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Show HN: I was curious about spherical helix, ended up making this visualization

visualrambling.space

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Show HN: I was curious about spherical helix, ended up making this visualization

#1

Post by damarberlari »

I was wondering how I can arrange objects along a spherical helix path, and read some articles on it.

I ended up learning about parametric equations again, and make this visualization to document what I learned:

https://visualrambling.space/moving-objects-in-3d/

feel free to visit and let me know what you think!

Show HN: I was curious about spherical helix, ended up making this visualization
visualrambling.space

Re: Show HN: I was curious about spherical helix, ended up making this visualization

#2

Post by RugnirViking »

It's a pretty basic primer to the subject, but good for kids learning maths. Could do with some callbacks to maths concepts like the circle equation ( x = r cos (t) and y = r sin (t) ).

Possible topics to branch further into would be polar coordinates and linear algebra basics (vectors, transformations, transformations in 3d space). If you the author aren't sure of such topics, I would recommend 3blue1brown yt videos on the matter

Possibly better for that than for programmers (given it doesn't include code or libraries used or anything about actually manipulating 3d objects like vertices, stretching and morphing to achieve the effect shown etc)

Re: Show HN: I was curious about spherical helix, ended up making this visualization

#3

Post by srean »

These used to be super important in early oceanic navigation. It is easier to maintain a constant bearing throughout the voyage. So that's the plan sailors would try to stick close to. These led to let loxodromic curves or rhumb lines.

https://en.m.wikipedia.org/wiki/Rhumb_line

Mercator maps made it easier to compute what that bearing ought to be.

https://en.m.wikipedia.org/wiki/Mercator_projection

This configuration is a mathematical gift that keeps giving. Look at it side on in a polar projection you get a logarithmic spiral. Look at it side on you get a wave packet. It's mathematics is so interesting that Erdos had to have a go at it [0]

On a meta note, today seems spherical geometry day on HN.

https://news.ycombinator.com/item?id=44956297

https://news.ycombinator.com/item?id=44939456

https://news.ycombinator.com/item?id=44938622

[0] Spiraling the Earth with C. G. J. Jacobi. Paul Erdös

https://pubs.aip.org/aapt/ajp/article-abstract/68/10/888/105...

Re: Show HN: I was curious about spherical helix, ended up making this visualization

#4

Post by Duanemclemore »

This is excellent. I'm always looking for good things to show my students on coordinate systems and geometry, and this joins the list. Thank you for diving down the rabbit hole and bringing this back for everyone.

If you want really great further consideration of creating geometric figures with parametric equations, Joseph Choma's book "Morphing" is an all-timer.

https://www.quercusbooks.co.uk/titles/joseph-choma/morphing/...

Re: Show HN: I was curious about spherical helix, ended up making this visualization

#9

Post by fluoridation »

For me personally it's simpler to think about it as having an f(theta, r) = r (cos(thetha), sin(theta)), interpreting theta as a compass direction and r as a distance to walk along a great circle. So g(t) = polar_to_R3(f(t k, t l)). Changing the relative sizes of k and l changes the tightness of the helix.

Re: Show HN: I was curious about spherical helix, ended up making this visualization

#10

Post by qwertytyyuu »

mostlyk wrote: post #8

This is super nice to view, could you share how you made it? I want to make something similar for Rotation Matrices

I think 3blue1brown might have an animation library, the same one he uses in his videos that might help with that
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