### Abstract

Given a fixed origin o in the d-dimensional grid, we give a novel definition of digital rays dig(op) from o to each grid point p. Each digital ray dig(op) approximates the Euclidean line segment op between o and p. The set of all digital rays satisfies a set of axioms analogous to the Euclidean axioms. We measure the approximation quality by the maximum Hausdorff distance between a digital ray and its Euclidean counterpart and establish an asymptotically tight ⊖ (log n) bound in the n × n grid. The proof of the bound is based on discrepancy theory and a simple construction algorithm. Without a monotonicity property for digital rays the bound is improved to O(1). Digital rays enable us to define the family of digital star-shaped regions centered at o which we use to design efficient algorithms for image processing problems.

Original language | English |
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Title of host publication | Proceedings of the 24th Annual Symposium on Computational Geometry 2008, SCG'08 |

Pages | 355-364 |

Number of pages | 10 |

DOIs | |

Publication status | Published - 2008 Dec 12 |

Event | 24th Annual Symposium on Computational Geometry, SCG'08 - College Park, MD, United States Duration: 2008 Jun 9 → 2008 Jun 11 |

### Publication series

Name | Proceedings of the Annual Symposium on Computational Geometry |
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### Other

Other | 24th Annual Symposium on Computational Geometry, SCG'08 |
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Country | United States |

City | College Park, MD |

Period | 08/6/9 → 08/6/11 |

### Keywords

- Digital geometry
- Discrete geometry
- Star-shaped regions
- Tree embedding

### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Computational Mathematics

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## Cite this

*Proceedings of the 24th Annual Symposium on Computational Geometry 2008, SCG'08*(pp. 355-364). (Proceedings of the Annual Symposium on Computational Geometry). https://doi.org/10.1145/1377676.1377737