2023/08/31 by Paolo Amore, Amore, Paolo, Valeria Hernández +6 · 1 citation
Computer Science · #Computational Geometry (cs.CG) #Computational Geometry and Mesh Generation #Digital Image Processing Techniques #FOS: Computer and information sciences #FOS: Physical sciences #Soft Condensed Matter (cond-mat.soft) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2308.16523
openalex publication_date 2023/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe an algorithm that allows one to find dense packing configurations of a number of congruent disks in arbitrary domains in two or more dimensions. We have applied it to a large class of two dimensional domains such as rectangles, ellipses, crosses, multiply connected domains and even to the cardioid. For many of the cases that we have studied no previous result was available. The fundamental idea in our approach is the introduction of "image" disks, which allows one to work with a fixed container, thus lifting the limitations of the packing algorithms of \citeNurmela97,Amore21,Amore23. We believe that the extension of our algorithm to three (or higher) dimensional containers (not considered here) can be done straightforwardly.