# Calculus for Computer Graphics

• John Vince
Textbook

1. Front Matter
Pages I-XIII
2. John Vince
Pages 1-1
3. John Vince
Pages 3-15
4. John Vince
Pages 17-30
5. John Vince
Pages 31-66
6. John Vince
Pages 67-74
7. John Vince
Pages 75-85
8. John Vince
Pages 87-115
9. John Vince
Pages 117-134
10. John Vince
Pages 135-151
11. John Vince
Pages 153-178
12. John Vince
Pages 179-207
13. John Vince
Pages 209-215
14. John Vince
Pages 217-217
15. Back Matter
Pages 219-227

### Introduction

Students studying computer animation and computer games have to be familiar with geometry, matrices, vectors, rotation transforms, quaternions, curves and surfaces, and as computer graphics software becomes increasingly sophisticated, calculus is also being used to resolve its associated problems.

The author draws upon his experience in teaching mathematics to undergraduates to make calculus appear no more challenging than any other branch of mathematics. He introduces the subject by examining how functions depend upon their independent variables, and then derives the appropriate mathematical underpinning and definitions. This gives rise to a function’s derivative and its antiderivative, or integral. Using the idea of limits, the reader is introduced to derivatives and integrals of many common functions. Other chapters address higher-order derivatives, partial derivatives, Jacobians, vector-based functions, single, double and triple integrals, with numerous worked examples, and over a hundred illustrations.

Calculus for Computer Graphics complements the author’s other books on mathematics for computer graphics, and assumes that the reader is familiar with everyday algebra, trigonometry, vectors and determinants. After studying this book, the reader should understand calculus and its application within the world of computer games and animation.

### Keywords

Calculus for Computer Animation Calculus for Computer Games Derivatives and Antiderivatives Exponential Functions Logarithmic Functions Partial Derivatives Polynomial Functions Trigonometric Functions

#### Authors and affiliations

• John Vince
• 1
1. 1.Bournemouth UniversityUnited Kingdom

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4471-5466-2
• Copyright Information Springer-Verlag London 2013
• Publisher Name Springer, London
• eBook Packages Computer Science
• Print ISBN 978-1-4471-5465-5
• Online ISBN 978-1-4471-5466-2
• Buy this book on publisher's site
Industry Sectors
Electronics
IT & Software
Telecommunications
Consumer Packaged Goods
Aerospace