрын
4:24 kinda reminds me of a Mandelbulb fractal hehe
@patty4449
3 ай бұрын
Not very accurate, think simpler and outside of the plane... The optimum placement is simple if you split the concept to a dot with rays and the direct orientation sequence to pi... Takes way less calculation and works on non spherical objects as well
@kenjohnson6101
3 ай бұрын
Can this be generalized to N dimensions?
@kenjohnson6101
3 ай бұрын
Here's the paper: scholar.rose-hulman.edu/cgi/viewcontent.cgi?article=1387&context=rhumj
@tuskiomisham
3 ай бұрын
you seem to be confusing two concepts. One is equally spacing points on the sphere, and two is maximizing the average distance between points on a sphere. technically speaking 5 points on a sphere can be equally spaced. it's not hard just draw Pentagon on the sphere. likewise maximizing the average distance between points on a sphere isn't hard either. there are many algorithms to do this. I can see why mixing the two concepts will make this difficult to do though
@menjolno
4 ай бұрын
youtube didn;''t just recommend me once, it was three times already
@Miguel_Noether
4 ай бұрын
Where is this guy now? 🤔
@asheep7797
3 ай бұрын
Seemingly still alive.
@JJ-fr2ki
4 ай бұрын
Anyone figure out how to solve the problem for an N-dimensional sphere?
@honkhonk8009
4 ай бұрын
yo why am I getting recommended this lmfao I fucking hate discrete math type shit.
@KennethHartsell
4 ай бұрын
Interesting math? Yes. Actually applicable to the real world? probably not. For the use case of where to put satellites in orbit. The heuristic doesn't consider weights of satellites near the poles being useless because nobody lives there. Also several hours of computer time to find an iterative optimal solution is much cheaper than a single rocket launch. Again, cool math but not a problem that needed solving.
@phoenixamaranth
3 ай бұрын
We have satellites that orbit over the poles already and line of site to a satellite doesn't mean you live directly under it. And it's pretty presumptuous to assume it wasn't a problem that needed solving. History is full of examples where edge case mathematics has turned out to have practical real world applications or advantages found years and decades later. His method is to improve calculation efficiency vs other known methods of solving the same problem. Embedded systems and near real-time applications always benefit from faster algorithms.
@punpcklbw
4 ай бұрын
Thanks for the research. The uniform placement of points on a sphere was used in quantizing normal vectors used by lighting in computer games. Quake 2 engine has 162 predefined vectors for encoding the normal of a vertex with a single byte (rather than 12 bytes that the brute-force way would take). They are placed in a pattern that resembles a subdivided octahedron. The method on the video could be used to generate any number of equally spaced vectors with ease.
@user-lm9pu3sq9d
4 ай бұрын
very cool, great job.
4 ай бұрын
Excelent !!
@imsatoboi
4 ай бұрын
Some people in the comments seem to think that ‘math’ is invented and people hold some sort of copyright over it. Guys , i get that someone might’ve figured it out before others , and thats an astonishing feat , but people who figure the same thing out themselves are not in anway inferior. I failed at maths fr. So i can be completely wrong. But lets just take a breath and enjoy the beauty in the process and how us humans are soo freakin cool. Peace.
@phoenixamaranth
3 ай бұрын
And most of them are ignorant of the point of his video and paper: that his method solves the problem in a faster way. He didn't claim to be the first to solve the problem. His point was he came up with a fast algorithm to solve the problem
@jonatan01i
4 ай бұрын
"it's impossible to place n points on a sphere" So that's why electrons have trouble deciding who goes where around the nuclei
@Ruktiet
2 ай бұрын
Lol no. You’re confusing classical models for atoms with quantum mechanical ones.
@juha-petrityrkko3771
4 ай бұрын
How does the even distribution help with the satellites, as they are constantly moving? We would need to prove that they stay at least near this optimal distribution.
@honkhonk8009
4 ай бұрын
idk he just saying shit ig lmfao
@phoenixamaranth
3 ай бұрын
Even when orbiting the satellites need spacing for optimal line of sight and distribution. We setup satellite networks now that are all about being spaced over optimal distances from each other
@anastasiaklyuch2746
4 ай бұрын
Not applicable with sattelites, since you don't need them over the whole poles or the whole ocean. It really depends on what is actually needed, but other uses are cool
@phoenixamaranth
3 ай бұрын
Why does everyone keep missing that he was talking about the mirror spacing on the satellite not the spacing of satellites?
@anastasiaklyuch2746
3 ай бұрын
@@phoenixamaranth I wasn't talking about the student satelite, but the optimal satellite placement at 4:50 plz watch more carefully before making such comments about everyone.
@phoenixamaranth
3 ай бұрын
@@anastasiaklyuch2746 Fair enough, my bad. I will point out we do run satellites over poles, oceans, etc. We run vertical satellites that orbit from pole to pole
@anastasiaklyuch2746
3 ай бұрын
@@phoenixamaranth Yeah, that does makes sence :) This also adds complexity of sattelite motion to how they are positioned, big stuff.
@anastasiaklyuch2746
4 ай бұрын
3 point is just as problematic as 5, since they don't divide the sphere in all dimentions. 2 create hemispheres, so that's fine, but 3 are bad.
