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Paper Abstract and Keywords
Presentation 2008-03-10 14:25
Consistent Digital Rays
Jinhee Chun, Matias Korman (Tohoku Univ.), Martin Noellenburg (Karlsruhe Univ.), Takeshi Tokuyama (Tohoku Univ.) COMP2007-61
Abstract (in Japanese) (See Japanese page) 
(in English) Given a fixed origin $o$ in the $d$-dimensional grid, we give a novel definition of {\em digital rays} $\dig(op)$ from $o$ to each grid point $p$. Each digital ray $\dig(op)$ approximates the Euclidean line segment $\seg{op}$ 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 $\Theta(\log n)$ bound in the $n\times n$ 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 $O(1)$.
Keyword (in Japanese) (See Japanese page) 
(in English) Digital Ray / Approximation Algorithm / Discrepancy / Computational Geometry / / / /  
Reference Info. IEICE Tech. Rep., vol. 107, no. 537, COMP2007-61, pp. 39-46, March 2008.
Paper # COMP2007-61 
Date of Issue 2008-03-03 (COMP) 
ISSN Print edition: ISSN 0913-5685    Online edition: ISSN 2432-6380
Copyright
and
reproduction		 All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034)
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Conference Information
Committee COMP  
Conference Date 2008-03-10 - 2008-03-10 
Place (in Japanese) (See Japanese page) 
Place (in English)  
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To COMP 
Conference Code 2008-03-COMP 
Language English 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Consistent Digital Rays 
Sub Title (in English)  
Keyword(1) Digital Ray  
Keyword(2) Approximation Algorithm  
Keyword(3) Discrepancy  
Keyword(4) Computational Geometry  
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1st Author's Name Jinhee Chun  
1st Author's Affiliation Tohoku University (Tohoku Univ.)
2nd Author's Name Matias Korman  
2nd Author's Affiliation Tohoku University (Tohoku Univ.)
3rd Author's Name Martin Noellenburg  
3rd Author's Affiliation Karlsruhe University (Karlsruhe Univ.)
4th Author's Name Takeshi Tokuyama  
4th Author's Affiliation Tohoku University (Tohoku Univ.)
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Speaker Author-4 
Date Time 2008-03-10 14:25:00 
Presentation Time 25 minutes 
Registration for COMP 
Paper # COMP2007-61 
Volume (vol) vol.107 
Number (no) no.537 
Page pp.39-46 
#Pages 8 
Date of Issue 2008-03-03 (COMP) 

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