Measuring regularity of convex polygons

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.

► Measures to evaluate to which extent a convex polygon is close to be regular.
► Different geometric characteristics of regularity are used to define the measures.
► The measures satisfy requirements that guarantee them to be well defined.
► Algorithms to compute the measures are described, and their complexity is analyzed.
► Experimental results are shown and discussed, for all the proposed measures.