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Rotations in 3d are not easy to understand.  This tutorial examines some of the problems surrounding 3d rotations and briefly explains the two rotation types , Euler and Quaternion. Rotations are only a problem in animation. Euler experiences gimbal problems and Quaternion's lack animation curves.

Running time:  5 mins 24 sec


Knowledge of these concepts is required: Basic Animation, objects ,

Andrew Silke is an award winning filmaker and has worked on projects such as Scooby Doo, Happy Feet and Avatar

XSI (coming)
Maya (coming)

Euler: Pronounced "oiler" Euler is a common method for calculating 3d rotations. Is popular because it uses 3 values X, Y Z angles.  Euler  requires a "rotation order" and can experie nce gimbal problems, the worst resulting in Gimbal Lock when 2 axes align.  this is why it's sometimes refered to as Gimbal, instead of Euler.

Quaternion: Method of rotation that uses four values, xyz and t.  XYZ are position values used to calculate a vector direction, and t is a roll value.

Gimbal: Gimbal is the effect caused when Euler rotation axes break the usual 90 degree angle difference on a rotation manipulator.  The extreme of this is gimbal lock when two axes align completely.

World/Local Coords: Rotation manipulators usually default to world or local (object) modes to rotate objects or components (verts edge faces). In local or object mode the manipulator will rotate with the object or section.  In "world" the rotate manipulator stays aligned to the xyz layout of the scene.

Manipulator: The widgit/tool that appears to help us visually click and rotate/move/ modify an object or selction.

Key or Keyframe: Setting a value and recording it on a time value (frame) in animation.

In between: The space (in time) between animation keyframes. usually the computer will fill in the motion with a direct path or corresponding numerical value that fits between the value of the keyframes.

TCB: Stands for Tension Continuity and Bias, values that affect the "ease in and out"  between keyframes. Used for quaternion rotations that don't have animation curves.

Quaternion Pole: A direction that sets the role value's up point for quaternions.

2010solar | | 2011-01-05 16
The main th...
ihandart - PS | | 2009-03-10 15
I forgot to mention that both the logo "gorilla" and the music are
fabulous. You would expect them to be annoying, but the timing and and the
particular details make them completely satisfying.
And using the text as well
as the video explanations is brilliant.
joeedh | | 2009-02-27 05
Great tutorial! Though quaternions aren't quite vector/angle pairs
mathematically (actually vector/cosine-of-angle, which is treated as a
four-dimensional vector and normalized).

A friend told me an interesting way to
look at quats: Weighted values between specific rotations. With everything else
zero, a quat value of x is 180 rotation around the axis, y is 180 around the y,
z is 180 around the z, and w is without any rotation.

So rotations using quats
is just weights between these rotations.
Nathan Vegdahl - Common misconception about quaternions | | 2009-02-23 08
This is a really good tutorial, and an extremely good explanation of Euler

However, your explanation of quaternions has some errors. You seem
to have quaternions confused with aim-and-roll rotations, where you specify an
aim vector for the object to point at, and a roll angle to rotate around that

Quaternion rotations are more closely related to axis-angle rotations,
where you specify an axis and an angle to rotate about that axis. Axis-angle
rotations take advantage of the unintuitive fact that for any two 3d
orientations you can always find a single axis of rotation that will rotate
between them.

Quaternions are still a bit more complex than that, however, and
understanding them involves a fair bit of trigonometry, and a taste for some
slightly twisted mind games.

It would also probably be helpful to be able to
play with quats in a piece of software that doesn't display quats as eulers in
the fcur...
andrewsilke | SAdministrator | 2009-03-21 02
Yeah cheers for the info guys, I ran it by a couple of more knowledgeable
friends and they seemed to think the quats checked out, this is how it was
explained to me by a games programmer, but I'm certainly no expert on quaternion
maths! So I've probably misinterpreted somewhere along the way.
andrearusky - TCB in maya ? | | 2009-02-21 11
so...i was watching a tutorial to make
a rukib cube animation..
the guy was
showing to set up the TCB rotation in 3DStudio max..
and then..he changed the
tension to linear..
i found how to use the Quaternion rotation in maya
(preference setup)
and also changed the curves to synchronized Quaternion
seems like the animation
i do curve i create are still in degrees , hence when i
rotate the pieces of the cubes..they go in funny positions during the
how to do ? to change that rotation order.. in maya

check what he did here:;
eature=PlayList&p;=EACA1A430E1CA3B9&playnext;=1&inde; x=27
andrewsilke | SAdministrator | 2009-03-21 02
Even though I'm a Maya guy I've never used quats in that program, it didn't seem
to work like Max when i checked it out.

To change the rotate order in Maya,
go to the attribute editor of an object (ctrl a), it's in the first couple of
tabs. I don't have Maya in front of me sorry.
Marc - Great! | | 2009-01-25 13
So basic yet one of the most problematic things I encountered (at least for me)
in 3D...Liked a lot!!!
Greg Hendrix | | 2008-12-17 22
Awesome tutorials!!
Cobster - Thanks | | 2008-12-14 10
An excellent, clear, knowledgable tutorial, I love the presentation and how it's
all for free too! Keep up the fantastic work!
Jurriaan - I knew it! | | 2008-12-08 13
I knew there was something going on there. Thanks for the clear video, as a user
I don't think enough about the why's so this is a great addition to my
zero | | 2008-12-06 15
thank you guys !!!!
Snoop Baron - Thanks | | 2008-12-04 17
Well done :)
dkala | | 2008-12-03 23
Thank you for sharing your knowledge .Finally a clear way to explain such
complicated things.I need one tutorial per day !!!
E.C. Flossie - Nice | | 2008-12-03 21
Nice way of presenting how it works in 3D, looking forward to the next video.
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