© 2009

Implicit Curves and Surfaces: Mathematics, Data Structures and Algorithms

  • Abel J. P. Gomes
  • Irina Voiculescu
  • Joaquim Jorge
  • Brian Wyvill
  • Callum Galbraith

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Mathematics and Data Structures

  3. Sampling Methods

    1. Pages 89-115
    2. Pages 117-140
  4. Reconstruction and Polygonisation

  5. Designing Complex Implicit Surface Models

  6. Back Matter
    Pages 319-351

About this book


Implicit techniques are a powerful tool that make it easier to describe smooth, intricate, and articulatable shapes via blending and solid geometry, and are becoming the technique of choice in an increasing number of graphics applications.

The mathematics, computational methods and data structures, as well as the algorithms required to render implicit curves and surfaces form the central theme of this book. The increasing importance of implicit objects in geometric modelling stems from the advantages these give over traditional modelling methods; the use of implicit techniques can help simplify complex actions such as point membership classification, which enables the detection of collisions in virtual environments and computer game scenarios.

Graduate students, researchers and developers in computer graphics, geometric modelling, virtual reality and computer games will find this an excellent resource and reference source for modelling and rendering complex geometric objects. The book can also be used as a core textbook for graduate level courses on implicit geometric modelling.


3D graphics Animation Dynamic Surfaces Implicit Curves and Surfaces Level Sets Numerical Methods Special Effects computer graphics modeling

Editors and affiliations

  • Abel J. P. Gomes
    • 1
  • Irina Voiculescu
    • 2
  • Joaquim Jorge
    • 3
  • Brian Wyvill
    • 4
  • Callum Galbraith
    • 5
  1. 1.Universidade da Beira InteriorCovilhaPortugal
  2. 2.Oxford University Computing Laboratory (OUCL)OxfordUnited Kingdom
  3. 3.Universidade Tecnica de LisboaLisboaPortugal
  4. 4.University of VictoriaVictoriaCanada
  5. 5.University of CalgaryCalgaryCanada

Bibliographic information


From the reviews:

“The book does contain many algorithm examples and … graphics examples, as well as a scattering of data structures but it would have benefited greatly from a chapter devoted entirely to graphics programming. … A computer graphics specialist who needs to learn how to actually implement the various algorithms would need to look elsewhere. … This book would be ideal as an introduction to the field for a beginning researcher, or for a graphics specialist who wants … introductory information on a particular algorithm.” (Alasdair McAndrew, ACM Computing Reviews, December, 2009)

“The book consist of eleven chapters organized in four parts and can be seen as a self-contained tool for graduate students, researchers, and interested practitioners from industry, regarding the usage of implicit curves and surfaces for computer graphics, geometric modelling, computer games etc. … The book ends with a rich reference section containing more than 400 papers, enforcing the idea that this work represents a valuable source for the reader.” (Mirel Cosulschi, Zentralblatt MATH, Vol. 1190, 2010)