  We consider the problem of synthesizing safety strategies for control
systems, also known as shields. Since the state space is infinite, shields are
typically computed over a finite-state abstraction, with the most common
abstraction being a rectangular grid. However, for many systems, such a grid
does not align well with the safety property or the system dynamics. That is
why a coarse grid is rarely sufficient, but a fine grid is typically
computationally infeasible to obtain. In this paper, we show that appropriate
state-space transformations can still allow to use a coarse grid at almost no
computational overhead. We demonstrate in three case studies that our
transformation-based synthesis outperforms a standard synthesis by several
orders of magnitude. In the first two case studies, we use domain knowledge to
select a suitable transformation. In the third case study, we instead report on
results in engineering a transformation without domain knowledge.
