Abstract:
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). [This report has been updated in April 2006, at the end of the reviewing process of its journal publication. Results stated are still as in the original 2004 report, but the report was improved at several places due to reviewers comments.]
Description:
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