  One-dimensional flexible objects are abundant in physics, from polymers to
vortex lines to defect lines and many more. These objects structure their
environment and it is natural to assume that the influence these objects exert
on their environment depends on the distance from the line-object. But how
should this be defined? We argue here that there is an intrinsic length scale
along the undulating line that is a measure of its "stiffness" (i.e.,
orientational persistence), which yields a natural way of defining the
variation of physical properties normal to the undulating line. We exemplify
how this normal variation can be determined from a computer simulation for the
case of a so-called bottle-brush polymer, where side chains are grafted onto a
flexible backbone.
