On the Axial Symmetry of 2D Star-Shaped Sets

An essential aspect of the study of shapes is the symmetry because of its importance from a theoretical point of view and its applicability in multiple real-life problems. In this manuscript, the axial symmetry of 2D star-shaped sets is analyzed. For such a purpose, different measures of axial symme...

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Detalles Bibliográficos
Autores: López Díaz, María Concepción, López Díaz, Miguel
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universidad de Oviedo (UNIOVI)
Repositorio:RUO. Repositorio Institucional de la Universidad de Oviedo
Idioma:inglés
OAI Identifier:oai:digibuo.uniovi.es:10651/79080
Acceso en línea:https://hdl.handle.net/10651/79080
https://dx.doi.org/10.1007/S10851-024-01222-W
Access Level:acceso abierto
Palabra clave:Kernel of a star-shaped set
Measure of axial symmetry
Radial function
Star-shaped set
Steiner point
Symmetry axis
Descripción
Sumario:An essential aspect of the study of shapes is the symmetry because of its importance from a theoretical point of view and its applicability in multiple real-life problems. In this manuscript, the axial symmetry of 2D star-shaped sets is analyzed. For such a purpose, different measures of axial symmetry of a star-shaped set are proposed and the concept of a best symmetry axis is also introduced. By means of them, families of symmetry measures for star-shaped sets quantifying the degree of symmetry of a set of that class are introduced. All of them are discussed in detail, providing their main properties and the existence of at least a best axis of symmetry, which could be not unique, for any star-shaped set. Some examples illustrate the concepts and results of the manuscript