Simultaneous straight-line drawing of a planar graph and its rectangular dual

TL;DR

This paper presents a method to produce simultaneous straight-line drawings of a planar graph and its rectangular dual, ensuring the primal graph is embedded within the dual's rectangular layout.

Contribution

It introduces a technique to resize the rectangular dual to accommodate a planar straight-line drawing of the primal graph, addressing a longstanding visualization challenge.

Findings

Rectangular duals can be resized to host primal straight-line drawings.

The approach maintains planarity and dual relationships.

Provides a constructive method for simultaneous graph and dual visualization.

Abstract

A natural way to represent on the plane both a planar graph and its dual is to follow the definition of the dual, thus, to place vertices inside their corresponding primal faces, and to draw the dual edges so that they only cross their corresponding primal edges. The problem of constructing such drawings has a long tradition when the drawings of both primal and dual are required to be straight-line. We consider the same problem for a planar graph and its rectangular dual. We show that the rectangular dual can be resized to host a planar straight-line drawing of its primal.