  The Nielsen-Ninomiya theorem, dubbed `fermion-doubling', poses a problem for
the naive discretization of a single (massless) Dirac cone on a two-dimensional
surface. The inevitable appearance of an additional, unphysical fermionic mode
can, for example, be circumvented by introducing an extra dimension to
spatially separate Dirac cones. In this work, we propose a geometry-independent
protocol based on a tight-binding model for a three-dimensional topological
insulator on a cubic lattice. The low-energy theory, below the bulk gap,
corresponds to a Dirac cone on its two-dimensional surface which can have an
arbitrary geometry. We introduce a method where only a thin shell of the
topological insulator needs to be simulated. Depending on the setup, we propose
to gap out the states on the undesired surfaces either by breaking the
time-reversal symmetry or by introducing a superconducting pairing. We show
that it is enough to have a thickness of the topological-insulator shell of
three to nine lattice constants. This leads to an effectively two-dimensional
scaling with minimal and fixed shell thickness. We test the idea by comparing
the spectrum and probability distribution to analytical results for both a
proximitized Dirac mode and a Dirac mode on a sphere which exhibits a
nontrivial spin-connection. The protocol yields a tight-binding model on a
cubic lattice simulating Dirac cones on arbitrary surfaces with only a small
overhead due to the finite thickness of the shell.
