  A special approach to examine spinor structure of 3-space is proposed. It is
based on the use of the concept of a spatial spinor defined through taking the
square root of a real-valued 3-vector. Two sorts of spatial spinor according to
P-orientation of an initial 3-space are introduced: properly vector or pseudo
vector one. These spinors, \eta and \xi, turned out to be different functions
of Cartesian coordinates. To have a spinor space model, you ought to use a
doubling vector space. The main idea is to develop some mathematical technique
to work with such extended models. Two sorts of spatial spinors are examined
with the use of curvilinear coordinates (y_{1},y_{2},y_{3}): cylindrical
parabolic, spherical and parabolic ones. Transition from vector to spinor
models is achieved by doubling initial parameterizing domain
G(y_{1},y_{2},y_{3}) \Longrightarrow \tilde{G}(y_{1},y_{2},y_{3}) with new
identification rules on the boundaries. Different spinor space models are built
on explicitly different spinor fields \xi(y) and \eta(y). Explicit form of the
mapping spinor field \eta(y) of pseudo vector model into spinor \xi(y) of
properly vector one is given, it contains explicitly complex conjugation.
