  A plane graph is rectilinear planar if it admits an embedding-preserving
straight-line drawing where each edge is either horizontal or vertical. We
prove that rectilinear planarity testing can be solved in optimal $O(n)$ time
for any plane series-parallel graph $G$ with $n$ vertices. If $G$ is
rectilinear planar, an embedding-preserving rectilinear planar drawing of $G$
can be constructed in $O(n)$ time. Our result is based on a characterization of
rectilinear planar series-parallel graphs in terms of intervals of orthogonal
spirality that their components can have, and it leads to an algorithm that can
be easily implemented.
