Digital planarity - A review

Digital planarity is defined by digitizing Euclidean planes in the three-dimensional digital space of voxels; voxels are given either in the grid point or the grid cube model. The paper summarizes results (also including most of the proofs) about different aspects of digital planarity, such as self-similarity, supporting or separating Euclidean planes, characterizations in arithmetic geometry, periodicity, connectivity, and algorithmic solutions. The paper provides a uniform presentation, which further extends and details a recent book chapter in (Klette and Rosenfeld 2004). Key words: digital planes, digital geometry, arithmetic geometry, 2D array periodicity, Sturmian words, geometric algorithms 1991 MSC: 52C99, 62H35, 65D18, 68U05

• Type: Journal
• Year: 2007
• Where: DAM
• Authors: Valentin E. Brimkov, David Coeurjolly, Reinhard Klette
• Keywords: Arithmetic Geometry, DAM 2007, Digital Planarity, Euclidean Planes