  We define a two-dimensional space called the spinor-plane, where all spinors
that can be decomposed in terms of Restricted Inomata-McKinley (RIM) spinors
reside, and describe some of its properties. Some interesting results
concerning the construction of RIM-decomposable spinors emerge when we look at
them by means of their spinor-plane representations. We show that, in
particular, this space accomodates a bijective linear map between
mass-dimension-one and Dirac spinor fields. As a highlight result, the
spinor-plane enables us to construct homotopic equivalence relations, revealing
an algebraic-topological link between these spinors. In the end, we develop a
simple method that provides the categorization of RIM-decomposable spinors in
the Lounesto classification, working by means of spinor-plane coordinates,
which avoids the often hard work of analising the bilinear covariant structures
one by one.
