  Background: An electron localization function was originally introduced to
visualize bond structures in molecules. It became a useful tool to describe
electron configurations in atoms, molecules and solids. In nuclear physics, a
nucleon localization function (NLF) has been used to characterize clusters in
light nuclei, fragment formation in fission and pasta phases in the inner crust
of neutron stars.
  Purpose: We use the NLF to study the nuclear response to fast rotation.
  Methods: We generalize the NLF to the case of nuclear rotation. The extended
expressions involve both time-even and time-odd local densities. Since current
density and density gradient contribute to the NLF primarily at the surface, we
propose a simpler spatial measure given by the kinetic-energy density.
Illustrative calculations for the superdeformed yrast band of $^{152}$Dy were
carried out by using the cranked Skyrme-Hartree-Fock method. We also employed
the cranked harmonic-oscillator model to gain insights into patterns revealed
by the NLF at high angular momentum.
  Results: In a deformed rotating nucleus, several NLFs can be introduced,
depending on the definition of the spin-quantization axis and self-consistent
symmetries of the system. The oscillating pattern of the NLF can be explained
by a constructive interference between the kinetic-energy and particle
densities. The nodal pattern seen in the NLF along the major axis of a rotating
nucleus comes from single-particle orbits with large aligned angular momentum.
The variation of the NLF along the minor axis is traced back to
deformation-aligned orbits.
  Conclusions: The NLF allows a simple interpretation of the shell structure
evolution in the rotating nucleus in terms of the angular-momentum alignment of
individual nucleons. We expect that the NLF will be useful for the
characterization of other collective modes and time-dependent processes.
