  Three-body systems that are continuously squeezed from a three-dimensional
(3D) space into a two-dimensional (2D) space are investigated. Such a squeezing
can be obtained by means of an external confining potential acting along a
single axis. However, this procedure can be numerically demanding, or even
undoable, especially for large squeezed scenarios. An alternative is provided
by use of the dimension $d$ as a parameter that changes continuously within the
range $2\leq d \leq 3$. The simplicity of the $d$-calculations is exploited to
investigate the evolution of three-body states after progressive confinement.
The case of three identical spinless bosons with relative $s$-waves in 3D, and
a harmonic oscillator squeezing potential is considered. We compare results
from the two methods and provide a translation between them, relating
dimension, squeezing length, and wave functions from both methods. All
calculations are then possible entirely within the simpler $d$-method, but
simultaneously providing the equivalent geometry with the external potential.
