research-article

Consistent digital rays

Authors:

Martin Nöllenburg,

Takeshi TokuyamaAuthors Info & Claims

SCG '08: Proceedings of the twenty-fourth annual symposium on Computational geometry

Pages 355 - 364

https://doi.org/10.1145/1377676.1377737

Published: 09 June 2008 Publication History

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 Θ(log n) bound in the n x 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.

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Cited By

Anzai SChun JKasai RKorman MTokuyama T(2010)Effect of corner information in simultaneous placement of K rectangles and tableauxProceedings of the 16th annual international conference on Computing and combinatorics10.5555/1886811.1886844(235-243)Online publication date: 19-Jul-2010
https://dl.acm.org/doi/10.5555/1886811.1886844
Anzai SChun JKasai RKorman MTokuyama T(2010)Effect of Corner Information in Simultaneous Placement of K Rectangles and TableauxComputing and Combinatorics10.1007/978-3-642-14031-0_27(235-243)Online publication date: 2010
https://doi.org/10.1007/978-3-642-14031-0_27
Chun JKasai RKorman MTokuyama T(2009)Algorithms for Computing the Maximum Weight Region Decomposable into Elementary ShapesProceedings of the 20th International Symposium on Algorithms and Computation10.1007/978-3-642-10631-6_117(1166-1174)Online publication date: 5-Dec-2009
https://dl.acm.org/doi/10.1007/978-3-642-10631-6_117

Index Terms

Consistent digital rays
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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cover image ACM Conferences

SCG '08: Proceedings of the twenty-fourth annual symposium on Computational geometry

June 2008

304 pages

ISBN:9781605580715

DOI:10.1145/1377676

Program Chair:
Monique Teillaud
INRIA Sophia Antipolis - Méditerranée, France

Copyright © 2008 ACM.

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Published: 09 June 2008

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SoCG08

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SoCG08: 24th Annual Symposium on Computational Geometry

June 9 - 11, 2008

MD, College Park, USA

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Overall Acceptance Rate 625 of 1,685 submissions, 37%

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Cited By

Anzai SChun JKasai RKorman MTokuyama T(2010)Effect of corner information in simultaneous placement of K rectangles and tableauxProceedings of the 16th annual international conference on Computing and combinatorics10.5555/1886811.1886844(235-243)Online publication date: 19-Jul-2010
https://dl.acm.org/doi/10.5555/1886811.1886844
Anzai SChun JKasai RKorman MTokuyama T(2010)Effect of Corner Information in Simultaneous Placement of K Rectangles and TableauxComputing and Combinatorics10.1007/978-3-642-14031-0_27(235-243)Online publication date: 2010
https://doi.org/10.1007/978-3-642-14031-0_27
Chun JKasai RKorman MTokuyama T(2009)Algorithms for Computing the Maximum Weight Region Decomposable into Elementary ShapesProceedings of the 20th International Symposium on Algorithms and Computation10.1007/978-3-642-10631-6_117(1166-1174)Online publication date: 5-Dec-2009
https://dl.acm.org/doi/10.1007/978-3-642-10631-6_117

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