Lecture Notes in Computer Science Edited by G. Goos, J. Hartmanis and J. van Leeuwen
2098
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Berlin Heidelberg New York Barcelona Hong Kong London Milan Paris Singapore Tokyo
Jin Akiyama Mikio Kano Masatsugu Urabe (Eds.)
Discrete and Computational Geometry Japanese Conference, JCDCG 2000 Tokyo, Japan, November 22-25, 2000 Revised Papers
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Series Editors Gerhard Goos, Karlsruhe University, Germany Juris Hartmanis, Cornell University, NY, USA Jan van Leeuwen, Utrecht University, The Netherlands Volume Editors Jin Akiyama Tokai University, Research Institute of Educational Development 2-28-4 Tomigaya, Shibuya-ku, Tokyo 151-0063, Japan E-mail:
[email protected] Mikio Kano Ibaraki University, Department of Computer and Information Sciences Hitachi 316-8511, Japan E-mail:
[email protected] Masatsugu Urabe Tokai University, Department of Mathematics 3-20-1 Orido Shimizu-shi, Shizuoka 424-8610, Japan E-mail:
[email protected] Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Discrete and computational geometry : Japanese conference ; revised papers / JCDCG 2000, Tokyo, Japan, November 22 - 25, 2000. Jin Akiyama ... (ed.). Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London ; Milan ; Paris ; Singapore ; Tokyo : Springer, 2001 (Lecture notes in computer science ; Vol. 2098) ISBN 3-540-42306-0 CR Subject Classification (1998): F.2, E.1, G.1-2, I.3.5 ISSN 0302-9743 ISBN 3-540-42306-0 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg New York a member of BertelsmannSpringer Science+Business Media GmbH http://www.springer.de © Springer-Verlag Berlin Heidelberg 2001 Printed in Germany Typesetting: Camera-ready by author Printed on acid-free paper SPIN: 10839451
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Preface
The Japan Conference on Discrete and Computational Geometry (JCDCG) has been held annually since 1997. One of the goals of this conference series is to bring together Japanese researchers from both academia and industry with researchers in these fields from abroad to share their recent results. JCDCG 2000 was held 22–25 November 2000 at Tokai University in Tokyo in conjunction with the celebration of World Mathematics Year 2000. A total of 120 participants from 20 countries attended. This volume consists of the papers presented at JCDCG 2000, which have been refereed and revised. Some papers which appear in short form in this volume also appear in fuller expanded versions in journals dedicated to computational geometry. The organizers of the conference thank the principal speakers for their interest and support: Imre Barany, Erik D. Demaine, Greg N. Fredrickson, Gyula Karolyi, Naoki Katoh, David Kirkpatrick, Joseph O’Rourke, Janos Pach, Jozsef Solymosi, William Steiger, Jorge Urrutia, and Allan Wilks. They thank the major sponsors for their generous contribution: The Research Institute of Educational Development of Tokai University, the Ministry of Education of Japan (for the grant-in-aid to A. Saito (A):10304008), and Tokai Education Instruments Co., Ltd.
April 2001 The Editors, Jin Akiyama Mikio Kano Masatsugu Urabe
Organizing Committee Chairs: Jin Akiyama and Mikio Kano Members: Tetsuo Asano, David Avis, Vasek Chvatal, Kiyoshi Hosono, Hiroshi Imai, Takako Kodate, Joseph O’Rourke, Toshinori Sakai, Xuehou Tan, Morimasa Tsuchiya, Masatsugu Urabe, and Jorge Urrutia.
