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.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

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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