Compact storage of additively weighted Voronoi diagrams

Voronoi diagrams and their dual tetrahedral structures are often utilized in various analyses of protein models where atoms are represented as balls. The additively weighted kind of Voronoi diagrams (aw-VD) is particularly useful in this area because it includes the variability of ball size. The dynamic behavior of proteins can be realistically modeled by a simulation of molecular dynamics recording atom positions at discrete snapshots of time. However, aw-VDs for these snapshots require a lot of storage. This is where domain-specific compression could help, but available algorithms are oriented primarily to the compression of ordinary tetrahedral meshes, not to aw-VDs whose dual tetrahedral structure may have anomalies complicating duality inversion and tetrahedral mesh traversal. Therefore, we propose a method that can compactly store the dual tetrahedral structure. The method is built on general ideas of an already known cut-border machine and improves these ideas in several ways so it can be applied to aw-VDs and perform well on protein data.