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Le 03/10/2018 à 02:34, Kenneth a écrit :
> To take a break from my other POV-ray chores, I made a simple animated demo of
> what an object looks like when it rotates (in POV-ray), as if free-falling under
> gravity-- but discounting wind resistance or any other extra force. Its a
> comparison between applying the rotations in two axes vs. three. I made the
> animation my own purposes (to easily refer to later), but it might be of
> interest to others as well.
>
> There's an obvious difference in the visual appearence of the objects. My own
> preference is for the 'two-rotation' scheme; it just looks more 'natural' (or
> more 'expected'?) Using all three rotation axes imparts an 'extra' force to the
> object-- kind of like wind resistance (which is also interesting, of course, but
> otherwise kind of strange.) The 3-axis scheme *might* also depend on the order
> of how those rotations are applied, to look 'more correct'-- not just straight
> <x,y,z>, in other words.
>
> Long ago, I originally thought that a free-falling object needed all three
> rotations to look natural. The idea seemed logical-- but the visual result
> didn't bear that out (to my eyes, anyway.) I guess I could do a thorough
> analysis of the applied 'vector forces' that cause an object to rotate in the
> first place -- but that's a lot of work ;-) For now, I'm curious as to which
> scheme you prefer, from a purely visual standpoint.
>
It's not the size which matters, it is how you use it.
From Euler's angles to describe a rotation, 2 angles are enough until
you want to adjust the rotation around the pole, then you need a third
angle. Any move made of 4 or more rotations can be simplified to just 3
Euler's angles, so 3 rotations is what is at most needed for any
positioning. Yet it is like saying that solving the Rubik's cube only
need at worst 17 (or 19 ?) moves, but some algorithms might generates a
hundred steps.
(and all the rotations can be composed in a single transformation, but
the equation is a bit complex)
composing rotations might not be what seems natural, especially when
they are done along fixed axes. Euler's angles have moving axis: the
first rotation is from the base(x, on z), but the second is from the
updated vector (on updated x), and so is the third (on updated z) which
in part compensate for the first one.
Natural moves usually try to conserve energy and have no acceleration.
In such setting, it is unlikely to see the axis of the last rotation be
moved by the change in the second angle: the gyroscopic effect (and our
expectation about it) would oppose to such change.
To summarize:
you need 3 angles (in Euler's system) to describes any orientation, but
natural fall would only change two angles during animation and such
change would be with a null second derivative for each unless you have
friction or engine in play.
On a table, with Inception totem:
The third angle is the proper rotation of the Inception totem, whereas
the second angle is the oscillation of the axis of the spinning top, the
speed of the oscillation being driven by the speed of the first angle.
The second angle is constant, for natural expectation of no friction.
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On 03/10/2018 13:13, Kenneth wrote:
> dick balaska <dic### [at] buckosoft com> wrote:
>> On 10/03/2018 06:48 AM, Bald Eagle wrote:
>>
>>>
>>> The distinction between 2 and 3-axis is artificial.
>>
>> For this application, I disagree. For a static image, yes, there is no
>> difference. But for an animation, hmm...
>> You can choose any one final vector using 2 axii, but to animate the
>> three rotations simultaneously requires all 3.
>
> Yet the visual result of using all three definitely looks...odd.
>
> Going back to first principles: An object starts out as being static (that is,
> no ROTATIONS at all.) Then a force has to impinge on it to start it rotating-- a
> 'point' force for simplicity's sake. That force has a direction vector, and acts
> on the object in 3 (de-composed) vector directions, toward the center of mass.
> The magnitudes of those three vectors depend on where the force was applied on
> the surface (relative to the object's center of mass) and the angle of contact
> with the surface. If I understand the concept of 'Euler angles' correctly, those
> three force vectors can be 'simplified/combined' into just two resulting
> rotations.
>
> That's about the limit of my understanding so far ;-)
>
>
>
>
Well here is my tuppence worth.
I think that it is the ratio of the rotations that makes 3 axes look
odd. in this animation the X axis rotates 3 times for one rotation of
the Z axis and the Y axis rotates twice.
(I am wedded to cyclic animations)
--
Regards
Stephen
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Attachments:
Download '0001-0599.mp4.mpg' (1679 KB)
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On 03/10/2018 16:58, Stephen wrote:
> Well here is my tuppence worth.
BTW the die are meshes made in blender and rendered in Pov.
--
Regards
Stephen
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On 03/10/2018 17:03, Stephen wrote:
> On 03/10/2018 16:58, Stephen wrote:
>> Well here is my tuppence worth.
>
> BTW the die are meshes made in blender and rendered in Pov.
>
Brain is taking a break. :(
The LH dice is rotating on 2 Axis, X&Y the RH one in all three.
--
Regards
Stephen
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Check out
https://en.wikipedia.org/wiki/Euler_angles
The trick is to rotate around the same axis twice. E.g.
rotate z
rotate x
rotate z
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On 10/03/2018 03:58 AM, dick balaska wrote:
> On 10/02/2018 08:34 PM, Kenneth wrote:
>
>> Long ago, I originally thought that a free-falling object needed all three
>> rotations to look natural. The idea seemed logical-- but the visual result
>> didn't bear that out (to my eyes, anyway.) I guess I could do a thorough
>> analysis of the applied 'vector forces' that cause an object to rotate in the
>> first place -- but that's a lot of work ;-) For now, I'm curious as to which
>> scheme you prefer, from a purely visual standpoint.
