The IMA Volumes in Mathematics and its Applications

Nonlinear Computational Geometry

Editors: Emiris, Ioannis Z, Sottile, Frank, Theobald, Thorsten (Eds.)

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About this book

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.

Table of contents (10 chapters)

  • Spectral Techniques to Explore Point Clouds in Euclidean Space, with Applications to Collective Coordinates in Structural Biology

    Cazals, Frédéric (et al.)

    Pages 1-34

  • Rational Parametrizations, Intersection Theory, and Newton Polytopes

    D’Andrea, Carlos (et al.)

    Pages 35-50

  • Some Discrete Properties of the Space of Line Transversals to Disjoint Balls

    Goaoc, Xavier

    Pages 51-83

  • Algebraic Geometry and Kinematics

    Husty, Manfred L. (et al.)

    Pages 85-107

  • Rational Offset Surfaces and their Modeling Applications

    Krasauskas, Rimvydas (et al.)

    Pages 109-135

Buy this book

eBook $159.00
price for USA (gross)
  • ISBN 978-1-4419-0999-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $209.00
price for USA
  • ISBN 978-1-4419-0998-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $209.00
price for USA
  • ISBN 978-1-4614-2509-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Nonlinear Computational Geometry
Editors
  • Ioannis Z Emiris
  • Frank Sottile
  • Thorsten Theobald
Series Title
The IMA Volumes in Mathematics and its Applications
Series Volume
151
Copyright
2010
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-1-4419-0999-2
DOI
10.1007/978-1-4419-0999-2
Hardcover ISBN
978-1-4419-0998-5
Softcover ISBN
978-1-4614-2509-0
Series ISSN
0940-6573
Edition Number
1
Number of Pages
XI, 239
Topics