© 2014

Mathematics for Computer Graphics


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

Table of contents

  1. Front Matter
    Pages I-XVII
  2. John Vince
    Pages 1-2
  3. John Vince
    Pages 3-9
  4. John Vince
    Pages 11-21
  5. John Vince
    Pages 23-31
  6. John Vince
    Pages 33-42
  7. John Vince
    Pages 43-63
  8. John Vince
    Pages 65-120
  9. John Vince
    Pages 121-134
  10. John Vince
    Pages 135-157
  11. John Vince
    Pages 159-201
  12. John Vince
    Pages 203-229
  13. John Vince
    Pages 231-263
  14. John Vince
    Pages 265-317
  15. John Vince
    Pages 319-360
  16. John Vince
    Pages 361-378
  17. John Vince
    Pages 379-379
  18. Back Matter
    Pages 381-391

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 in this updated and expanded fourth edition.

The first four chapters revise number sets, algebra, trigonometry and coordinate systems, which are employed in the following chapters on vectors, transforms, interpolation, 3D curves and patches, analytic geometry, and barycentric coordinates. Following this, the reader is introduced to the relatively new topic of geometric algebra, and the last two chapters provide an introduction to differential and integral calculus, with an emphasis on geometry.

Mathematics for Computer Graphics covers all of the key areas of the subject, including:

  • Number sets
  • Algebra
  • Trigonometry
  • Coordinate systems
  • Transforms
  • Quaternions
  • Interpolation
  • Curves and surfaces
  • Analytic geometry
  • Barycentric coordinates
  • Geometric algebra
  • Differential calculus
  • Integral calculus

This fourth edition contains over 120 worked examples and over 270 illustrations, which are central to the author’s descriptive writing style. Mathematics for Computer Graphics 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.


Computer Aided Design (CAD) Computer Animation Computer Games Computer Graphics Mathematic Applications in Computer Science

Authors and affiliations

  1. 1.Bournemouth UniversityBournemouthUnited Kingdom

About the authors

Prof John Vince began working in computer graphics at Middlesex Polytechnic in 1968. His research activities centered on computer animation software and resulted in the PICASO and PRISM animation systems. Whilst at Middlesex, he designed the UK’s first MSc course in Computer Graphics and developed a popular program of short courses in computer animation for television designers. In 1986 he joined Rediffusion Simulation as a Research Consultant and worked on the development of real-time computer systems for commercial flight simulators. In 1992 he was appointed Chief Scientist of Thomson Training Simulation Ltd. In 1995 he was appointed Professor of Digital Media at the National Centre for Computer Animation at Bournemouth University and in 1999 he was made Head of Academic Group for Computer Animation. He was awarded a DSc by Brunel University in recognition of his work in computer graphics. He has written and edited over 40 books on computer graphics, computer animation and virtual reality, including the following Springer titles:

  • Calculus for Computer Graphics (2013)
  • Matrix Transforms for Computer Games and Animation (2012)
  • Expanding the Frontiers of Visual Analytics and Visualization (2012)
  • Quaternions for Computer Graphics (2011)
  • Rotation Transforms for Computer Graphics (2011)

Bibliographic information

  • Book Title Mathematics for Computer Graphics
  • Authors John Vince
  • Series Title Undergraduate Topics in Computer Science
  • Series Abbreviated Title Undergraduate Topics Computer Sci.
  • DOI
  • Copyright Information Springer-Verlag London 2014
  • Publisher Name Springer, London
  • eBook Packages Computer Science Computer Science (R0)
  • Softcover ISBN 978-1-4471-6289-6
  • eBook ISBN 978-1-4471-6290-2
  • Series ISSN 1863-7310
  • Series E-ISSN 2197-1781
  • Edition Number 4
  • Number of Pages XVII, 391
  • Number of Illustrations 282 b/w illustrations, 0 illustrations in colour
  • Topics Computer Graphics
    Mathematical Applications in Computer Science
  • Buy this book on publisher's site
Industry Sectors
IT & Software


From the book reviews:

“This book is undoubtedly a very well written book. The chapters are short, easy to follow and understand. … it is a neatly compiled book that many math enthusiasts may want to have on their bookshelves. … a really good book both technically as well as pedagogically.” (Leslie P. Piegl, zbMATH, Vol. 1295, 2014)

“The book’s 16 chapters cover a broad range of relevant mathematical topics. … The logics in the book are presented very clearly, and readers from all levels with an understanding of arithmetic, algebra, trigonometry, and geometry will find this book easy to follow. The worked examples are very helpful in practical projects as well. … this is a very useful book and I highly recommend it as a reference for those who are studying or working in computer graphics-related fields.” (Zhaoqiang Lai, Computing Reviews, August, 2014)