A Note on Rectilinearity and Angular Resolution

Abstract

We connect two aspects of graph drawing, namely angular resolution, and the possibility to draw with all angles an integer multiple of 2π/ d. A planar graph with angular resolution at least π/2 can be drawn with all angles an integer multiple of π/2 (rectilinear). For d ≠ 4, d > 2, an angular resolution of 2π/ d does not imply that the graph can be drawn with all angles an integer multiple of 2π/ d. We argue that the exceptional situation for d=4 is due to the absence of triangles in the rectangular grid.

Keywords : Rectilinear drawing, plane graph, angular resolution, integer flow.