  We prove a noncompact version of Haagerup and R{\o}rdam's result about
continuous paths of the rotation $C^*$-algebras. It gives a continuous Moyal
deformation of Euclidean plane. Moveover, the construction is generalized to
noncommutative Euclidean spaces of dimension $d\ge 2$. As a corollary, we
obtain Lip$^{\frac12}$ continuous maps for the generators of noncommutative
$d$-tori.
