This study was undertaken to determine the geometric form of the surfa
ce on which a fixed point on the head moves as a result of neck motion
. Motion of a retroreflective marker on the glabella of six normal sub
jects was stereoscopically recorded by two video cameras, during a var
iety of neck motions, performed on command. Near real-time computer an
alysis in three dimensions of the video images showed the marker moved
on a surface that very closely approximated an elliptical paraboloid
(with tendency to a hemisphere), after extraneous shoulder motion had
been eliminated. Parameters defining the elliptical paraboloids were o
btained. Using a reflex microscope, the shape of the articular facets
on skull base and superior facets of C1 and C2 of 6 normal subjects we
re examined. The shapes of all these facets were calculated and also f
ound to be elliptical paraboloids.