Skip to main content
  • Book
  • © 2014

SAGA – Advances in ShApes, Geometry, and Algebra

Results from the Marie Curie Initial Training Network

  • Gathers results of workshops in the SAGA Project, held between March, 2010 and October, 2012
  • Presents the work of both young researchers and experienced experts
  • Discusses such topics as approximate and sparse implicitization and surface parametrization; algebraic tools for geometric computing and more

Part of the book series: Geometry and Computing (GC, volume 10)

Buy it now

Buying options

eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

This is a preview of subscription content, log in via an institution to check for access.

Table of contents (15 chapters)

  1. Front Matter

    Pages i-xiii
  2. Introduction to ShApes, Geometry, and Algebra

    • Tor Dokken, Georg Muntingh
    Pages 1-8
  3. Change of Representation

    1. Front Matter

      Pages 9-9
    2. Numerical Methods for Implicitisation and Their Applications

      • Oliver J. D. Barrowclough
      Pages 11-37
    3. Sparse Implicitization via Interpolation

      • Ioannis Z. Emiris, Tatjana Kalinka, Christos Konaxis
      Pages 39-51
  4. Geometric Computing: Algebraic Tools

    1. Front Matter

      Pages 75-75
    2. Singular Zeros of Polynomial Systems

      • Angelos Mantzaflaris, Bernard Mourrain
      Pages 77-103
    3. Plane Mixed Discriminants and Toric Jacobians

      • Alicia Dickenstein, Ioannis Z. Emiris, Anna Karasoulou
      Pages 105-121
    4. Rational Bézier Formulas with Quaternion and Clifford Algebra Weights

      • Rimvydas Krasauskas, Severinas Zubė
      Pages 147-166
  5. Algebraic Geometry for CAD Applications

    1. Front Matter

      Pages 167-167
    2. Algebraic Spline Geometry: Some Remarks

      • Ragni Piene
      Pages 169-175
    3. On the Dimension of Spline Spaces on Triangulations

      • Nelly Villamizar, Bernard Mourrain
      Pages 177-197
  6. Practical Industrial Problems

    1. Front Matter

      Pages 239-239
    2. Bisectors and Voronoï Diagram of a Family of Parallel Half-Lines

      • I. Adamou, M. Fioravanti, L. Gonzalez-Vega, B. Mourrain
      Pages 241-279

About this book

This book summarizes research carried out in workshops of the SAGA project, an Initial Training Network exploring the interplay of Shapes, Algebra, Geometry and Algorithms.

Written by a combination of young and experienced researchers, the book introduces new ideas in an established context. Among the central topics are approximate and sparse implicitization and surface parametrization; algebraic tools for geometric computing; algebraic geometry for computer aided design applications and problems with industrial applications.

Readers will encounter new methods for the (approximate) transition between the implicit and parametric representation; new algebraic tools for geometric computing; new applications of isogeometric analysis and will gain insight into the emerging research field situated between algebraic geometry and computer aided geometric design.

Editors and Affiliations

  • SINTEF ICT, Oslo, Norway

    Tor Dokken, Georg Muntingh

Bibliographic Information

Buy it now

Buying options

eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access