We study straight-line drawings of planar graphs with few segments and few slopes. Optimal results are obtained for all trees. Tight bounds are obtained for outerplanar graphs, 2-trees, and planar 3-trees. We prove that every 3-connected plane graph on n vertices has a plane drawing with at most 52n segments and at most 2n slopes. We prove that every cubic 3-connected plane graph has a plane drawing with three slopes (and three bends on the outerface). In a companion paper, drawings of non-planar graphs with few slopes are also considered.
Dujmovic, V., Eppstein, D., Suderman, M., & Wood, D. R. (2007). Drawings of planar graphs with few slopes and segments. Computational Geometry: Theory and Applications, 38(3), 194-212. https://doi.org/10.1016/j.comgeo.2006.09.002