  Given a planar graph $G$ and an integer $b$, OrthogonalPlanarity is the
problem of deciding whether $G$ admits an orthogonal drawing with at most $b$
bends in total. We show that OrthogonalPlanarity can be solved in polynomial
time if $G$ has bounded treewidth. Our proof is based on an FPT algorithm whose
parameters are the number of bends, the treewidth and the number of degree-2
vertices of $G$. This result is based on the concept of sketched orthogonal
representation that synthetically describes a family of equivalent orthogonal
representations. Our approach can be extended to related problems such as
HV-Planarity and FlexDraw. In particular, both OrthogonalPlanarity and
HV-Planarity can be decided in $O(n^3 \log n)$ time for series-parallel graphs,
which improves over the previously known $O(n^4)$ bounds.
