  $Q$ is a quiver of type $\tilde A(n-1,1)$ if its graph is of affine type
$\tilde A_{n-1}$ and if its arrows have a certain orientation. We develop a
bijection between the set of indecomposable $kQ$-modules whose dimension
vectors are positive real roots of the root system associated to $Q$ and a
certain set of planar curves. We prove that the number of self-intersections of
the curve which corresponds to the module $M$ is equal to the dimension of
$\text{Ext}^1_{kQ}(M,M)$. We also prove that, for many pairs of modules
$(M,N)$, the number of intersections between the corresponding two curves is
equal to the dimension of $\text{Ext}^1_C (M,N)$, where $C$ is the cluster
category of $kQ$-mod.
