  We describe a high order technique to generate quadrilateral decompositions
and meshes for complex two dimensional domains using spectral elements in a
field guided procedure. Inspired by cross field methods, we never actually
compute crosses. Instead, we compute a high order accurate guiding field using
a continuous Galerkin (CG) or discontinuous Galerkin (DG) spectral element
method to solve a Laplace equation for each of the field variables using the
open source code Nektar++. The spectral method provides spectral convergence
and sub-element resolution of the fields. The DG approximation allows meshing
of corners that are not multiples of $\pi/2$ in a discretization consistent
manner, when needed. The high order field can then be exploited to accurately
find irregular nodes, and can be accurately integrated using a high order
separatrix integration method to avoid features like limit cycles. The result
is a mesh with naturally curved quadrilateral elements that do not need to be
curved a posteriori to eliminate invalid elements. The mesh generation
procedure is implemented in the open source mesh generation program NekMesh.
