I came across this same problem when designing my IEC fusor.

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.

Google must have started using a new method for efficiently spacing points on a sphere, for video recommendations.

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.

Ah, the confident infallibility of youth.

Use it to unfold it into a generally polygonal or circular map that isn't stretched or squished

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.

this solves my chem problems

Does this algorithm not find a better way to space 5 points?

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.

"computationally efficient" also shows the laggiest simulation ive ever seen (no hate, i love the math and video)

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!!

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.

#blessed_by_the_algorithm

tbh.. Solid Work, man 🎉

4:24 kinda reminds me of a Mandelbulb fractal hehe

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

Can this be generalized to N dimensions?

Here's the paper: scholar.rose-hulman.edu/cgi/viewcontent.cgi?article=1387&context=rhumj

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

youtube didn;''t just recommend me once, it was three times already

Where is this guy now? 🤔

Anyone figure out how to solve the problem for an N-dimensional sphere?

yo why am I getting recommended this lmfao I fucking hate discrete math type shit.

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.

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.

very cool, great job.

Excelent !!

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.

"it's impossible to place n points on a sphere" So that's why electrons have trouble deciding who goes where around the nuclei

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.

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

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.

What language is that? It’s not Java or c#. It is python?

why did the youtube-algorithm randomly decide to show a bunch of people a 7 year old video

God 2017 is 7 years ago. Fuck

Nice cooking lecture

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

This is awesome! Cudos.

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❤

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

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.

I Will be borrowing this for gamedev

Babe babe!! Wake up!!! New computationally efficient method for equally spaced points on a sphere just dropped!!

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.

🤍

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.

2017 is 7 years ago? 😦

Have you ever heard of quaternions ?

you can't comb a furry ball without curls