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...
| Autores: | , |
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| Formato: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Recursos: | Universidad de Oviedo (UNIOVI) |
| Repositorio: | RUO. Repositorio Institucional de la Universidad de Oviedo |
| Idioma: | inglés |
| OAI Identifier: | oai:digibuo.uniovi.es:10651/76377 |
| Acesso em linha: | https://hdl.handle.net/10651/76377 https://dx.doi.org/10.1007/s10851-024-01222-w |
| Access Level: | acceso abierto |
| Palavra-chave: | Kernel of a star-shaped set · Measure of axial symmetry · Radial function · Star-shaped set · Steiner point · Symmetry axis |
| Resumo: | 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. |
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