Intersection Properties of Finite Disk Collections

Jesús F. Espinoza () and Cynthia G. Esquer-Pérez
Additional contact information
Jesús F. Espinoza: Departamento de Matemáticas, Universidad de Sonora, Hermosillo 83000, Sonora, Mexico
Cynthia G. Esquer-Pérez: Departamento de Matemáticas, Universidad de Sonora, Hermosillo 83000, Sonora, Mexico

Mathematics, 2024, vol. 12, issue 4, 1-20

Abstract: In this article, we study the intersection of a finite collection of disks in Euclidean space by examining spheres of various dimensions and their poles (extreme values with respect to canonical projections) contained within the intersection’s boundary. We derive explicit formulae for computing these extreme values and present two applications. The first application involves computing the smallest common rescaling factor for the radii of the disk system, which brings the system to a single point of intersection. This calculation allows us to compute the generalized Čech filtration, a crucial tool for the topological data analysis of weighted point clouds. The second application focuses on determining the minimal Axis-Aligned Bounding Box (AABB) for the intersection of a finite collection of disks in Euclidean space, addressing a significant problem in computational geometry. We consider that this work aims to contribute to the fields of topological data analysis and computational geometry by providing new tools for analyzing complex geometric structures.

Keywords: disk system; intersection of systems of disks; generalized ?ech complex; minimal axis-aligned bounding box (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/4/547/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/4/547/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:4:p:547-:d:1337050

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().