- Often nonlinear, underdetermined or overdetermined, possibly ill-conditioned.
- Complexity of determining solution proportional to number of free links.
- One free joint between two fixed ones can be solved fairly efficiently, for example, with only one spare degree of freedom.
- Extra constraints may be needed to obtain a unique and stable solution.
- Example: Requiring a joint to point downwards as a gross approximation to gravity
- Joint motion constraints (hinge vs. revolute vs. ball) are also useful.

- Additional optimization objectives
- Resulting optimization problem solved iteratively as an animation proceeds.
- Example optimization objectives:
- minimize the kinetic energy of structure;
- minimize the total elevation of the structure;
- minimize the maximum (or average) angular torque.

CS488/688: Introduction to Interactive Computer Graphics

University of Waterloo

Computer Graphics Lab