simquad -- generate uniform simple quadrangulations

1. Introduction

This project implements a random generator for uniform simple quadrangulations of the 2-sphere with a given number of quadrangles. It is based on the bijection between simple quadrangulations and 1-blossoming trees by Fusy (2010, PhD thesis at École Polytechnique), and a generating procedure for random blossoming trees by Addario-Berry and Albenque (2017, The Annals of Probability).

1. Usage

Usage: simquad [OPTION...] simquad -- generate uniform simple quadrangulations

-N, --num=NUM Simulate NUM many samples. -r, --randgen=RANDGEN Use the pseudo random generator RANDGEN. Available options are taus2, gfsr4, mt19937, ranlux, ranlxs0, ranlxs1, ranlxs2, ranlxd1, ranlxd2, mrg, cmrg, ranlux389. The default is taus2. -s, --size=SIZE Generate a uniform planted simple quadrangulation with s >= 6 faces, s + 2 vertices, and 2s edges. Has to be greater than or equal to six. -S, --seed=SEED Specify the seed of the random generator in the first thread. Thread number k will receive SEED + k - 1 as seed. The default is to set SEED to the systems timestamp (in seconds). -t, --threads=THREADS Distribute the workload on THREADS many threads. The default value is the number of CPU cores. -?, --help Give this help list --usage Give a short usage message -V, --version Print program version

Mandatory or optional arguments to long options are also mandatory or optional for any corresponding short options.

Each generated map is represented by a list of half edge data structures in the format {next, previous, opposite}. The total output is a list of lists, each element corresponding to a map.

1. Example

simquad -s 10 {{{32,34,2},{3,9,1},{4,2,38},{9,3,5},{6,8,4},{7,5,37},{8,6,22},{5,7,15},{2,4,10},{11,40,9},{12,10,14},{40,11,13},{14,16,12},{15,13,11},{16,14,8},{13,15,17},{18,24,16},{19,17,21},{24,18,20},{21,23,19},{22,20,18},{23,21,7},{20,22,30},{17,19,25},{26,39,24},{27,25,29},{39,26,28},{29,31,27},{30,28,26},{31,29,23},{28,30,32},{33,1,31},{34,32,36},{1,33,35},{36,38,34},{37,35,33},{38,36,6},{35,37,3},{25,27,40},{10,12,39}}}

1. LICENSE

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/.

Simquad

Install / Use

README