Calculus for Computer Graphics

Description

Students studying different branches of computer graphics need 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 3rd edition, the author extends the scope of the original book to include vector differential operators and differential equations and 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 almost two hundred 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. Front Matter Pages i-xviii PDF Introduction John Vince Pages 1-3 Functions John Vince Pages 5-18 Limits and Derivatives John Vince Pages 19-34 Derivatives and Antiderivatives John Vince Pages 35-74 Higher Derivatives John Vince Pages 75-84 Partial Derivatives John Vince Pages 85-99 Integral Calculus John Vince Pages 101-133 Area Under a Graph John Vince Pages 135-152 Arc Length and Parameterisation of Curves John Vince Pages 153-186 Surface Area John Vince Pages 187-214 Volume John Vince Pages 215-248 Vector-Valued Functions John Vince Pages 249-259 Vector Differential Operators John Vince Pages 261-283 Tangent and Normal Vectors John Vince Pages 285-316 Continuity John Vince Pages 317-326 Curvature John Vince Pages 327-342 Solving Differential Equations John Vince Pages 343-365 Conclusion John Vince Pages 367-367