CS 551/651: Computer Animation
Fall 2003
Professor Brogan
Homework 1
Due:
1) We want to analyze the
computational complexity of some algorithms we are studying in this course so
we can project their feasibility to tomorrow’s animators. Assume an average 2003 computer is able to
perform inverse kinematics of a 6 DOF robotic arm in 1 second. If Moore’s Law predicts a doubling of
performance every 18 months (which isn’t exactly what he predicted, but we’ll
go with it), a computer 10 years from now will be 64 times more powerful. If, in the year 2013, we observe that the
simulation of the 6 DOF robotic arm executes 64 times
faster, could we perform IK on a 64*6 DOF arm in 1 second? If not, how man DOFs
would you expect to be able to animate? Support
your answer with analysis of the computational complexity of the IK algorithm
2) Address the same
question with regard to the scalability of the technique described in the Through the Lens paper.
3) The Spacetime Constraints paper uses Sequential Quadratic Programming to solve a
constrained optimization problem. What
does the “quadratic” part of the optimization technique’s name have to do with
the way the technique works? What are
the benefits and disadvantages of constraining part of the technique to be
quadratic?
Use of outside resources: You may use
any resources you find in books or the web.
You may not work together.