  Zermelo navigation is not only a fundamental tool in Finsler geometry but
also a fundamental approach to the geometrization of dynamics in physics. In
this paper, we consider the Zermelo navigation problem on optical Riemannian
space and, via Zermelo/Randers/spacetime triangle, explore the generation of
new spacetimes from pre-existing ones. Whether the Randers metric has
reversible geodesics corresponds to the presence of time-reversal symmetry in
the generated spacetime. In cases where the Randers metric has reversible
geodesics, we utilize a radial vector field to generate new static spacetimes
from existing ones. For example, we can generate Schwarzschild, Rindler, de
Sitter, and Schwarzschild-de Sitter spacetimes from flat spacetime. In fact,
the Zermelo navigation method allows for the derivation of a variety of static
spacetimes from flat spacetime. For multi-parameter spacetimes, they can be
generated through various navigation paths. However, for some spacetimes, not
all navigation paths may exist. In the second scenario, when the Randers metric
does not have reversible geodesics, we employ a rotational vector field to
transform non-flat static metrics into slowly rotating spacetimes.
Alternatively, using a mixed vector field, we generate slowly rotating
spacetimes starting from flat spacetime. We provide examples of generating Kerr
spacetimes and Kerr-de Sitter spacetimes.
