CS229 Homework 5

Due Monday, Oct 23 in class.


The spacetime approach bogs down when one of two things becomes large:
  1. The time period spanned by the animation (specifically, the number of variables used to represent any DOF over time)
  2. The number of degrees of freedom of the character

Addressing Time complexity

The work of Michael Cohen and his colleagues (in SIGGRAPH '92 and '94) has focused on tools to reduce the complexity of animations that run for longer time periods. His '92 paper allowed the user to run the optimization over specific windows of time. His '94 paper created a hierarchical representation of the curve for each DOF. Motion could then be optimized in a top-down way, starting with low frequency representations of motion and adding successively higher frequency representations where needed.

Addressing degree-of-freedom complexity

Cohen's '92 paper addressed degree-of-freedom (DOF) complexity as well. His spacetime windows definition allowed the user to specify a restricted number of DOF's as well as a restricted time period. Popovic and Witkin addressed the DOF problem by simplifying the character, thus manually minimizing complexity in this dimension. The approaches presented to date for reducing DOF complexity, however, do not have the conceptual generality and elegance of the hierarchical wavelet representation of curves over time.

The Question

How would you design a general, elegant hierarchical representation of DOF? You might want to start by thinking of a character similar to a rope or a snake. Your final solution should ideally work for any type of articulated character, however.


Nancy Pollard