3 papers
math.NA2025
Centroidal Voronoi Tessellations as Electrostatic Equilibria: A Generalized Thomson Problem in Convex Domains
Zachary Mullaghy
We present a variational framework in which Centroidal Voronoi Tessellations (CVTs) arise as local minimizers of a generalized electrostatic energy functional. By modeling interior…
math.NA2025
The Geometric Refinement Transform: A Novel Uncountably Infinite Transform Space
Zachary Mullaghy
This work introduces a novel and general class of continuous transforms based on hierarchical Voronoi based refinement schemes. The resulting transform space generalizes classical…
math.NA2025
Centroidal Voronoi Refinement in the Geometric Refinement Transform: Symmetry, Stability, and Optimal Reconstruction
Zachary Mullaghy
We extend the Geometric Refinement Transform (GRT) by introducing centroidal Voronoi tessellations (CVTs) into the refinement process, enhancing symmetry, reconstruction accuracy,…