  In this article, we use the relationship between cluster scattering diagrams
and stability scattering diagrams to relate quiver representations with these
diagrams. With a notion of positive crossing of a path $\gamma$, we show that
if $\gamma$ has positive crossing in the scattering diagram, then it goes in
the opposite direction of the Auslander-Reiten quiver of $Q$. We then give the
Hall algebra theta functions which recover the cluster character formula by the
Euler characteristic map. At last, we define the Hall algebra broken lines and
then are able to give the stratification of the quiver Grassmannians by the
bending of the broken lines.
