REGULARITY MEASURES FOR CONVEX POLYGONS
R. Chalmeta, F. Hurtado, V. Sacristán, M. Saumell

We propose new measures to evaluate to which extent the shape of a given convex polygon is close to be regular, focusing on a range of characteristics of regularity: optimal ratio area-perimeter, equality of angles and edge lengths, regular fitting, angular and areal symmetry. We prove that our measures satisfy several reasonable requirements that guarantee them to be well defined, and provide algorithms for their efficient computation. We supply experimental results on all the proposed measures on a wide set of polygons. The project includes an application for computing and visualizing all the measures.

• Publications
  
• Master thesis of Maria Saumell (in Catalan). Extended abstract from Proc. 25th European Workshop in Computational Geometry, pp. 125-129, 2009 (in English).
• Master thesis of Ramon Chalmeta (in Catalan). Extended abstract from Proc. XIV Spanish Meeting on Computational Geometry, pp. 71-74, 2011 (in English).
• R. Chalmeta, F. Hurtado, V. Sacristán, M. Saumell. Measuring regularity of convex polygons. In Computer-Aided Design, Vol. 45, pp. 93–104, 2013.
  
• Collection of convex polygons with their mesurement results (see the master thesis of Ramon Chalmeta for detais on the files format and on the description of the collection of polygons).
  
• Download application
• Requirements
• Linux OS (Ubuntu 9.10 or more)
• Runing instructions
1. Download and unzip the folder lib.zip and copy its content into the /usr/lib folder of your computer.
2. Download and unzip the folder Aplicacio.zip anywhere in your computer. 
3. Run the file named PFC, which is located in the folder Aplicacio/Executable/app.
   
• User's guide (in Catalan).