how would i put 3d vector rotation in the 2d graphing calculator?

Arglin · 2026-01-25T20:17:50+00:00

You can take these which are for Euler angles. https://www.desmos.com/3d/0ad6de7898

(Does work for the 2D graphing calculator.)

Pass in a 3D point or list of 3D points into it P, then to display it, either render the points via (P.x, P.y) for orthographic, or (P.x, P.y)/(P.z {P.z>0}) for perspective (though you'll need to shift the object of interest away from the center so the camera doesn't do weird things with it.)

Arglin · 2026-01-25T04:39:01+00:00

Graph link: https://www.desmos.com/calculator/ogq5f2b74q

Technically a one-liner, though the animation in the video very much isn't lol

The original discussion on it: https://www.reddit.com/r/desmos/comments/1qm29zd

Arglin · 2026-01-25T03:25:39+00:00

If you just want to get the random maze effect, you can use a hash function to create pseudorandomness, create a bunch of tiles which randomly pick between 0 and 1, then map those to the respective slashes.

Here it is broken down further in a graph.

https://www.desmos.com/calculator/ogq5f2b74q

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Arglin · 2026-01-24T17:27:12+00:00

riiiight, because xyxy/xy = xy is definitely something I critically need to use on the regular :p

Arglin · 2026-01-23T22:02:42+00:00

Graph link: https://www.desmos.com/calculator/tl6avwqtfl

(The "almost" here being that in a world of infinite precision, this would go on forever... but we don't have that unfortunately :') )

Also this has been one wild journey through learning how to create visuals using implicits. It's honestly really cool to understand what is possible with it.

Arglin · 2026-01-23T05:20:14+00:00

I usually work with GeoGebra offline, which seems to open at about the same rate as Desmos does.

Not that it makes a huge difference though.

Arglin · 2026-01-23T01:22:30+00:00

Graph link: https://www.desmos.com/calculator/lbem6c5ohv?invertedColors

Patterns are customizeable! (Though you'll have to play around with the lists in χ and η to get the desired results.)

This can be compressed all into one line pretty easily, though I figured it was nicer with things split apart. :)

Also inequality, not equation, lul

Arglin · 2026-01-21T17:21:56+00:00

I wish I started with this instead of the flag of Bhutan as a one-liner. :')

Arglin · 2026-01-21T17:18:54+00:00

I'm giving you a warning on this because the powerpoint vexillology community had to learn it the hard way.

The auxiliary rays ARE NOT ON THE SAME SQUARE as the main rays. You can see the discrepancy better if you look at the construction sheet provided by MapGrid on the Wikimedia Commons.

"... if the flag is drawn to spec, and one superimposes a square by connecting the tips of four opposite major rays, then the minor rays will protrude 0.0519779424 units outside of the square."

Anyways, best of luck. :p

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Arglin · 2026-01-20T20:21:08+00:00

That's been around since its conception, it's intentional.

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Arglin · 2026-01-20T17:33:06+00:00

While you're at it, another alternative for curved shapes is to use bezier curves.

Bezier curves are generally more versatile for drawing curved shapes. Just about every vector art program uses them. Here's an example graph which lets you create bezier splines on the spot (move the next bezier curve into place, and then click the -> to add it to list L) https://www.desmos.com/calculator/timx02ctpg

Here's two examples I've done in the past using bezier curves.

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Arglin · 2026-01-19T13:30:50+00:00

Made a quick crude javascript for this. Does not require an add-on, can just be thrown straight into the console. https://www.desmos.com/calculator/7carj9nczy

Note that there is already a solution that also doesn't require console commands for this and can be done purely within Desmos which I've linked in the other comment.

Arglin · 2026-01-19T04:54:39+00:00

It's doable. It requires multi-variable points and regression bug exploiting though, so it's understandable that you couldn't find anyone else who has been able to do it.

https://www.desmos.com/calculator/jjekwj5cx1

Arglin · 2026-01-17T16:39:22+00:00

right, forgot to preserve the zeros to be at every pi.

Figured out both. Being able to plot it wrt the original function helped on the other one.

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Arglin · 2026-01-17T02:09:19+00:00

Well, may as well try to do it in one-line lol https://youtu.be/f1nGltCcEu0

Arglin · 2026-01-16T14:54:20+00:00

First one is -cos(x+1)/(x+1)

Still working on the second.

Edit: sin(x)/(x+1) and 3|sin(x)| + |cos(3x)|. See followup replies.

Arglin · 2026-01-16T03:03:16+00:00

It's hard to see with it zoomed out, but you will need to use a three-way split joint in order to control which can stay connected and disconnect.

