Show HN: I was curious about spherical helix, ended up making this visualization
7 comments
·August 20, 2025srean
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
On a meta note, today seems spherical geometry day on HN.
https://news.ycombinator.com/item?id=44956297
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)
mostlyk
This is super nice to view, could you share how you made it? I want to make something similar for Rotation Matrices
1970-01-01
That is beautiful animation. This is a great example of a visual lesson that leaves a chalkboard in the dust (ha).
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/...
maxbaines
Best thing I have seen on HN in ages. Also interesting for a CNC geek.
fleebee
I love this. It's pretty and really easy to digest.
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!