Intersection Properties of Finite Disk Collections

Jesús F. Espinoza; Cynthia G. Esquer-Pérez

doi:10.20944/preprints202401.1083.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 11 January 2024 / Approved: 12 January 2024 / Online: 15 January 2024 (13:45:06 CET)

In this work we study the intersection properties of a finite disk system in the euclidean space. We accomplish this by utilizing subsets of spheres with varying dimensions and analyze specific points within them, referred to as poles. Additionally, we introduce two applications: estimating the common scale factor for the radii that makes the re-scaled disks intersects in a single point, this is the \v{C}ech scale, and constructing the minimal Axis-Aligned Bounding Box (AABB) that encloses the intersection of all disks in the system.

Disk system; Intersection of systems of disks; generalized Čech complex; minimal axis-aligned bounding box

Computer Science and Mathematics, Computational Mathematics

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Intersection Properties of Finite Disk Collections

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