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Paper Abstract and Keywords
Presentation 2012-06-21 17:10
Notes on weighted Delaunay triangulations and discrete Ricci flow -- Relation between weighted Delaunay triangulations and circle packing metrics --
Toshihiro Tanuma, Hiroshi Imai (Univ. of Tokyo) COMP2012-25
Abstract (in Japanese) (See Japanese page) 
(in English) This research is related to weighted Delaunay triangulations and a discrete Ricci flow. Specifically, we consider the following two topics about the relation between weighted Delaunay triangulations and circle packing metrics. First, we investigate a condition that a triangulation given by a circle packing metric is a weighted Delaunay triangulation. As one of its solutions, we show that the triangulation becomes a weighted Delaunay triangulation when, for any edge, the intersection angle of circles corresponding to its endpoints is less than ϕ/2. Secondly, we state necessary and sufficient conditions for the existence of weighted Delaunay triangulations and the uniqueness of them by using circle packing metrics and the discrete Ricci flow. This is another proof of Springborn’s result about the existence and uniqueness of weighted Delaunay triangulations.
Keyword (in Japanese) (See Japanese page) 
(in English) Weighted Delaunay triangulation / Discrete Ricci flow / Circle packing metric / Circle pattern / / / /  
Reference Info. IEICE Tech. Rep., vol. 112, no. 93, COMP2012-25, pp. 103-109, June 2012.
Paper # COMP2012-25 
Date of Issue 2012-06-14 (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 2012-06-21 - 2012-06-21 
Place (in Japanese) (See Japanese page) 
Place (in English) Hokkaido University 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To COMP 
Conference Code 2012-06-COMP 
Language English (Japanese title is available) 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Notes on weighted Delaunay triangulations and discrete Ricci flow 
Sub Title (in English) Relation between weighted Delaunay triangulations and circle packing metrics 
Keyword(1) Weighted Delaunay triangulation  
Keyword(2) Discrete Ricci flow  
Keyword(3) Circle packing metric  
Keyword(4) Circle pattern  
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1st Author's Name Toshihiro Tanuma  
1st Author's Affiliation University of Tokyo (Univ. of Tokyo)
2nd Author's Name Hiroshi Imai  
2nd Author's Affiliation University of Tokyo (Univ. of Tokyo)
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Speaker
Date Time 2012-06-21 17:10:00 
Presentation Time 25 
Registration for COMP 
Paper # IEICE-COMP2012-25 
Volume (vol) IEICE-112 
Number (no) no.93 
Page pp.103-109 
#Pages IEICE-7 
Date of Issue IEICE-COMP-2012-06-14 


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