Conventional SPH methods typically use a uniform particle spacing, which can be computationally expensive when fine resolution is required only in localized regions. In many practical applications, high resolution is needed only in limited areas of the computational domain, while coarser resolution is sufficient elsewhere. Variable spatial resolution is often introduced through particle splitting and coalescence to address this issue. Still, such approaches involve dynamic changes in particle mass and neighbor connectivity, which can compromise conservation properties and numerical stability. In this study, we generalize coordinate transformations commonly used in finite-difference methods to construct an SPH formulation with spatially varying but time-invariant resolution. Our group previously proposed an SPH formulation based on a vertical coordinate transformation, which enabled smooth resolution variation without particle splitting or coalescence, but it was restricted to a single spatial direction and did not examine numerical convergence. Here, we extend the coordinate transformation to all spatial directions, incorporate the resulting formulation into an Eulerian SPH framework, and assess numerical convergence and accuracy using several benchmark problems.