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Implicit Curves and Surfaces: Mathematics, Data Structures and Algorithms

By Abel Gomes , Irina Voiculescu , Joaquim Jorge , Brian Wyvill , Callum Galbraith

Implicit Curves and Surfaces: Mathematics, Data Structures and Algorithms Cover Image

In presenting the mathematics, computational methods and data structures, as well as the algorithms needed to render implicit curves and surfaces, the authors show how implicit objects can easily describe smooth, intricate, and shapes that articulate.

Full Description

  • ISBN13: 978-1-8488-2405-8
  • 366 Pages
  • User Level: Students
  • Publication Date: May 12, 2009
  • Available eBook Formats: PDF
  • eBook Price: $99.00
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Full Description
Implicit objects have gained increasing importance in geometric modeling, visualisation, animation, and computer graphics, because their geometric properties provide a good alternative to traditional parametric objects. This book presents the mathematics, computational methods and data structures, as well as the algorithms needed to render implicit curves and surfaces, and shows how implicit objects can easily describe smooth, intricate, and articulatable shapes, and hence why they are being increasingly used in graphical applications. Divided into two parts, the first introduces the mathematics of implicit curves and surfaces, as well as the data structures suited to store their sampled or discrete approximations, and the second deals with different computational methods for sampling implicit curves and surfaces, with particular reference to how these are applied to functions in 2D and 3D spaces.
Table of Contents

Table of Contents

  1. Part 1 Mathematics and Data Structures.
  2. Mathematical Fundamentals.
  3. Spatial Data Structures.
  4. Part II Sampling Methods.
  5. Root Isolation Methods.
  6. Interval Arithmetic.
  7. Root Finding Methods.
  8. Part III Reconstruction and Polygonisation.
  9. Continuation Methods.
  10. Spatial Partitioning Methods.
  11. Implicit Surface Fitting.
  12. Part IV Designing Complex Implicit Surface Models.
  13. Skeletal Implicit Modelling Techniques.
  14. Natural Phenomenae
  15. I Static Modelling.
  16. Natural Phenomenae
  17. II Animation.
  18. Index.
  19. References.
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