Measuring regularity of convex polygons

Authors:
Ramon Chalmeta;Ferran Hurtado;Vera SacristáN;Maria Saumell
Affiliations:
Departament de Matemítica Aplicada II, Universitat Politècnica de Catalunya, Jordi Girona 1-3, 08034 Barcelona, Spain;Departament de Matemítica Aplicada II, Universitat Politècnica de Catalunya, Jordi Girona 1-3, 08034 Barcelona, Spain;Departament de Matemítica Aplicada II, Universitat Politècnica de Catalunya, Jordi Girona 1-3, 08034 Barcelona, Spain;Department of Applied Mathematics, Charles University, Malostranské nám. 25, 118 00 Praha 1, Czech Republic
Venue:
Computer-Aided Design
Year:
2013

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Abstract

We propose several 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 a number of reasonable requirements that guarantee them to be well defined, and provide efficient algorithms for their computation. All these algorithms have been implemented, and we provide experimental results on all the proposed measures.