Lecture Notes in Computer Science 3604

Transcription

1 Lecture Notes in Computer Science 3604 Commenced Publication in 1973 Founding and Former Series Editors: Gerhard Goos, Juris Hartmanis, and Jan van Leeuwen Editorial Board David Hutchison Lancaster University, UK Takeo Kanade Carnegie Mellon University, Pittsburgh, PA, USA Josef Kittler University of Surrey, Guildford, UK Jon M. Kleinberg Cornell University, Ithaca, NY, USA Friedemann Mattern ETH Zurich, Switzerland John C. Mitchell Stanford University, CA, USA Moni Naor Weizmann Institute of Science, Rehovot, Israel Oscar Nierstrasz University of Bern, Switzerland C. Pandu Rangan Indian Institute of Technology, Madras, India Bernhard Steffen University of Dortmund, Germany Madhu Sudan Massachusetts Institute of Technology, MA, USA Demetri Terzopoulos New York University, NY, USA Doug Tygar University of California, Berkeley, CA, USA Moshe Y. Vardi Rice University, Houston, TX, USA Gerhard Weikum Max-Planck Institute of Computer Science, Saarbruecken, Germany

2 Ralph Martin Helmut Bez Malcolm Sabin (Eds.) Mathematics of Surfaces XI 11th IMA International Conference Loughborough, UK, September 5-7, 2005 Proceedings 13

3 Volume Editors Ralph Martin Cardiff University School of Computer Science 5 The Parade, Roath, Cardiff, UK, CF24 3AA Ralph.Martin@cs.cf.ac.uk Helmut Bez Loughborough University Department of Computer Science Loughborough, UK, LE11 3TU h.e.bez@lboro.ac.uk Malcolm Sabin Numerical Geometry Ltd 26 Abbey Lane, Cambridge, UK, CB5 9EP malcolm@geometry.demon.co.uk Library of Congress Control Number: CR Subject Classification (1998): I.3.5, I.3, I.1, G.2, G.1, F.2, I.4 ISSN ISBN Springer Berlin Heidelberg New York ISBN Springer 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. Violations are liable to prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springeronline.com Springer-Verlag Berlin Heidelberg 2005 Printed in Germany Typesetting: Camera-ready by author, data conversion by Scientific Publishing Services, Chennai, India Printed on acid-free paper SPIN: /

4 Preface This volume collects the papers accepted for presentation at the 11th IMA Conference on the Mathematics of Surfaces, held at Loughborough University, 5th 7th September As with all earlier conferences in the series, contributors to this volume come from many countries. The papers presented here reflect the interest in a subject of relevance to mathematics, engineering, and computer science, especially in domains such as computer-aided design, computer vision, and computer graphics. The papers in the present volume include eight invited papers, as well as a larger number of submitted papers. They cover a range of ideas from underlying theoretical tools to industrial and medical uses of surfaces. The latter category includes such diverse topics as surfaces in car design, and modelling of teeth, while the former includes papers on Voronoi diagrams, linear systems, estimation of curvatures on meshes, operators on meshes, intersection of subdivision surfaces, approximate parameterization, condition numbers, Pythagorean hodographs, artifacts in B-spline surfaces, Bézier surfaces of minimal energy, line subdivision, subdivision surfaces, level sets and symmetry, the topology of algebraic surfaces, curve analysis, interpolation with positivity, and conversion of cyclides to NURBS. Other papers concentrate on particular algorithms arising from applications, such as embedding graphs in manifolds, recovery of 3D shape from shading, finding optimal feedrates for machining, detection of creases in range data, and filling holes in range data. We would like to thank all those who attended the conference and helped to make it a success. We are particularly grateful to Lucy Nye at the Institute of Mathematics and Its Applications for her hard work in organizing many aspects of the conference, and to Alfred Hofmann and Frank Holzwarth of Springer for their help in publishing this volume. Following this Preface is a list of distinguished researchers who formed the International Programme Committee, and who freely gave their time in helping to assess papers for these proceedings. Due to their work, many of the papers have been considerably improved. Our thanks go to all of them, and to other people who they called upon to help with refereeing. June 2005 Ralph Martin, Helmut Bez, Malcolm Sabin

