Implicit Curves and Surfaces: Mathematics, Data Structures and Algorithms

Authors: Gomes, A., Voiculescu, I., Jorge, J., Wyvill, B., Galbraith, C.

  • The first book to provide a general framework for both implicit curves and surfaces including their mathematical foundations, data structures, computational methods and algorithms
  • Includes both static and dynamic classes of implicit surfaces
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About this Textbook

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.

Reviews

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)


Table of contents (11 chapters)

  • Mathematical Fundamentals

    Pages 7-40

  • Spatial Data Structures

    Pages 41-62

  • Root Isolation Methods

    Pages 67-87

  • Interval Arithmetic

    Pages 89-115

  • Root-Finding Methods

    Pages 117-140

Buy this book

eBook n/a
  • ISBN 978-1-84882-406-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
Hardcover n/a
  • ISBN 978-1-84882-405-8
  • Free shipping for individuals worldwide
Softcover n/a
  • ISBN 978-1-4471-5877-6
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Implicit Curves and Surfaces: Mathematics, Data Structures and Algorithms
Authors
Copyright
2009
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London
eBook ISBN
978-1-84882-406-5
DOI
10.1007/978-1-84882-406-5
Hardcover ISBN
978-1-84882-405-8
Softcover ISBN
978-1-4471-5877-6
Edition Number
1
Number of Pages
XIV, 351
Topics