  An interesting class of orthogonal representations consists of the so-called
turn-regular ones, i.e., those that do not contain any pair of reflex corners
that "point to each other" inside a face. For such a representation H it is
possible to compute in linear time a minimum-area drawing, i.e., a drawing of
minimum area over all possible assignments of vertex and bend coordinates of H.
In contrast, finding a minimum-area drawing of H is NP-hard if H is
non-turn-regular. This scenario naturally motivates the study of which graphs
admit turn-regular orthogonal representations. In this paper we identify
notable classes of biconnected planar graphs that always admit such
representations, which can be computed in linear time. We also describe a
linear-time testing algorithm for trees and provide a polynomial-time algorithm
that tests whether a biconnected plane graph with "small" faces has a
turn-regular orthogonal representation without bends.