5 Organization The Mathematics of Surfaces XI conference was organized by the Insitute of Mathematics and Its Applications (Catherine Richards House, 16 Nelson St., Southend-on-Sea, Essex, SS1 1EF, UK), and Loughborough University. Organizing Committee Helmut Bez Ralph Martin Malcolm Sabin Loughborough University, UK Cardiff University, UK Numerical Geometry Ltd., UK Program Committee Bob Cripps Gerald Farin Peter Giblin Ron Goldman Tim Goodman Hans Hagen Edwin Hancock Shimin Hu Bert Jüttler Myung-Soo Kim Tom Lyche Nick Patrikalakis Jorg Peters Hong Qin Martin Rumpf Georg Umlauf Wenping Wang Joe Warren Mike Wilson Franz-Erich Wolter Guoliang Xu University of Birmingham Arizona State University University of Liverpool Rice University University of Dundee University of Kaiserslautern University of York Tsinghua University Johannes Kepler University Seoul National University University of Oslo MIT University of Florida State University of New York University of Duisberg University of Kaiserslautern Hong Kong University Rice University University of Leeds University of Hannover Chinese Academy of Sciences

6 Table of Contents Free-Form Surface Construction in a Commercial CAD/CAM System Florian Albat, Rainer Müller... 1 Polyhedral Gauss Maps and Curvature Characterisation of Triangle Meshes Lyuba Alboul, Gilberto Echeverria Manifold Embedding of Graphs Using the Heat Kernel Xiao Bai, Richard C. Wilson, Edwin R. Hancock Detection of Surface Creases in Range Data Alexander Belyaev, Elena Anoshkina Efficient Linear System Solvers for Mesh Processing Mario Botsch, David Bommes, Leif Kobbelt Smoothing of Time-Optimal Feedrates for Cartesian CNC Machines Casey L. Boyadjieff, Rida T. Farouki, Sebastian D. Timar Plausible 3D Colour Surface Completion Using Non-parametric Techniques Toby P. Breckon, Robert B. Fisher Determining the Topology of Real Algebraic Surfaces Jin-San Cheng, Xiao-Shan Gao, Ming Li Level Sets of Functions and Symmetry Sets of Surface Sections André Diatta, Peter Giblin, Brendan Guilfoyle, Wilhelm Klingenberg An Heuristic Analysis of the Classification of Bivariate Subdivision Schemes Neil A. Dodgson Global Curve Analysis via a Dimensionality Lifting Scheme Gershon Elber Conversion of Dupin Cyclide Patches into Rational Biquadratic Bézier Form Sebti Foufou, Lionel Garnier, Michael J. Pratt

7 VIII Table of Contents Multi-sided Attribute Based Modeling Kun Gao, Alyn Rockwood On Normals and Control Nets Ingo Ginkel, Jorg Peters, Georg Umlauf Line Subdivision Hiroshi Kawaharada, Kokichi Sugihara Euclidean Voronoi Diagrams of 3D Spheres: Their Construction and Related Problems from Biochemistry Deok-Soo Kim, Donguk Kim, Youngsong Cho The Importance of Polynomial Reproduction in Piecewise-Uniform Subdivision Adi Levin A Hybrid Approach to Extracting Tooth Models from CT Volumes Sheng-Hui Liao, Wei Han, Ruo-Feng Tong, Jin-Xiang Dong Bézier Surfaces of Minimal Internal Energy Yongwei Miao, Huahao Shou, Jieqing Feng, Qunsheng Peng, A. Robin Forrest Positivity-Preserving Scattered Data Interpolation Abd. Rahni Mt. Piah, Tim N.T. Goodman, Keith Unsworth Artifacts in Box-Spline Surfaces Malcolm A. Sabin, Ursula H. Augsdörfer, Neil A. Dodgson Spatial Pythagorean Hodograph Quintics and the Approximation of Pipe Surfaces Zbyněk Šír, Bert Jüttler Modelling Surface Normal Distribution Using the Azimuthal Equidistant Projection William A.P. Smith, Edwin R. Hancock New Trends in Digital Shape Reconstruction Tamás Várady, Michael A. Facello Backward Errors and Condition Numbers of Regular and Singular Points on Algebraic Curves Joab R. Winkler

8 Table of Contents IX Approximate Rational Parameterization of Implicitly Defined Surfaces Elmar Wurm, Bert Jüttler, Myung-Soo Kim Convergence Analysis of Discrete Differential Geometry Operators over Surfaces Zhiqiang Xu, Guoliang Xu, Jia-Guang Sun A Marching Method for Computing Intersection Curves of Two Subdivision Solids Xu-Ping Zhu, Shi-Min Hu, Chiew-Lan Tai, Ralph R. Martin Author Index