N Equidistant Points on a Sphere

Here is a link to the paper I wrote about it:

[Waffle]

This approximation is also incredibly useful for raytracing, it allows randomly picking points on a hemisphere while still getting even coverage, which is needed to pick directions for light rays.

[defelix]

I am working on a 3D sphere design in CAD that involves equidistant point and had no idea this was an "impossible problem". Now I understand why I was struggling! Thanks for making me feel sane!

[amberjetsalape]

This guy should have been going places... wow I just had a random thought and decided to search.. and here it is

[pabloandresfocke]

This is amazing! It's so beautiful when maths and informatics come together.

[grahamnelson]

I needed a list system to store game tile information in a game which you can traverse a globe. I've been racking my brain in this problem for some time. This should work. Thank you!

[Swayzee]

That's awesome! Do you have a sphere points website? Crafters could use something like this. I have to put 120 nails into a sphere. It would be great to put that number in somewhere, be able to include the size of my sphere and then print out a template -- maybe shaped like this () -- that has dots on it, so I can cut it out and mark the dots all over my sphere. ;)

[chrisbovington]

Thank you! I don't have anything close to your understanding of math and I do not know programming but this problem has been bothering me for years.

[bchui]

I am more interested in the analytical proof that such algorithm exist. Especially, what kind of polygonal tiles they are for different numbers of n (n=4, the tiles are equilateral triangles, n=6 are squares....) Are there any published papers you can refer to?

[billbenedict]

Point of order: Equidistant is not the same as equally spaced. There is one answer for equidistant - the tetrahedron (4 points). But I like the results of your algorithm, and an approximation for equally spaced points is what I was looking for.

[Vreejack]

I was just starting to tackle this problem. The spiral idea was the first straightforward idea that occurred to me, so thanks for doing this work. I think I'm going to need something scalable and recursive, though. Would all the points from one set match points from one with a higher density?

[smudgybrown]

This is so cool Jonathan, well done.
I'm using UE4 to display country flags (199 off) around a sphere, not quite there yet, but determined to crack it.
Unfortunately my maths is a bit lacking now, lol.
All the best.

[CreationTribe]

Wow - beautiful man. Very interesting approach. How do you only have 96 up-votes?

[sylowlover]

I'd be interested to see how constructing normalized root systems from 3-node dynkin diagrams would work in terms of efficiency. 2-node dynkin diagrams already produce evenly spaced points on a circle and the 3-node ones seem to be very evenly spaced when choosing certain orders for m(a, b).

[wirsing]

this is beautiful and cool at the same time.

[e]

I wonder why prior research on the problem been so extensive at LLNL, and Sandia?

[uguugames]

Cool this is pretty nice. I made an implementation of this in c# for unity, so i can have reasonably spaced spawners around a planet. Works rather nice for larger numbers. Low numbers (like 10-20 ish) have some visible clumping, but that's fine.

[tothm]

Given a radius and a number of points, is there a function that would calculate the average distance.

[iffanhannanu]

I am currently thinking about this problem but for equi-distributed points on an n-sphere.

[devendraverma]

Hey It is very interesting could you helm me. How can we draw c60 like structure which have some pentagon and hexagonal grid of particles

[JmanNo]

Hello Jonathan could you create touching circles around each point n 5 to 21?
And do a series of fair dices by lathe down the sphere poles to flat circle areas?
for 5-21 maybe?