IEICE Technical Committee Submission System
Conference Paper's Information
Online Proceedings
[Sign in]
Tech. Rep. Archives
 Go Top Page Go Previous   [Japanese] / [English] 

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
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)
Download PDF COMP2012-25

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  
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)
3rd Author's Name  
3rd Author's Affiliation ()
4th Author's Name  
4th Author's Affiliation ()
5th Author's Name  
5th Author's Affiliation ()
6th Author's Name  
6th Author's Affiliation ()
7th Author's Name  
7th Author's Affiliation ()
8th Author's Name  
8th Author's Affiliation ()
9th Author's Name  
9th Author's Affiliation ()
10th Author's Name  
10th Author's Affiliation ()
11th Author's Name  
11th Author's Affiliation ()
12th Author's Name  
12th Author's Affiliation ()
13th Author's Name  
13th Author's Affiliation ()
14th Author's Name  
14th Author's Affiliation ()
15th Author's Name  
15th Author's Affiliation ()
16th Author's Name  
16th Author's Affiliation ()
17th Author's Name  
17th Author's Affiliation ()
18th Author's Name  
18th Author's Affiliation ()
19th Author's Name  
19th Author's Affiliation ()
20th Author's Name  
20th Author's Affiliation ()
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 

[Return to Top Page]

[Return to IEICE Web Page]

The Institute of Electronics, Information and Communication Engineers (IEICE), Japan