Mathematics for Computer Graphics

John Vince explains a comprehensive range of mathematical techniques and problem-solving strategies associated with computer games, computer animation, special effects, virtual reality, CAD and other areas of computer graphics in this completely revised and expanded sixth edition.

The first five chapters cover a general introduction, number sets, algebra, trigonometry and coordinate systems, which are employed in the following chapters on determinants, vectors, matrix algebra, complex numbers, geometric transforms, quaternion algebra, quaternions in space, interpolation, curves and patches, analytical geometry and barycentric coordinates. Following this, the reader is introduced to the relatively new subject 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
• Complex numbers
• Coordinate systems
• Determinants
• Vectors
• Quaternions
• Matrix algebra
• Geometric transforms
• Interpolation
• Curves and surfaces
• Analytic geometry
• Barycentric coordinates
• Geometric algebra
• Differential calculus
• Integral calculus

This sixth edition contains approximately 150 worked examples and over 330 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 software and setting the scene for further reading of more advanced books and technical research papers.

Table of Contents

1 Introduction

2 Numbers

3 Algebra

4 Trigonometry

5 Coordinate Systems

6 Determinants

7 Vectors

8 Matrix Algebra

9 Complex Numbers

10 Geometric Transforms

11 Quaternion Algebra

12 Quaternions in Space

13 Interpolation

14 Curves and Patches

15 Analytic Geometry

16 Barycentric Coordinates

17 Geometric Algebra

18 Calculus: Derivatives

19 Calculus: Integration

20 Worked Examples

Appendix A Limit of (sin8)/8

Appendix B Integrating cosn8

About the Author

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.