1. Human Body SQ representation
Left arm
Right arm

2. Left arm Abbreviations: B – Body;
LS – Left Shoulder; LA – Left Arm; E – Elbow;
LF – Left Forearm.
Parameters: angle position of the Shoulder;
Transformation: B - LS
Superquadrics:

3. Left arm Transformation: LS - LA
We can express the arm rotation as a current frame rotation sequence:
1° rotation  among x (clockwise)
2° rotation  among z (anticlockwise)
3° rotation  among y (clockwise)
4° translation of a2 along y
Therefore the parameters for Left Arm are:
, , , δ that depend upon gesture
(LS,RS,LHJ,RHJ) parameters that depend upon anthropometric

4. Left arm Transformation: LA - E Transformation: E - LF
We can express the forearm rotation as a current frame rotation sequence:
1° rotation δ among x (clockwise)
2° translation of -a2 along y
Full transformation: B - LF

5. Right arm

6. Right arm Transformation: B - RS Abbreviations:
B – Body; RS – Right Shoulder; RA – Right Arm; E – Elbow;
RF – Right Forearm.
Superquadrics:
Parameters: angle position of the Shoulder;

7. Right arm Transformation: RS - RA
We can express the arm rotation as a current frame rotation sequence:
1° rotation  among x (clockwise)
2° rotation  among z (clockwise)
3° rotation  among y (anticlockwise)
4° translation of a2 along y
Therefore the parameters for Right Arm are:
, , , δ that depend upon gesture
(LS,RS,LHJ,RHJ) parameters that depend upon anthropometric

8. Right arm Transformation: RA - E Transformation: E - RF
We can express the forearm rotation as a current frame rotation sequence:
1° rotation δ among x (clockwise)
2° translation of -a2 along y
Full transformation: B - RF

9. Left leg
Version 1 – axes Z of limbs directed like axis Z of the Body

10. Left leg Abbreviations: B – Body;
LHJ – Left Hip Joint; LH – Left Hip; K – Knee;
LL – Left Leg.
Parameters: angle position of the Left Hip Joint;
Transformation: B - LHJ

11. Left leg Transformation: LHJ - LH
We can express the leg rotation as a current frame rotation sequence:
1° rotation  among x (clockwise)
2° rotation  among y (anticlockwise)
3° rotation  among z (clockwise)
4° translation of -a3 along z
Therefore the parameters for Left Leg are:
, , , δ that depend upon gesture
(LS,RS,LHJ,RHJ) parameters that depend upon anthropometric

12. Left leg Transformation: LH - K Transformation: K - LL
We can express the leg rotation as a current frame rotation sequence:
1° rotation δ among y (clockwise)
2° translation of a3 along z
Full transformation: B - LL

13. Right leg
Version 1 – axes Z of limbs directed like axis Z of the Body

14. Right leg Abbreviations: B – Body;
RHJ – Right Hip Joint; RH – Right Hip; K – Knee;
RL – Right Leg.
Transformation: B - RHJ
Parameters: angle position of the Left Hip Joint;

15. Right leg Transformation: RHJ - RH
We can express the leg rotation as a current frame rotation sequence:
1° rotation  among x (anticlockwise)
2° rotation  among y (anticlockwise)
3° rotation  among z (anticlockwise)
4° translation of -a3 along z
Therefore the parameters for Right Leg are:
, , , δ that depend upon gesture
(LS,RS,LHJ,RHJ) parameters that depend upon anthropometric

16. Right leg Transformation: RH - K Transformation: K - RL
We can express the leg rotation as a current frame rotation sequence:
1° rotation  among y (clockwise)
2° translation of a3 along z
Full transformation: B - RL