(Disney Meets Darwin)

Appendix B
The Motor Control Scheme for the 3D Articulated Figures

Attributes of motions within the whole collection of joints are created by one number series generating function, as a way to coordinate them. This function takes five control parameters (determined by five genes) as input, and generates a periodic series as output (with each number of the series corresponding to one joint angle in the figure). The pseudo code example below illustrates the function. 


INPUT: parameters from genes: (size, start, step  low, high) 	
       number_of_joints

 integers:       size, start, step, number_of_joints
 real numbers: 	low, high

  BEGIN
   number = start

   LOOP from index=1 to index=number_of_joints:
    (
    number = number + step  
    output_parameter[index] = low + (number MOD size)/size * (high - low)
    )

  END

OUTPUT: a periodic series of real-number parameter values
The purpose of this scheme is essentially to allow a small number of parameters to determine an indefinitely long series of values to control actions in multiple limbs, where the number of limbs is arbitrarily large. The series is periodic to encourage regularity, yet with a large number of possible polyrhythms in the total figure's motions. Thus, a figure can move all its limbs either in total synchrony, with various wave motions, in alternating fashions, or in irregular ways. The periodic series generator is used six times (with six associated five genes as inputs) to determine settings for the following six motion attributes, along the whole series of joints: 

amplitude of sine wave displacement in the pitch angle of the joint
amplitude of sine wave displacement in the veer angle of the joint 
phase offset of the pitch angle sine wave
phase offset of the veer angle sine wave
on-off switch to enable or disable the joint's pitch angle motion
on-off switch to enable or disable the joint's veer angle motion

In addition, there is one global rate gene which controls the overall frequency of sine motions in all the joints.



Appendix C
The Physics Model for the Articulated Figures


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