Generalized cylinders

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, $ (x(s),y(s),z(s))$, for some parameter $ s
\in [0,1]$. Instead of a constant radius, a radius function $ r(s)$ is defined along the spine. The value $ r(s)$ is the radius of the circle obtained as the cross section of the generalized cylinder at the point $ (x(s),y(s),z(s))$. The normal to the cross-section plane is the tangent to the spine curve at $ s$.

Steven M LaValle 2012-04-20