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Vector Analysis for Computer Graphics

  • Textbook
  • © 2007

Overview

Authors:
  1. John Vince

    1. Bournemouth University, UK

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  • Approaches vector analysis from a geometric standpoint, with an emphasis on applications in computer graphics

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Table of contents (11 chapters)

  1. Front Matter

    Pages I-XIII
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  2. Scalars and Vectors

    • John Vince
    Pages 1-10

  3. Vector Representation

    • John Vince
    Pages 11-59

  4. Straight Lines

    • John Vince
    Pages 61-99

  5. The Plane

    • John Vince
    Pages 101-121

  6. Reflections

    • John Vince
    Pages 123-127

  7. Intersections

    • John Vince
    Pages 129-177

  8. Rotating Vectors

    • John Vince
    Pages 179-200

  9. Vector Differentiation

    • John Vince
    Pages 201-211

  10. Projections

    • John Vince
    Pages 213-224

  11. Rendering

    • John Vince
    Pages 225-239

  12. Motion

    • John Vince
    Pages 241-245

  13. Back Matter

    Pages 253-253
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Keywords

About this book

In my last book, Geometry for Computer Graphics, I employed a mixture of algebra and vector analysis to prove many of the equations used in computer graphics. At the time, I did not make any distinction between the two methodologies, but slowly it dawned upon me that I had had to discover, for the first time, how to use vector analysis and associated strategies for solving geometric problems. I suppose that mathematicians are taught this as part of their formal mathematical training, but then, I am not a mathematician! After some deliberation, I decided to write a book that would introduce the beginner to the world of vectors and their application to the geometric problems encountered in computer graphics. I accepted the fact that there would be some duplication of formulas between this and my last book; however, this time I would concentrate on explaining how problems are solved. The book contains eleven chapters: The first chapter distinguishes between scalar and vector quantities, which is reasonably straightforward. The second chapter introduces vector repres- tation, starting with Cartesian coordinates and concluding with the role of direction cosines in changes in axial systems. The third chapter explores how the line equation has a natural vector interpretation and how vector analysis is used to resolve a variety of line-related, geometric problems. Chapter 4 repeats Chapter 3 in the context of the plane.

Reviews

From the reviews:

"Vince’s book applies to more than computer graphics: it is a resource for many areas in applied mathematics. … Students in computer graphics courses would find it very useful if their class discussions moved into the mathematical fundamentals underlying the tools. … Undergraduate students especially lack the mathematics background that this book provides. … It is comprehensive and coherent, and a good addition to the library of any computational scientist." (Anthony J. Duben, ACM Computing Reviews, Vol. 49 (8), August, 2008)

Authors and Affiliations

  • Bournemouth University, UK

    John Vince

Bibliographic Information

  • Book Title: Vector Analysis for Computer Graphics

  • Authors: John Vince

  • DOI: https://doi.org/10.1007/978-1-84628-804-3

  • Publisher: Springer London

  • eBook Packages: Computer Science, Computer Science (R0)

  • Copyright Information: Springer-Verlag London 2007

  • Hardcover ISBN: 978-1-84628-803-6Published: 18 June 2007

  • eBook ISBN: 978-1-84628-804-3Published: 15 May 2007

  • Edition Number: 1

  • Number of Pages: XIII, 259

  • Number of Illustrations: 185 b/w illustrations

  • Topics: Computer Graphics, Geometry, Math Applications in Computer Science

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