© 2017

Mathematics for Computer Graphics

  • Covers a broad range of relevant mathematical topics, from algebra to calculus

  • Includes over 320 colour illustrations and scores of worked examples

  • Takes the reader from humble introductory ideas through to some advanced concepts

  • One of the few student texts on introductory mathematics including a chapter on geometric algebra


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

Table of contents

  1. Front Matter
    Pages i-xix
  2. John Vince
    Pages 1-4
  3. John Vince
    Pages 5-30
  4. John Vince
    Pages 31-49
  5. John Vince
    Pages 51-63
  6. John Vince
    Pages 65-76
  7. John Vince
    Pages 77-93
  8. John Vince
    Pages 95-117
  9. John Vince
    Pages 119-151
  10. John Vince
    Pages 153-215
  11. John Vince
    Pages 217-232
  12. John Vince
    Pages 233-257
  13. John Vince
    Pages 259-306
  14. John Vince
    Pages 307-336
  15. John Vince
    Pages 337-372
  16. John Vince
    Pages 373-429
  17. John Vince
    Pages 431-470
  18. John Vince
    Pages 471-489
  19. John Vince
    Pages 491-491
  20. Back Matter
    Pages 493-505

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 completely revised and expanded fifth edition.

The first five chapters cover a general introduction, number sets, algebra, trigonometry and coordinate systems, which are employed in the following chapters on vectors, matrix algebra, transforms, interpolation, curves and patches, analytic geometry and barycentric coordinates. Following this, the reader is introduced to the relatively new topic of geometric algebra, followed by two chapters that introduce differential and integral calculus. Finally, there is a chapter on worked examples.

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

·        Number sets

·        Algebra

·        Trigonometry

·        Coordinate systems

·        Determinants

·        Vectors

·        Quaternions

·        Matrix algebra

·        Geometric transforms

·        Interpolation

·        Curves and surfaces

·        Analytic geometry

·        Barycentric coordinates

·        Geometric algebra

·        Differential calculus

·        Integral calculus

This fifth edition contains over 120 worked examples and over 320 colour 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.


Transcendental Numbers Geometric Algebra Barycentric Coordinates Computer Graphics Software Mathematical Techniques

Authors and affiliations

  1. 1.Breinton,United Kingdom

About the authors

Professor 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:

• Mathematics for Computer Graphics (2014)

• 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 Ltd. 2017
  • Publisher Name Springer, London
  • eBook Packages Computer Science Computer Science (R0)
  • Softcover ISBN 978-1-4471-7334-2
  • eBook ISBN 978-1-4471-7336-6
  • Series ISSN 1863-7310
  • Series E-ISSN 2197-1781
  • Edition Number 5
  • Number of Pages XIX, 505
  • Number of Illustrations 0 b/w illustrations, 292 illustrations in colour
  • Topics Computer Graphics
    Mathematical Applications in Computer Science
  • Buy this book on publisher's site
Industry Sectors
IT & Software


“A broad range of mathematical topics is covered in the 18 chapters of this book. … I think 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, April, 2018)​

“The book’s target audience is computer graphics students and professionals in this area. … the information is presented in a minimalist fashion and is very easy to digest. Highly recommended for its crispness and the quality of the material.” (Naga Narayanaswamy, Computing Reviews, July, 2018)