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

visualrambling.space

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

#73

When I first opened it, its basically a bunch of static pages that made absolutely no sense. My first question was 'why is this garbage being #1 on HN?' Then I realized that, unlike the early web with banners of "best viewed in Netscape navigator", this was an unstated "best viewed in google chrome". Alas. At least please check and validate if the site works in Firefox, or notify appropriately. Because this demonstra…

For me, it doesn't work entirely in Librewolf 142 (shows the text, and some tags moving around an otherwise black screen), but does work in Firefox Nightly.

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

#74
post #16

Okay, I have some followup questions. Are the points equally spaced? I.e. the cube's |∆p| is constant? I see you scale z by the sin. What happens of you don't?

Without scaling the rate of change of the given curve would not be constant.

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

#76
post #60

I can't tell why, but I'm getting terrible performance on Linux/Brave. The CPU spikes immediately on visit. I'm on a powerful machine (32 GiB RAM, Intel i9 w/ 24 cores).

> I can't tell why Let's find out where this sentence goes! > Linux Would look into that. > Brave. Definitely would look into that. > 32 GiB RAM, Intel i9 w/ 24 cores This part is not relevant

How is that not relevant?

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

#77
post #60

Earlier quoted context omitted.

> I can't tell why Let's find out where this sentence goes! > Linux Would look into that. > Brave. Definitely would look into that. > 32 GiB RAM, Intel i9 w/ 24 cores This part is not relevant

How is that not relevant?

Because any non-broken combination of browser and software platform can run this on any PC made this century. It runs fine on my terrible Atom Chromebook, even.

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

#79
post #24

Awesome visualizations. The part that I was expecting to see but didn't: how can you move at a constant speed? For the original purpose of positioning objects along a path, it doesn't matter. But when moving, you can see it's moving much more slowly at the beginning and end (mostly determined by the radius). What if I want it to travel at a constant rate? Or even apply an easing function to the speed? I'm sure there'…

>I'm sure there's some fancy mathematical trick that would just do it. If I were only more comfortable with math... my handwavy sketch would be to compute the speed function by differentiating the formulas to get dx, dy, and dz and passing them through the Pythagorean equation, then reparameterize on a t' variable using the inverse of the speed function? Maybe? I feel like I'm speaking using words I don't understand.

What you're looking for is called arc length parameterization. Basically, you need to compose the curve with the inverse of its arc length function. Aside from a few special curve families, closed-form solutions don't exist.

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

#80

I was wondering about the “correctness” of the z-axis movement for the spherical helix. You could pick lots of different functions, including simple linear motion (z = c * t). This would obviously affect the thickness and consistency of the “peels”. The equation used creates a visually appealing result but I’m wondering what a good goal would be in terms of consistency in the distance between the spirals, or evenness…

Just a thought: Make the velocity of the path constant. There should be some way to take a derivative an set it to a constant and solve for z. ( or really reparameterize the curve t' = f(t)) so the velocity is constant.

Actually, now that I think about it, choosing z = c * t is kind of both influencing how the path is parameterized as well as the path carved out on the sphere.

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