TorusDraw

TorusDraw is a Matlab-based program designed for drawing toroidal maps on a 2D plane by representing their universal covers. It utilizes advanced circle packing algorithms to transform combinatorial map data into meaningful geometric coordinates.

Core Features

Pure Matlab Implementation: Does not require any external toolboxes. Supports exports to PostScript, BMP, and other standard formats.
Flexible Visualization: Choose to render edges, primary circles, dual edges, or dual circles.
Numerical Optimization: Employs a gradient-based method to minimize the error functional of the circle packing.
Integration: Seamlessly works with the PlanGraph package via the PlanGraphToTorusDraw function to generate necessary input files.

Algorithm Reference

The coordinate extraction is based on the polynomial-time circle packing methodology defined by:

Bojan Mohar, "Circle packings of maps in polynomial time", European Journal of Combinatorics (1997).

Examples & Usage

The following examples demonstrate different visualization modes using the test structure: thetest.plg, thetest.spa, thetest.bip.

Edges Only

TD_CreateGraph('thetest',[-10 10 -10 10],[1 0 0 0],[0 0 1 0 0 0],[0 0],[1 0;0 1])

Edges + Circles

TD_CreateGraph('thetest',[-10 10 -10 10],[1 0 0 0],[0 0 1 1 0 0],[0 0],[1 0;0 1])

Radial Graph

Map obtained by taking the union of vertices and faces as the new vertex set.

TD_CreateGraph('thetest',[-10 10 -10 10],[1 0 0 0],[0 1 1 0 0 0],[0 0],[1 0;0 1])

Illustrations

Download

TorusDraw Package (ZIP)