Analytical Honeycomb Geometry for Raster and Volume Graphics

In this paper we investigate the advantages of using hexagonal grids in raster and volume graphics. In 2D, we present a hexagonal graphical model based on a hexagonal grid. In 3D, we introduce two honeycomb graphical models in which the voxels are hexagonal prisms, and we show that these are the only possible models under certain reasonable conditions. In the framework of the proposed models, we design twoand three-dimensional analytical honeycomb geometry of linear objects, as well as of circles and spheres. We demonstrate certain advantages of the honeycomb models and address algorithmic and complexity issues.