Planar lattice walks are combinatorial objects which arise in statistical
mechanics in both the modeling of polymers and percolation theory.
Much work has been done to classify the generating functions of walks
restricted to the first quadrant quarter-plane as algebraic, D-finite, or non-D-finite.
We consider walks restricted to two regions: an eighth-plane wedge and a
three-quarter-plane region. We find combinatorial criteria to define families
of walks with algebraic generating functions in those regions, as well as an
isomorphism that maps nearly one fourth of the walks in the eighth-plane to
walks in the quarter-plane. Further, we find evidence of a family of walks
whose generating functions are non-D-finite in any wedge smaller than a half-plane.