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Calculus for Computer Graphics

  • John Vince

Table of contents

  1. Front Matter
    Pages i-xvii
  2. John Vince
    Pages 1-3
  3. John Vince
    Pages 5-18
  4. John Vince
    Pages 19-33
  5. John Vince
    Pages 35-70
  6. John Vince
    Pages 71-79
  7. John Vince
    Pages 81-91
  8. John Vince
    Pages 93-120
  9. John Vince
    Pages 121-137
  10. John Vince
    Pages 169-195
  11. John Vince
    Pages 197-223
  12. John Vince
    Pages 225-232
  13. John Vince
    Pages 233-265
  14. John Vince
    Pages 267-275
  15. John Vince
    Pages 277-290
  16. John Vince
    Pages 291-291
  17. Back Matter
    Pages 293-303

About this book

Introduction

Students studying different branches of computer graphics 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. 

In this 2nd edition, the author extends the scope of the original book to include applications of calculus in the areas of arc-length parameterisation of curves, geometric continuity, tangent and normal vectors, and curvature. 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 and seventy colour illustrations. 

This book 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 graphics, 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 Vector Fields

Authors and affiliations

  • John Vince
    • 1
  1. 1.Bournemouth UniversityHerefordUK

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-11376-6
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Computer Science
  • Print ISBN 978-3-030-11375-9
  • Online ISBN 978-3-030-11376-6
  • Buy this book on publisher's site