Mathematics for Computer Graphics

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.

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