  A magnetic impurity on a superconducting substrate induces in-gap
Yu-Shiba-Rusinov (YSR) bound states, whose intricate spatial structure
crucially influences the possibilities of engineering collective impurity
states. By means of a saddle-point approximation we study the scattering
processes giving rise to YSR states in gapped, two-dimensional superconductors.
Further, we develop a theory which relates through a simple analytical
expression an arbitrary energy dispersion of normal electrons in a
two-dimensional host to the spatial features of the YSR states. Namely, we find
that flatter segments of the Fermi surface with large Fermi velocity enhance
the local density of states (LDOS) around the impurity. Our analytical
approximation is quantitatively accurate against tight-binding calculations on
various lattices with different Fermi surfaces, and it allows to predict the
shape and orientation of YSR states observed in scanning tunneling spectroscopy
experiments. We illustrate our results with a model of $\mathrm{NbSe}_2$.
