Show HN: The prime knots in 3D | Hacker News Reader

Show HN: The prime knots in 3D

github.prideout.net

45 pointsprideout17 comments

I was inspired to make this after reading "The Knot Book" by Colin Adams. If you click "Rolfsen Table" at the bottom, you'll see the entire gallery.

Mesmerizing...really well done. Thanks for sharing, and for the book recommendation!

This is cool, but what's the point of using the bounce easing? It just makes you wait an extra second before you can get a good look at the new model.

You're right, I sorta overdid it with the easing animation.

I agree you overdid it. Also on the table view, the highlighted row spins too fast.

But other than those minor quibbles, it's neat!

Really, that's the only complaint I could make, it's quite lovely!

This is beautiful and really well done. I especially like how the light reflects naturally as the knot rotates. How did you achieve that effect?

Thanks! The fragment shader performs simple lighting with one stationary point light that has ambient, specular, and diffuse components. There are actually no true reflections, although that would be fun thing to work on.

The bounce is too hard. Also, what do the numbers mean?

Agreed! The numbers are the Alexander-Briggs identifiers for the prime knots:

- The big number is the number of crossings.

- The subscript is its officially designated index within the set of knots that have the same number of crossings.

- If there's a superscript, then it's a link, and the superscript represents the number of components.

Ah, cool. I was thinking that maybe 4sub1 should be a '3'.

Any chance of being able to rotate the model using a mouse/touch?

For example, 8²₃ means...

- The crossing number of given knot(s) is 8. In the other words, when you put the knot(s) to the flat floor, there are 8 crossings.

- There are 2 independent knots there. They are colored differently so you can easily see this. The collection of knots is also called a link.

- The subscript is numbered in the predefined arbitrary order starting with 1. There are many different knot notations, but this particular one is called Alexander-Briggs notation.

Where's the unknot?

Yes, it's sacrilege, but I omitted the trivial knot from the main table! You can get to it in a roundabout way, by clicking any other knot in the top row (e.g., the trefoil).

What about the empty link?

Very nice work.

They are pretty

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