Future Vision and Trends on Shapes, Geometry and Algebra

  • Raffaele De Amicis
  • Giuseppe Conti
Conference proceedings

Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 84)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Raffaele De Amicis, Giuseppe Conti, André Stork
    Pages 1-12
  3. Wenrui Hao, Bei Hu, Andrew J. Sommese
    Pages 39-53
  4. Ioannis Z. Emiris, Anna Karasoulou
    Pages 55-71
  5. Ibrahim Adamou, Mario Fioravanti, Laureano Gonzalez-Vega
    Pages 73-94
  6. Andoni Mujika, Nagore Barrena, Sara García, David Oyarzun
    Pages 107-116
  7. Chiara Pellegrini, Anna Rimoldi, Massimiliano Sala
    Pages 117-134
  8. Aitor Moreno, Álvaro Segura, Harbil Arregui, Jorge Posada, Álvaro Ruíz de Infante, Natxo Canto
    Pages 135-149
  9. Thomas A. Grandine
    Pages 151-162

About these proceedings


Mathematical algorithms are a fundamental component of Computer Aided Design and Manufacturing (CAD/CAM) systems. This book provides a bridge between algebraic geometry and geometric modelling algorithms, formulated within a computer science framework.

Apart from the algebraic geometry topics covered, the entire book is based on the unifying concept of using algebraic techniques – properly specialized to solve geometric problems – to seriously improve accuracy, robustness and efficiency of CAD-systems. It provides new approaches as well as industrial applications to deform surfaces when animating virtual characters, to automatically compare images of handwritten signatures, and to improve control of NC machines.

This book further introduces a noteworthy representation based on 2D contours, which is essential to model the metal sheet in industrial processes. It additionally reviews applications of numerical algebraic geometry to differential equations systems with multiple solutions and bifurcations.

Future Vision and Trends on Shapes, Geometry and Algebra is aimed specialists in the area of mathematics and computer science on the one hand and on the other hand at those who want to become familiar with the practical application of algebraic geometry and geometric modelling such as students, researchers, and doctorates.


Algebraic Geometry Computer Aided Design Geometric Modelling Polynomial Systems Symbolic Computation

Editors and affiliations

  • Raffaele De Amicis
    • 1
  • Giuseppe Conti
    • 2
  1. 1.Fondazione GraphitechPovo, TrentoItaly
  2. 2.Fondazione GraphitechPovo, TrentoItaly

Bibliographic information

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