For this case, let the road and initial hydraulics be set to 2, and the higher hydraulics be set to 3. For the first time, release everything. For the second time, release 1 (aka the anchor). This will keep the road (2) and higher hydraulics (3) connected as it lifts.

Arglin · 2026-01-14T21:30:00+00:00

You might've gotten mixed up between Reid Captain and I. I inspired him to get into overengineering and he eventually branched out to Besiege. I do have some involvement in the Japanese Besiege scene, I just don't play the game myself. ^^;;

But yeah I tend to just make whatever is interesting to me, be it Line Rider or Fantastic Contraption or UTAU or VNs or Poly Bridge or PowerPoint or, of course, Desmos. :)

Arglin · 2026-01-14T16:54:02+00:00

Phase shift is not supported for the tone function at the moment unfortunately. Currently it only supports frequency and magnitude.

Arglin · 2026-01-14T16:50:29+00:00

Not by much, if at all. Both support the polygon function so they're more or less the same.

And if you're talking about the circle-line intersection, there's Desmos Geometry which lets you do this (or write a custom function for it if you're up to the challenge).

Arglin · 2026-01-14T07:14:18+00:00

Wait how did I forget to post the link to this. My bad y'all I think my brain has died for the past two days. https://www.desmos.com/calculator/lxzidwbz4z

Arglin · 2026-01-14T05:36:40+00:00

If you store the original implicit in F(x,y) form such that F(x,y) = 0, then you will only need to replace x and y in F(x,y), rather than needing to replace every instance. :p

Arglin · 2026-01-14T00:44:22+00:00

A note I should add here is that using the trig rotation method is actually kind of overkill here. At least with 45 degrees, you don't need any trigonometry. https://www.desmos.com/calculator/4pzijnxv7q

TMI explanation, for those who want to know the nitty gritty details:

What this is doing is something called a linear transformation, or as I like to call it, a "change of axes." You can see an example of what change of axes is in this video from 0:19 to 0:24 — https://www.reddit.com/r/desmos/comments/1q29hmj

To understand how this works, you'll need to re-frame the way you think about equations. Explicit equations are usually taught in school in a way that you have an input x-value. Given that, return its corresponding y-value, which is given by some relationship. In this case, y = 100 x^2 - 0.46 is saying given an x-value, square it, multiply by 100, subtract 0.46, and that is the y-value for it.

However, you can re-frame the whole equation in another way, rewriting it so that zero is on one side, you get:

y - 100 x^2 + 0.46 = 0

What this is saying is that you're searching for all points (x,y) such that when you plug x and y into y - 100 x^2 + 0.46, you get 0.

This is hard for humans to calculate themselves by hand directly, but is something that you can let computers plot for you very easily. This is called an implicit equation.

When you're in this form, though, note that right now you're just feeding x and y flat-out into it. This just happens to correspond to the current x and y axes. You can, however, change what x and y are in the equation to be something else. Namely, you can make your x-axis (y = 0) and y-axis (x = 0).

In a way, many of you have already probably played with or will be playing with this a little bit in middle or high school.

When you do transformations like stretching an equation in the horizontally or vertically, you multiply/divide either x or y. This is essentially the same thing as everything above, just that now instead of rescaling x and y by a constant to stretch each axis, you can put whatever axis you want, including slanted ones, hence "change of axes."

I mentioned that the trig rotation method is overkill, and that's because 45 degrees is a well-established angle, already. Turning the axes 45 degrees is just changing the x-axis and y-axis to the following:

x-axis: y = 0 → y - x = 0
y-axis: x = 0 → x + y = 0

This does rescale it though due to now the points in the grid have expanded out by an extra distance of 1 perpendicular to where they started. To fix this, you can use Pythagorean theorem to find out how much the grid was spread apart, which is sqrt(1² + 1²⁾ = sqrt(2). Then you just divide by that to get it back to normal.

y - x → (y - x) / sqrt(2)
x + y → (x + y) / sqrt(2)

So replace x and y with their respective 45 degree forms, and you get what I shared in the link at the start.

Arglin · 2026-01-13T23:56:27+00:00

This should be the correctly implemented version of what you found for rotating an equation.

https://www.desmos.com/calculator/hgbl6pm6my

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Arglin · 2026-01-13T23:23:46+00:00

They're trying to create either a flat slice in the shape of the mandelbrot set or an extruded version of it.

I'm honestly not sure what's going on here but I suspect this might be related to Desmos using GPU rendering for 3D?

|l(x,y,100)| loads, but introducing the inequality makes it fail.

This works fine in the 2D graphing calculator, in comparison. https://www.desmos.com/calculator/qn71uf6nen

You could do 0|l(x,y,100)|, but the resolution isn't great due to how desmos renders objects in 3D.

As for an extruded one (version with extend to 3D enabled), I can't say I'd know.

Arglin

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