Table of Contents
Papers Dudeney Dissections of Polygons and Polyhedrons - A Survey - . . . . . . . . . . J. Akiyama and G. Nakamura
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Universal Measuring Devices without Gradations . . . . . . . . . . . . . . . . . . . . . . . 31 J. Akiyama, H. Fukuda, G. Nakamura, T. Sakai, J. Urrutia, and C. Zamora-Cura A Note on the Purely Recursive Dissection for a Sequentially n-Divisible Square . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 J. Akiyama, G. Nakamura, A. Nozaki, and K. Ozawa Sequentially Divisible Dissections of Simple Polygons . . . . . . . . . . . . . . . . . . 53 J. Akiyama, T. Sakai, and J. Urrutia Packing Convex Polygons into Rectanguler Boxes . . . . . . . . . . . . . . . . . . . . . 67 H. Alt and F. Hurtado On the Number of Views of Polyhedral Scenes . . . . . . . . . . . . . . . . . . . . . . . . 81 B. Aronov, H. Br¨ onnimann, D. Halperin, and R. Schiffenbauer Problems and Results Around the Erd˝ os-Szekeres Convex Polygon Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 I. B´ ar´ any and G. K´ arolyi On Finding Maximum-Cardinality Symmetric Subsets . . . . . . . . . . . . . . . . . 106 P. Brass Folding and Unfolding Linkages, Paper, and Polyhedra . . . . . . . . . . . . . . . . . 113 E.D. Demaine On the Skeleton of the Metric Polytope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 A. Deza, K. Fukuda, D. Pasechnik, and M. Sato Geometric Dissections That Swing and Twist . . . . . . . . . . . . . . . . . . . . . . . . . 137 G.N. Frederickson On Convex Decompositions of Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 K. Hosono, D. Rappaport, and M. Urabe Volume Queries in Polyhedra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 J. Iacono and S. Langerman
VIII
Table of Contents
Sum of Edge Lengths of a Graph Drawn on a Convex Polygon . . . . . . . . . . 160 H. Ito, H. Uehara, and M. Yokoyama On Double Bound Graphs with Respect to Graph Operations . . . . . . . . . . . 167 S. Iwai, K. Ogawa, and M. Tsuchiya Generalized Balanced Partitions of Two Sets of Points in the Plane . . . . . . 176 A. Kaneko and M. Kano On Paths in a Complete Bipartite Geometric Graph . . . . . . . . . . . . . . . . . . . 187 A. Kaneko and M. Kano Approximating Uniform Triangular Meshes for Spheres . . . . . . . . . . . . . . . . . 192 N. Katoh, H. Kojima, and R. Taniguchi The Construction of Delaunay Diagrams by Lob Reduction . . . . . . . . . . . . . 205 P. Kauffmann and J.C. Spehner Geometric Transformations in Plane Triangulations . . . . . . . . . . . . . . . . . . . . 217 K. Kawarabayashi, A. Nakamoto, Y. Oda, and M. Watanabe Separation Sensitive Kinetic Separation Structures for Convex Polygons . . 222 D. Kirkpatrick and B. Speckmann On Acute Triangulations of Quadrilaterals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 H. Maehara Intersecting Red and Blue Line Segments in Optimal Time and Precision . 244 A. Mantler and J. Snoeyink Tight Error Bounds of Geometric Problems on Convex Objects with Imprecise Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 T. Nagai and N. Tokura Triangle Contact Systems, Orthogonal Plane Partitions and their Hit Graphs 264 A. Nakamoto Note on Diagonal Flips and Chromatic Numbers of Quadrangulations on Closed Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274 A. Nakamoto and S. Negami An Extension of Cauchy’s Arm Lemma with Application to Curve Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 J. O’Rourke On the Complexity of the Union of Geometric Objects . . . . . . . . . . . . . . . . . 292 J. Pach
Table of Contents
IX
Structure Theorems for Systems of Segments . . . . . . . . . . . . . . . . . . . . . . . . . 308 J. Pach and J. Solymosi 3-dimensional Single Active Layer Routing . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 A. Recski and D. Szeszl´er Nonregular Triangulations, View Graphs of Triangulations, and Linear Programming Duality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330 F. Takeuchi Efficient Algorithms for Searching a Polygonal Room with a Door . . . . . . . 339 X. Tan A New Structure of Cylinder Packing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351 Y. Teshima, Y. Watanabe, and T. Ogawa Efficient Algorithms for the Minimum Diameter Bridge Problem . . . . . . . . 362 T. Tokuyama Illuminating Both Sides of Line Segments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370 C.D. T´ oth
Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381
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12
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22
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Dudeney Dissections of Polygons and Polyhedrons - A Survey -
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Jin Akiyama and Gisaku Nakamura
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