Nonlinear Computational Geometry

  • Ioannis Z. Emiris
  • Frank Sottile
  • Thorsten Theobald
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 151)

Table of contents

  1. Front Matter
    Pages 1-8
  2. Carlos D’Andrea, Martín Sombra
    Pages 35-50
  3. Manfred L. Husty, Hans-Peter Schröcker
    Pages 85-107
  4. Rimvydas Krasauskas, Martin Peternell
    Pages 109-135
  5. Wenping Wang, Yang Liu
    Pages 221-233
  6. Ioannis Z. Emiris, Frank Sottile, Thorsten Theobald
    Pages 235-239
  7. Back Matter
    Pages 1-5

About these proceedings

Introduction

An original motivation for algebraic geometry was to understand curves and surfaces in three dimensions. Recent theoretical and technological advances in areas such as robotics, computer vision, computer-aided geometric design and molecular biology, together with the increased availability of computational resources, have brought these original questions once more into the forefront of research. One particular challenge is to combine applicable methods from algebraic geometry with proven techniques from piecewise-linear computational geometry (such as Voronoi diagrams and hyperplane arrangements) to develop tools for treating curved objects. These research efforts may be summarized under the term nonlinear computational geometry.

This volume grew out of an IMA workshop on Nonlinear Computational Geometry in May/June 2007 (organized by I.Z. Emiris, R. Goldman, F. Sottile, T. Theobald) which gathered leading experts in this emerging field. The research and expository articles in the volume are intended to provide an overview of nonlinear computational geometry. Since the topic involves computational geometry, algebraic geometry, and geometric modeling, the volume has contributions from all of these areas. By addressing a broad range of issues from purely theoretical and algorithmic problems, to implementation and practical applications this volume conveys the spirit of the IMA workshop.

Keywords

Computational Dimension Geometry Nonlinear algebra algebraic curve algebraic geometry computational geometry

Editors and affiliations

  • Ioannis Z. Emiris
    • 1
  • Frank Sottile
    • 2
  • Thorsten Theobald
    • 3
  1. 1.Dept. Informatics & TelecommunicationsNational University of AthensAthensGreece
  2. 2.Dept. MathematicsTexas A & M UniversityCollege StationU.S.A.
  3. 3.Zentrum Mathematik (M10)TU MünchenGarchingGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-0999-2
  • Copyright Information Springer-Verlag New York 2010
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4419-0998-5
  • Online ISBN 978-1-4419-0999-2
  • Series Print ISSN 0940-6573