Geodesic Centroidal Voronoi Tessellations: Theories, Algorithms and Applications

The work focuses on geodesic centroidal Voronoi tessellations, or GCVTs, which are ways to divide up curved surfaces like 3D models into regions where each region has a center point that is the average of the points in it, measured along the surface rather than straight through space. These structures are built directly on the mesh of the 3D object, making them intrinsic to its shape. The authors note that such divisions can help with tasks like finding points quickly or organizing data on images, videos, and 3D models that live on low-dimensional surfaces inside higher-dimensional spaces. They also discuss the difficulties in creating the actual connected structures for these tessellations and figuring out how much time and memory they need. Because the paper is a summary of prior efforts by the same group, it emphasizes potential uses in graphics and vision due to fast lookup properties rather than detailing new proofs or experiments.