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| 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 |
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| 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) | |
| Download PDF | COMP2012-25 |
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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 | Author-1 |
| Date Time | 2012-06-21 17:10:00 |
| Presentation Time | 25 minutes |
| Registration for | COMP |
| Paper # | COMP2012-25 |
| Volume (vol) | vol.112 |
| Number (no) | no.93 |
| Page | pp.103-109 |
| #Pages | 7 |
| Date of Issue | 2012-06-14 (COMP) |
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