A new set of equations describing the time evolution of torsion and cu
rvature for an inextensible curve is developed. Combined with our rece
ntly developed Slender Body Theory approach to such problems, these eq
uations were applied to simulate three-dimensional ciliary beats, whil
e allowing for cilia interactions. The computer animation technique, w
hich was originally designed to display two-dimensional beats, has bee
n enhanced to accommodate the new three-dimensional results.