[x3d-public] Basic Animataion data

[Joe D Williams]

glossary:
Transform rotation value

* Euler angle - typical mocap-derived
  animation data = x,y,z
     (x,y,z = degrees)
Mocap data represents:
  * Bone or Segment orientation
      or
 * parent Joint rotation
Either interpretation represents
 same animation


* matrix = axis-angle = x,y,z,a
     x,y,z = radians,
     a = scale factor

X3D Default
Easy to hand-edit


* Unit quaternion = w,x,y,z

      w+x+y+z = 1 = unit q

Most common authoring tool internal and transport form
Easy to add unit quats for realtime interpolated animation
Can use hand-edit as
 w=scale factor and x,y,z are axes
 if careful to maintain uq


* Standards-Track Lossless conversion between forms.

First, please notice that this Animation data is
aimed at describing keyframe animation of
a set of hierarchal "Joint" nodes.

Animation data is provided as arrays of:
keyframe root position data,
keyframe rotation data for each joint,
number of keyframes,
target key time frame interval

The data is used by defining the root position and each joint rotation 
at each key time. For film and video there is often no need for a list 
of key times indexed to each keyvalue because the frame interval is 
fixed.

Notice that typically, there is no consideration for non-monotonic key 
times, although it is highly unlikely to encounter an X3D browser that 
does not allow non-monotonic key times. Why, allow non-monotonic key 
times? Because it is usually convenient for the author to consider 
each joint individually and individually define the interval between 
associated keyvalue data points, and to minimize the actual number of 
key times and thus keyvalues.

At this time, in order for an X3D HAnim to use most types of mocap 
data it would only be required:

1. Connect the joint names
2. Convert the input data form to axis-angle,
3, Construct the interpolators and timers for each joint

This style of animation depends mainly or solely on application of 
individual rotations to individual joints in a set of hierarchal 
'Joint' nodes at each key time to produce the keyframe. Current best 
practice for this style of animation uses unit quaternions due to 
efficiency. Even though the most throughly complete technical solution 
remains axis-angle matrix transformations, the unit quats are easy to 
transport and used natively in many animation creation and development 
tools.

So, the choice of gltf to only transport quaternions should cause X3D 
and HAnim to address the idea of built-in quaternion support. As is 
well-shown, the maths of these three forms are well defined and 
conversion interactions are well understood.

* At this time we are creating prototype support for BVH x,y,z ffps 
import, it seems only reasonable to encourage import of both Euler 
angle and unit quaternion forms.

Background

Quaternions, Interpolation and Animation
Erik B. Dam Martin Koch Martin Lillholm
erikdam at diku.dk myth at diku.dk grumse at diku.dk
Technical Report DIKU-TR-98/5
Department of Computer Science
University of Copenhagen
Universitetsparken 1
DK-2100 Kbh Denmark
July 17, 1998

Interesting Material.
I have a copy of a pdf.

Appendix A - Conventions

Coordinate system
(slightly reworded by me to aim at X3D and HAnim)

X3D and HAnim use a right-handed coordinate system. In computer 
graphics some use a left-handed coordinate system. This allows the 
z-axis to point "into" the screen which seems natural for some styles 
of authoring.  However, since X3D primarily uses coordinates for 
animations driven by mathematical derivations and for Humanoid 
animations, VRML and X3D have chosen to use the mathematical standard, 
the right-handed coordinate system.

Rotation.

This means that the default Humanoid pose gaze is facing +z.
The +z axis for the character points "out" of the screen,
+y is up,
and +x is towards the character's left, viewer's right.
The default X3D viewpoint is oriented to look toward -z.

The direction of positive, or increasing rotation about an axis is 
obtained by the right-hand rule:

Hold the axis with right hand and the thumb pointing in the positive 
direction of the axis.

Adding positive rotation will rotate in the direction of the fingers.

It just happens that HAnim Joint rotations can be vizualized in terms 
of x=pitch, y=yaw, and z=roll.

Again, hold the Joint, as if you were holding the appropriate axis 
with right hand and the thumb pointing in the positive direction of 
the axis.

A positive rotation will rotate the Joint and move child hierarchies 
in the direction your fingers are wrapped around the axis.

For instance, consider a roll (positive z-axis) animation of a Joint, 
as would be appropriate for HAnim right hand fingers from the default 
pose.. The fingers are pointing down and thumb pointing toward +z. To 
move the fingers as if grasping the z-axis, rotate the finger joint(s) 
to increase their z-axis rotation.

Amazingly enough, this results in the character's right hand wrapping 
around the z-axis with the thumb pointed +z, and illustrates the 
right-hand rule perfectly.

Incidentally, this means that to get proper orientation for a gaze 
from the 'standard' eyeball location, then you can yaw the viewpoint 
+pi radians.

Transport Animations

In order to transport animations between 'standard' H-Anim characters, 
to accomplish the HAnim 'standard' initial pose prior to animation the 
Joint is defined to be at X3D default orientation, +z is out of the 
screen, +y is up, and +x is towards the character's left.

The default initial value for all Joints:
X3D axis-angle (matrix) form is 0 0 1 0
and for unit quatenions is 1 0 0 0

An illustration:
[standard X3D default transformations
X3D coordinate axes]
z (+ out toward viewer)
y (+ up)
x (+ character's left)
Rotation about z brings x into y
Rotation about y brings z into x
Rotation about x brings y into z


 Schlag, 1994] John Schlag.
Using geometric constructions to
interpolate orientation with quaternions.
Graphics Gems IV, pages 230-236, 1994.

[Shoemake & Du, 1994] Ken Shoemake & Tom Du. Matrix animation and 
polar decomposition.
ftp://ftp.cis.upenn.edu/pub/graphics/shoemake/polar-decomp.ps.Z, 1994.

Shoemake, 1994b] Ken Shoemake. Quaternions. 
ftp://ftp.cis.upenn.edu/pub/graphics/-
shoemake/quatut.ps.Z, 1994.

Thanks and Best,
Joe