A *generalized cylinder* is a generalization of an ordinary
cylinder. Instead of being limited to a line, the center axis is a
continuous *spine curve*,
, for some parameter
. Instead of a constant radius, a radius function is
defined along the spine. The value is the radius of the
circle obtained as the cross section of the generalized cylinder at
the point
. The normal to the cross-section plane
is the tangent to the spine curve at .

Steven M LaValle 2012-04-20