Some Regularity Measures for Convex Polygons
نویسندگان
چکیده
We propose new measures to evaluate to which extent the shape of a given convex polygon is close to the shape of some regular polygon. We prove that our parameters satisfy several reasonable requirements and provide algorithms for their efficient computation. The properties we mostly focus on are the facts that regular polygons are equilateral, equiangular and have radial symmetry.
منابع مشابه
Measuring regularity of convex polygons: experimental results
We aim to evaluate to which extent the shape of a given convex polygon is close to be regular, focusing on diverse characteristics of regularity: optimal ratio area-perimeter, equality of angles and edge lengths, regular fitting, angular and areal symmetry. We have designed and implemented algorithms to compute the resulting measures and we provide and discuss experimental results on a large se...
متن کاملA method for the enumeration of various classes of column-convex polygons
2 Abstract. We present a new method that allows to enumerate various classes of column-convex polygons, according to their perimeter and their area. The rst step of this method leads to a functional equation which deenes implicitly the generating function of the class under consideration. The second step consists in solving this equation. We apply systematically our method to all the usual clas...
متن کاملQuadratic serendipity finite elements on polygons using generalized barycentric coordinates
We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon, our construction produces 2n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n(n + 1)/2 basis functions known to obtain quadratic convergence....
متن کاملMeasuring Convexity via Convex Polygons
This paper describes a general approach to compute a family of convexity measures. Inspired by the use of geometric primitives (such as circles) which are often fitted to shapes to approximate them, we use convex polygons for this task. Convex polygons can be generated in many ways, and several are demonstrated here. These polygons are scaled and translated to ensure that they fit the input sha...
متن کاملDecompositions, Partitions, and Coverings with Convex Polygons and Pseudo-triangles
We propose a novel subdivision of the plane that consists of both convex polygons and pseudo-triangles. This pseudo-convex decomposition is significantly sparser than either convex decompositions or pseudo-triangulations for planar point sets and simple polygons. We also introduce pseudo-convex partitions and coverings. We establish some basic properties and give combinatorial bounds on their c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009