© 2010

Mathematics for Computer Graphics


Part of the Undergraduate Topics in Computer Science book series (UTICS)

Table of contents

  1. Front Matter
    Pages i-xv
  2. John Vince
    Pages 1-3
  3. John Vince
    Pages 5-11
  4. John Vince
    Pages 13-19
  5. John Vince
    Pages 21-26
  6. John Vince
    Pages 27-34
  7. John Vince
    Pages 35-57
  8. John Vince
    Pages 59-117
  9. John Vince
    Pages 119-133
  10. John Vince
    Pages 135-160
  11. John Vince
    Pages 161-206
  12. John Vince
    Pages 207-235
  13. John Vince
    Pages 237-270
  14. John Vince
    Pages 271-288
  15. John Vince
    Pages 289-289
  16. Back Matter
    Pages 291-293

About this book


John Vince explains a wide range of mathematical techniques and problem-solving strategies associated with computer games, computer animation, virtual reality, CAD, and other areas of computer graphics.

Covering all the mathematical techniques required to resolve geometric problems and design computer programs for computer graphic applications, each chapter explores a specific mathematical topic prior to moving forward into the more advanced areas of matrix transforms, 3D curves and surface patches. Problem-solving techniques using vector analysis and geometric algebra are also discussed.

All the key areas are covered including:

• Numbers

• Algebra

• Trigonometry

• Coordinate geometry

• Transforms

• Vectors

• Curves and surfaces

• Barycentric coordinates

• Analytic geometry.

Plus – and unusually in a student textbook – a chapter on geometric algebra is included.

With plenty of worked examples, the book provides a sound understanding of the mathematics required for computer graphics, giving a fascinating insight into the design of computer graphics software, and setting the scene for further reading of more advanced books and technical research papers.


3D 3D graphics Interpolation Partition Splines animation computer animation computer graphics reflection

Authors and affiliations

  1. 1.Ringwood, HampshireUnited Kingdom

About the authors

John Vince has been writing books for 25 years. Previous publications with Springer include:

Geometric Algebra: An Algebraic System for Computer Games and Animation Springer, 2009, ISBN 978-1-84882-378-5

Vector Analysis for Computer Graphics

Springer, 2007, ISBN 978-1-84628-803-6

Mathematics for Computer Graphics

Springer, 2006, ISBN 1-84628-034-6

Introduction to Virtual Reality

Springer, 2004, ISBN 1-85233-739-7

More information can be found at

Bibliographic information


From the reviews of the third edition:

“Slim volume could be a computer graphics student’s (and professor’s) next best friend. … the style of writing is crisp and the approach is practical. Although the theory is light, rigorous detailed derivations on each topic, sometimes from more than one approaches are plentiful and characterize the author’s approach throughout the entire book. It is surprising to find really practical mathematics packaged in fewer than 300 pages. For those studying or teaching computer graphics, this book will be a valuable companion to have on hand.” (Anthony J. Duben, ACM Computing Reviews, September, 2010)