  Recently we developed a formalism for the scattering from linear and acyclic
branched structures build of mutually non-interacting sub-units.{[}C. Svaneborg
and J. S. Pedersen, J. Chem. Phys. 136, 104105 (2012){]} We assumed each
sub-unit has reference points associated with it. These are well defined
positions where sub-units can be linked together. In the present paper, we
generalize the formalism to the case where each reference point can represent a
distribution of potential link positions. We also present a generalized
diagrammatic representation of the formalism. Scattering expressions required
to model rods, polymers, loops, flat circular disks, rigid spheres and
cylinders are derived. and we use them to illustrate the formalism by deriving
the generic scattering expression for micelles and bottle brush structures and
show how the scattering is affected by different choices of potential link
positions.
