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$Q$ 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 abijection between the set of indecomposable $kQ$-modules whose dimensionvectors are positive real roots of the root system associated to $Q$ and acertain set of planar curves. We prove that the number of self-intersections ofthe 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 isequal to the dimension of $\text{Ext}^1_C (M,N)$, where $C$ is the clustercategory of $kQ$-mod.

Computation of extension spaces for the path algebra of type $\tilde A(n-1,1)$ using planar curves