We investigate the bend minimization problem with respect to a new drawing style called
orthogonally convex drawing
, which is orthogonal drawing with an additional requirement that each inner face is drawn as an
orthogonally convex polygon
. For the class of bi-connected plane graphs of maximum degree 3, we give a necessary and sufficient condition for the existence of a no-bend orthogonally convex drawing, which in turn, enables a linear time algorithm to check and construct such a drawing if one exists. We also develop a flow network formulation for bend-minimization in orthogonally convex drawings, yielding a polynomial time solution for the problem. An interesting application of our orthogonally convex drawing is to characterize internally triangulated plane graphs that admit floorplans using only orthogonally convex modules subject to certain boundary constraints.