All basic dimensions in a single needle

[Hyperelastic]

You can’t create or define dimensions by moving a body. You have to assume that the body exists in a space of n dimensions. That assumption determines what kinds of motions the body can undergo.

I believe what the OP is talking about are generalized coordinates. For example, the state of a rigid bar hinged at one end can be described by a single generalized coordinate: the angle the bar makes with some reference line. Assuming the OP is talking a about a real, physical needle, its state can be described by six generalized coordinates (three translational and three rotational), plus a large number of generalized coordinates giving its deformation.

If the needle is an imaginary, rigid one-dimensional body in three-dimensional space, then it takes five generalized coordinates to define its state. Namely, three coordinates giving the location of some point on the needle, and two giving the angles the needle makes with two reference lines. (You don’t need the third because a one-dimensional needle can’t spin like a rolling log. There’s nothing to spin around that axis.)

By state, I mean position, orientation and deformation (not velocity or any other derivatives of those).

[cmyk]

@TriPolar

Well this is difference between computer graphics and mathematical geometry. We have a granularity in the real world based on pixels and the mechanism of our eyes, so nothing is really 0 or 1 dimensional in representation, and in reality everything is 3 dimensional (except for black holes maybe). Innumerable CPU cycles have been wasted computing graphics at greater resolution than necessary since the minimum is really one pixel. Luckily CPU cycles are a growing and limitless resource. But there have been problems in some information with a ‘disappearing star’ effect. Accurately modeling stars many light years away gives them an actual size much smaller than any pixel and an algorithm that does not account for this may have them blink in and out of virtual existence through spacial transformation.

Anyway, cool video. The random-ish path of the needle point will tend to make a blurry image that is more spherical in appearance at a slower rate of rotation than the simplest progression along two axes of rotation, and distribute the overlap the path of the path of the needle end around the sphere instead of having it concentrate at a pair of poles.

It looks like a 3D spirograph. Anyhow, in between waiting for a render on something I’m doing, I tweaked the rotation as you mentioned (or at least how I described above). I’ll upload the result soon.

@Chronos

cmyk, in order for your needle to trace out the full sphere (technically, never, but I’m parsing that as “for any given point on the sphere and any given nonzero distance from that point, to eventually get within that distance”), the ratios of your rotation speeds need to be irrational. What you’ve got there will repeat itself after 21 of the shortest rotation, if those are the actual numbers you used.

funny you mention that, as I starting using real numbers, it would always result in a repeating pattern pretty fast, so I did try using a mix of irrational numbers (pi, phi, etc.), but the software I use rounds the sub-frames to only the second decimal place :dubious: If I wanted to get to that level of accuracy, I’d have to write and implement some kind of function or formula, rather than just manually keying frames, and I’m just am lowly CG guy. Anyway, thanks for the iteration calc… I think you’re right, too, by looking again at the simulation.

[Chronos]

Anyway, thanks for the iteration calc… I think you’re right, too, by looking again at the simulation.

All it is is the least common multiple of 1, 1.75, and 3. And even truncated to the second decimal place, phi should still work pretty well.

[cmyk]

Ahh, cool, thanks Chronos! I’ll give it a shot…