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 $s$ .