  In this article, for positive integers $n\geq m\geq 1$, the parameter spaces
for the isomorphism classes of the generic point arrangements of cardinality
$n$, and the antipodal point arrangements of cardinality $2n$ in the Eulidean
space $\mathbb{R}^m$ are described using the space of totally nonzero
Grassmannian $Gr^{tnz}_{mn}(\mathbb{R})$. A stratification
$\mathcal{S}^{tnz}_{mn}(\mathbb{R})$ of the totally nonzero Grassmannian
$Gr^{tnz}_{mn}(\mathbb{R})$ is mentioned and the parameter spaces are
respectively expressed as quotients of the space
$\mathcal{S}^{tnz}_{mn}(\mathbb{R})$ of strata under suitable actions of the
symmetric group $S_n$ and the semidirect product group $(\mathbb{R}^*)^n\rtimes
S_n$. The cardinalities of the space $\mathcal{S}^{tnz}_{mn}(\mathbb{R})$ of
strata and of the parameter spaces $S_n\backslash
\mathcal{S}^{tnz}_{mn}(\mathbb{R}), ((\mathbb{R}^*)^n\rtimes S_n)\backslash
\mathcal{S}^{tnz}_{mn}(\mathbb{R})$ are enumerated in dimension $m=2$.
Interestingly enough, the enumerated value of the isomorphism classes of the
generic point arrangements in the Euclidean plane is expressed in terms of the
number theoretic Euler-totient function. The analogous enumeration questions
are still open in higher dimensions for $m\geq 3$.
