Before revision:  In order to prove these results, we strengthen the result of Da Lozzo et al., and prove that a planar graph G and a single pseudoline \mathcal{C have an aligned drawing with a prescribed convex drawing of the outer face.
After revision:  In order to prove these results, we strengthen the result of Da Lozzo et al., and prove that a planar graph G and a single pseudoline \mathcal L have an aligned drawing with a prescribed convex drawing of the outer face.