>>
>
> My caboose landing is a 2 axis rotation. I'm not sure why I didn't even
> try 3, that would have made sense.
>
> Your 3 axis, it looks like sometimes it changes direction while falling.
>
Is this due "gimbal lock?"
Just me echoing what I've read, but I think you have to go to use
Quauterions to avoid certain angle ambiguities.
was exposed to gimble lock on seeing a recent posting of yours. I've not
gotten to testing the thought or reviewing your code though - and
probably won't for a long while yet. Still occupied with solvers and
related numerical methods.
Bill P.
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I think that there's a "look_at" type positioning of the object, and a "sky"
type twisting.
With regard to the "look" and "feel" of the motion, I do believe that Stephen
and TdG agree with me that 1 more thing is "too much".
Consider the external ballistics of a projectile.
Usually one imparts spin to stabilize it in flight, and this gives it a
rotational inertia that must be overcome to twist it perpendicular to the axis
of rotation. The faster it spins, the less it nutates.
So I think that you may have a tumble with a bit of wobble, but adding a 3rd
element of motion just doesn't seem to "fit in" to the scheme of things.
https://www.google.com/search?q=projectile+stabilization+spin
Of tangential, somewhat related interest is how calculators do sin cos, etc,
which IIRC has it's origin in flight computers.
https://www.google.com/search?q=cordic
https://www.qc.cuny.edu/Academics/Degrees/DMNS/Faculty%20Documents/Sultan1.pdf
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Le_Forgeron <jgr### [at] freefr> wrote:
>
> Natural moves usually try to conserve energy and have no acceleration.
> In such setting, it is unlikely to see the axis of the last rotation be
> moved by the change in the second angle: the gyroscopic effect (and our
> expectation about it) would oppose to such change.
>
The gyroscopic effect: THAT'S an additional real-world 'force' that didn't occur
to me at all-- kind of like the forth (invisible) man in the room :-O And it's
quite fundamental to the discussion, IMO. I assume that even a *slowly* rotating
object would exhibit a gyroscopic effect, to some degree. Simple <x,y,z>
rotations in a computer certainly don't take that into account-- which might
explain the apparent difference between using 3 axes of (computer) rotation, and
what we 'expect' to see based on real-world spinning objects in free fall.
For argument's sake, let's say that real-world free-falling rotation of an
object *is* around all 3 axes. Maybe it is, maybe it isn't--but my mental
concept of the effect of the gyroscopic force is that it may 'smooth out' the
jitter/wobble caused by the 3rd-axis rotation-- leading to the expectation that
a computer simulation of TWO-axis rotation looks more 'natural.' Put another
way: If the effect of gyroscopic spin could be included in POV-ray's rotations,
would the apparently weird result of 3-axis rotation 'smooth out' to look more
like two-axis rotation?
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Stephen <mca### [at] aolcom> wrote:
> >
> Well here is my tuppence worth.
> I think that it is the ratio of the rotations that makes 3 axes look
> odd. in this animation the X axis rotates 3 times for one rotation of
> the Z axis and the Y axis rotates twice.
.....
> The LH dice is rotating on 2 Axis, X&Y the RH one in all three.
>
I have to admit that they do look 'smoother' than mine.
But to my eyes, it looks like the LH dice has 3-axes(!), and the RH dice *maybe*
has only two(?). I'm seeing the LH dice 'reverse rotation' every now and then.
Could you post the respective clock rotations for both? I'd like to try them
out.
Did you use
rotate <x,y,z>?
Or something like
rotate...
rotate...
rotate...
?
To your point about the ratios: Just conjecturing, I would say that keeping the
rotations to set ratios (whatever thay may be) in order to get smoothness in the
result, sounds like invoking "special rules"-- when the original cause of the
rotations (the original impinging force in the 'real world') may not be so
accomodating ;-) The original applied vector force may have wildly different
ratios for its 3 de-composed axis-aligned forces-- naturally resulting in
different ratios between the 3 POV-ray rotation amounts. (OR two final rotation
amounts, re: Euler???)
But as a *practical* matter, maybe you're on to something! At least the RH dice
(die?) does *look* smoother.
My two-cents worth ;-)
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Le_Forgeron <jgr### [at] freefr> wrote:
> >
> It's not the size which matters, it is how you use it.
LOL!
>
> composing rotations might not be what seems natural, especially when
> they are done along fixed axes. Euler's angles have moving axis: the
> first rotation is from the base(x, on z), but the second is from the
> updated vector (on updated x), and so is the third (on updated z) which
> in part compensate for the first one.
Yes; that seems to be the primary idea and reason for Euler's mathmatical
invention.
>
> To summarize:
> you need 3 angles (in Euler's system) to describes any orientation, but
> natural fall would only change two angles during animation and such
> change would be with a null second derivative for each unless you have
> friction or engine in play.
Yeah! That's what *I* think :-)
(...as I thumb through my calculus books with a quizzical look on my face...)
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