@AdrianBoyko
3 ай бұрын
1 point is maximally asymmetric
@dragonsagesummoner6071
4 ай бұрын
What language is that? It’s not Java or c#. It is python?
@hgilbert
4 ай бұрын
First I thought it was Prolog. But just checked Wolfram's site. Looks like it's Mathematica. During Lockdown I was trying to teach myself but gave up. 1 month free trial was over.
@ngc-fo5te
4 ай бұрын
It's Mathematica
@hodgeyhodge8414
4 ай бұрын
Idea: simulate some little magnets repelling each-other on the surface, and let them come into equilibrium. I'd code this myself but I have a skill issue. It obviously wouldn't be compuationally efficient, lol
@nicholasfinch4087
4 ай бұрын
when analog methods probably would be faster than a computer doing it. 😂
@skycrafter1509
4 ай бұрын
why did the youtube-algorithm randomly decide to show a bunch of people a 7 year old video
@xanderlastname3281
4 ай бұрын
KZitem does that some times
@themammoth67
4 ай бұрын
Ye
@MelindaGreen
4 ай бұрын
Because it doesn't treat viewers as points on a sphere
@CLOUDEE33
4 ай бұрын
Wait fax
@CLOUDEE33
4 ай бұрын
Why 7 year old vid
@xaf15001
4 ай бұрын
God 2017 is 7 years ago. Fuck
@rider2fois
4 ай бұрын
Nice cooking lecture
@joshuawhitworth6456
4 ай бұрын
I figured out the math to Holographic Waves.... Perhaps you might find it useful... Math to Holographic Wave Lengths 1÷(1÷Y×Z+Y)=A,B,C,...÷(A+B+C+...)=1 These are the rules.... Solve for every whole number less than Y. Then add them together Y = any whole number Z = any whole number less than Y including zero. A,B, and C are the various numbers you end up with for each whole number less than Y. Here's an example. Keep in mind I cut the numbers short do to them being infinitely long.... 1÷(1÷3×0+3)= 0.33333 1÷(1÷3×1+3)= 0.30000 1÷(1÷3×2+3)= 0.27272 0.33333+0.30000+0.27272=0.90606 0.33333÷0.90606=0.36789 0.30000÷0.90606=0.33110 0.27272÷0.90606=0.30100 When you add them together they should equal one... 0.36789+0.33110+0.30100= 1
@joshuawhitworth6456
4 ай бұрын
This is awesome! Cudos.
@user-vp9xy8fk6u
4 ай бұрын
3:23 You simply selected the number 0.1 + 1.2n for this area. Perhaps it would be better to use the Euler function? The unevenness in your method depends precisely on the divisibility en.m.wikipedia.org/wiki/Euler%27s_totient_function I did the cool job❤
@profdc9501
4 ай бұрын
Here's another method based on Geodesic Packings: Design of a spherical focal surface using close-packed relay optics Hui S. Son, Daniel L. Marks, Joonku Hahn, Jungsang Kim, and David J. Brady
@Troloze
4 ай бұрын
3:14 isn't it possible to determine a function that gets the most efficient function for each number of points? Or at least for intervals? seems like a better idea than to use a single function for all values.
@lukepowers8122
4 ай бұрын
thats what a neural network does
@lucaballarati9694
4 ай бұрын
I Will be borrowing this for gamedev
@christianherrera4729
4 ай бұрын
Babe babe!! Wake up!!! New computationally efficient method for equally spaced points on a sphere just dropped!!
@nicholasfinch4087
4 ай бұрын
Babe! We've been asleep for 7 years!
@xane256
3 ай бұрын
Babe: “Honey, he doesn’t even show the distribution of point-point distances”
@danielmilyutin9914
4 ай бұрын
I did this with solving physics-like optimization problem. Where points repell each other. And I added viscosity to stop their movement. It was quite ago.
@Fluoman_
4 ай бұрын
I think I used your code!
@danielmilyutin9914
4 ай бұрын
@@Fluoman_ impossible. I didn't publish it. It was a little hobby in scilab lang.
@Fluoman_
4 ай бұрын
@@danielmilyutin9914 damn. Well, somebody had the same idea then.
@danielmilyutin9914
4 ай бұрын
@@Fluoman_ Yep. It was quite on surface.
@Kyoz
4 ай бұрын
🤍
@nartoomeon9378
4 ай бұрын
I recall, a spiral you used, seems like a method to get perfect flat 2-dimensional net of a 2-sphere. I forget the name, but it is a spiral stripe between poles with infinite small width. Maybe, it has various width in different places, but if they infinitesimal, that not so important.
@nartoomeon9378
4 ай бұрын
@@mariokapalka7364 Euler curve yes?
@jowillll
4 ай бұрын
2017 is 7 years ago? 😦
@phoenixamaranth
3 ай бұрын
Right? Doesn't that feel crazy?
@phpn99
4 ай бұрын
Have you ever heard of quaternions ?
@TearonQ
4 ай бұрын
comment made 1 day ago video made 7 years ago hmm
@automatescellulaires8543
4 ай бұрын
@@TearonQ Hi there. I guess youtube algorithm decided we should watch this now. I wish i could have seen it 7 years ago.
@TearonQ
4 ай бұрын
@@automatescellulaires8543 lol
@tuskiomisham
3 ай бұрын
@@TearonQ dude just gave a 1 day old comment a heart. he's chillin.
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