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.

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On 3-10-2018 2:34, Kenneth wrote:
> 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.
>


Visually indeed, the 2-axis rotation looks more "natural" than the 
3-axis rotation. However, I wonder if it is correct and my hunch would 
be that in RL rotation would imply 3-axis rotation nonetheless. This 
/must/ have been investigated somewhere, mustn't it?

-- 
Thomas

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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.
-- 
dik
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Thomas de Groot <tho### [at] degrootorg> wrote:

>
> Visually indeed, the 2-axis rotation looks more "natural" than the
> 3-axis rotation. However, I wonder if it is correct and my hunch would
> be that in RL rotation would imply 3-axis rotation nonetheless. This
> /must/ have been investigated somewhere, mustn't it?
>

It *would* seem that every CGI company on the planet must have thought this out
in detail long ago (as to which scheme is actually correct), as it's a rather
FUNDAMENTAL idea relating to falling or exploding objects. I likewise wonder if
there is an original technical paper somewhere that deals with it-- rather than
each CGI techie just using math/physics principles on his or her own to come up
with the proper scheme when it's necessary (and without taking the time to write
up a paper.) Strangely, I've never done a search for such a technical article;
I've been using the 'two-axis' scheme for a long time, just because it *looks*
more natural. SIGGRAPH *must* have something about it, I'm guessing; but I'm not
sure what to search for.

The interesting thing about two-axis rotation is that the object *eventually*
assumes every possible orientation, at least according to the many visual tests
I've done (or else I'm much mistaken!)

I haven't really tested 3-axis rotation as much I'd like; I'm still wondering if
the *order* of POV-ray rotations matters in that case. (It does NOT seem to
matter for the two-axis scheme, or even which axes are used-- although I haven't
*thoroughly* tested that either.) I have a hunch that for 3-axes, the y-rotation
should come first. I can't even verbalize why-- but I'd like to see if that
could eliminate the crazy behavior. Nothing but a hunch!

There's also the matter of 'real world' physics vs. computer simulations of
them. A real object doesn't have 'artificial' <x,y,z>-ordered movements--
everything happens simultaneously instead!

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"Kenneth" <kdw### [at] gmailcom> wrote:

> The interesting thing about two-axis rotation is that the object *eventually*
> assumes every possible orientation, at least according to the many visual tests
> I've done (or else I'm much mistaken!)

I was going to point out that if you think about this from a spherical
coordinate standpoint - there is no difference.

The distinction between 2 and 3-axis is artificial.

Perhaps you're just "adding" or "fiddling" too much - adding a jitter where
there ought to be a flow.

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On 3-10-2018 12:48, Bald Eagle wrote:
> "Kenneth" <kdw### [at] gmailcom> wrote:
> 
>> The interesting thing about two-axis rotation is that the object *eventually*
>> assumes every possible orientation, at least according to the many visual tests
>> I've done (or else I'm much mistaken!)
> 
> I was going to point out that if you think about this from a spherical
> coordinate standpoint - there is no difference.
> 
> The distinction between 2 and 3-axis is artificial.
> 
> Perhaps you're just "adding" or "fiddling" too much - adding a jitter where
> there ought to be a flow.
> 

Yes, that is an important, if not fundamental, point.

-- 
Thomas

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dick balaska <dic### [at] buckosoftcom> wrote:

>
> My caboose landing is a 2 axis rotation.

Yes, I noticed that ;-) In fact, it was while working on my own animated demo
that I first viewed your animation-- so I paid particular attention to that
caboose, ha.

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Thomas de Groot <tho### [at] degrootorg> wrote:
> On 3-10-2018 12:48, Bald Eagle wrote:

> >
> > The distinction between 2 and 3-axis is artificial.
> >
> > Perhaps you're just "adding" or "fiddling" too much - adding a jitter where
> > there ought to be a flow.
> >
>
> Yes, that is an important, if not fundamental, point.
>

In my mind's eye, I see that this could indeed be the case-- that the third
rotation is kind of 'mixing with' (and messing with) the other two... because
the initial two are already enough to orient the object. Kind of like a
'redundant force' that ends up being split up between the initial two rotations,
in a weird way. (BTW, I'm still pondering the 'Euler angle' discussion from a
recent thread, and how it relates to this stuff.)

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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, how do you say in English...
There are two increments vs. three increments.  Take my caboose,
3 axises would be 1) it's laying on it's side (x), 2) it's standing on
it's end (z), 3) it is rotating around the y.
You can choose any one final vector using 2 axii, but to animate the
three rotations simultaneously requires all 3.


-- 
dik
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dick balaska <dic### [at] buckosoftcom> 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 ;-)

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