Surprised to not see Acko.net mentioned in comments already - he uses similar aids in one of his blog posts to break down complex numbers and ultimately fractals.
Likely right up your street!
Show HN: I was curious about spherical helix, ended up making this visualization
111–120 of 140 posts
Re: Show HN: I was curious about spherical helix, ended up making this visualization
#112These 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…
Except the helix curve shown in OP is NOT a loxodrome or rhumb line.
It has equal spacing on the surface between lines, a loxodrome can't have that property since by definition it must cross the meridians at the same angle at all times. That means it always gets denser near the poles.
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Start with the curve:
x = 10 · cos(π·t/2) · sin(0.02·π·t)
y = 10 · sin(π·t/2) · sin(0.02·π·t)
z = 10 · cos(0.02·π·t)
Convert to spherical coordinates (radius R=10):
λ(t) = π/2 · t (longitude)
φ(t) = π/2 - 0.02·π·t (latitude)
Compute derivative d(λ)/d(φ):
d(λ)/dt = π/2
d(φ)/dt = -0.02·π
d(λ)/d(φ) = (π/2)/(-0.02·π) = -25 (constant)
A true rhumb line must satisfy:
d(λ)/d(φ) = tan(α) · sec(φ)
which depends on latitude φ.
Since φ(t) changes, sec(φ) changes, so no fixed α can satisfy this.
Conclusion: the curve is not a rhumb line.
this is how one should look for varying intersection angles:
Re: Show HN: I was curious about spherical helix, ended up making this visualization
#113> If you like this, please consider following me on Twitter and sharing this with your friends. I do like this and will share with a couple of friends. But I no longer have a Twitter account and will definitely not rejoin. Would you consider adding an RSS or JSON feed to your website? Or make a Mastodon account, those provide RSS feeds by default.
Man, that whole ‘please make an RSS or JSON feed for me’ request reads like Richard Stallman emailing himself a webpage to print out later, let them use Twitter or whatever medium they wants
That’s a pretty bad faith interpretation. As if a polite suggestion to add a low-effort, universal, unrestricted, and easily automatable alternative would in any way affect what they currently use. The author is asking people to follow them, it benefits them. Letting them know the ways in which people want to do it is a good thing, and it takes a special kind of curmudgeon considerably more obnoxious than Stallman to invent some fault with that.
Re: Show HN: I was curious about spherical helix, ended up making this visualization
#114I believe there is a typo here: y = 10 * sin(πt/2) * sin(0.02 * πt) On the previous two slides the end is sin(0.2 * πt)
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Re: Show HN: I was curious about spherical helix, ended up making this visualization
#115thanks for sharing, really interesting
Re: Show HN: I was curious about spherical helix, ended up making this visualization
#116Really nice visualisation. Does anyone know of any tooling I could use to do some plotting like this in 3D space even a fraction as nice looking as OPs? I'm not a web dev but I am a dev, but would prefer something high enough level that I can focus on the "what" (to plot) rather than the "how".
In the olden 8-bit days, we would have to do this in BASIC or assembler with a 3D library that we would have to write ourselves. Then we would run out of memory. Later on - about a quarter of a century ago - we had VRML which enables anyone to just focus on the what rather than the how. But VRML always needed a plugin to download, which was no fun at all in the dial-up days. We almost had a 3D web, but no, it ended u…
> In the olden 8-bit days
I hear you.
My first real experience with drawing anything was with Postscript, but then I did my fair share of blitting, and a bit of OpenGL. These days I'm just looking to visualise some data in a nice looking way with minimal effort.
> if you want 3D plots without having to reinvent the wheel, three.js is fit for purpose, with the right CodePen example
Amazing, thanks for the tips.
Re: Show HN: I was curious about spherical helix, ended up making this visualization
#117These 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…
To quote the storytelling quality of Erdos's abstract:
"The simple requirement that one should move on the surface of a sphere with constant speed while maintaining a constant angular velocity with respect to a fixed diameter, leads to a path whose cylindrical coordinates turn out to be given by the Jacobian elliptic functions."
Re: Show HN: I was curious about spherical helix, ended up making this visualization
#118It seems like it might be cool but between the background animation and the resource intensiveness I'm having trouble actually reading it. Is there a mostly-text version somewhere?
Re: Show HN: I was curious about spherical helix, ended up making this visualization
#119This is super nice to view, could you share how you made it? I want to make something similar for Rotation Matrices
AnimeJS, and possibly Three.js
Re: Show HN: I was curious about spherical helix, ended up making this visualization
#120Neat! I was curious as well after reading it and here's a quick parametric visualizer to play with what was described in the text (thanks, Claude!): https://codepen.io/CaptainKeyframe/pen/zxvWVNo