The Program TorusDraw

TorusDraw

The program TorusDraw is devoted to drawing Toroidal maps on the plane.
The best way to represent a toroidal map is to take its universal cover and put it on the plane
The maps are given combinatorially and the program extract a meaningful set of real coordinates by a circle packing algorithm explained in the paper Circle packings of maps in polynomial time by Bojan Mohar
The main feature of this program are:
- It is a matlab program that does not need any toolbox. So, TorusDraw can export to postscript, bmp, etc.
- It allows one to choose to draw the edges, the circles or the dual edges and dual circles.
- The minimization of the error functionnal is done by a gradient method
- The three files necessary for one minimization are created by the plangraph function PlanGraphToTorusDraw
Examples of usage The example below are done for a specific structure: thetest.plg, thetest.spa, thetest.bip
- using the command
  TD_CreateGraph('thetest',[-10 10 -10 10],[1 0 0 0],[0 0 1 0 0 0],[0 0],[1 0;0 1])
  
  edges
- using the command
  TD_CreateGraph('thetest',[-10 10 -10 10],[1 0 0 0],[0 0 1 1 0 0],[0 0],[1 0;0 1])
  
  edges + circles
- using the command
  TD_CreateGraph('thetest',[-10 10 -10 10],[1 0 0 0],[1 0 0 1 0 0],[0 0],[1 0;0 1])
  
  dual edges + circles
- using the command
  TD_CreateGraph('thetest',[-10 10 -10 10],[1 0 0 0],[0 1 1 0 0 0],[0 0],[1 0;0 1])
  
  edges + dual circles
- using the command
  TD_CreateGraph('thetest',[-10 10 -10 10],[1 0 0 0],[0 1 1 0 0 0],[0 0],[1 0;0 1])
  
  radial graph (map obtained by taking as vertex set the set of vertices and faces of the original map and edge set being of the form (v, F) if the vertex v belong to the face F)
- using the command
  TD_CreateGraph('thetest',[-10 10 -10 10],[1 0 0 0],[0 1 1 0 0 0],[0 0],[1 0;0 1])
  
  edges + fundamental domain

TorusDraw

Illustrations