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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.
Linear Algebra for Computational Sciences and Engineering by Ferrante Neri
Publication Date: 2019-08-12
This book presents the main concepts of linear algebra from the viewpoint of applied scientists such as computer scientists and engineers, without compromising on mathematical rigor. Based on the idea that computational scientists and engineers need, in both research and professional life, an understanding of theoretical concepts of mathematics in order to be able to propose research advances and innovative solutions, every concept is thoroughly introduced and is accompanied by its informal interpretation. Furthermore, most of the theorems included are first rigorously proved and then shown in practice by a numerical example. When appropriate, topics are presented also by means of pseudocodes, thus highlighting the computer implementation of algebraic theory. It is structured to be accessible to everybody, from students of pure mathematics who are approaching algebra for the first time to researchers and graduate students in applied sciences who need a theoretical manual of algebra to successfully perform their research. Most importantly, this book is designed to be ideal for both theoretical and practical minds and to offer to both alternative and complementary perspectives to study and understand linear algebra.
Ray Tracing: a Tool for All by Jon Peddie
Publication Date: 2019-08-22
This is the first book to offer a comprehensive overview for anyone wanting to understand the benefits and opportunities of ray tracing, as well as some of the challenges, without having to learn how to program or be an optics scientist. It demystifies ray tracing and brings forward the need and benefit of using ray tracing throughout the development of a film, product, or building -- from pitch to prototype to marketing. Ray Tracing and Rendering clarifies the difference between conventional faked rendering and physically correct, photo-realistic ray traced rendering, and explains how programmer's time, and backend compositing time are saved while producing more accurate representations with 3D models that move. Often considered an esoteric subject the author takes ray tracing out of the confines of the programmer's lair and shows how all levels of users from concept to construction and sales can benefit without being forced to be a practitioner. It treats both theoretical and practical aspects of the subject as well as giving insights into all the major ray tracing programs and how many of them came about. It will enrich the readers' understanding of what a difference an accurate high-fidelity image can make to the viewer -- our eyes are incredibly sensitive to flaws and distortions and we quickly disregard things that look phony or unreal. Such dismissal by a potential user or customer can spell disaster for a supplier, producer, or developer. If it looks real it will sell, even if it is a fantasy animation. Ray tracing is now within reach of every producer and marketeer, and at prices one can afford, and with production times that meet the demands of today's fast world.
Unreal for Mobile and Standalone VR by Cornel Hillmann
Publication Date: 2019-04-13
Apply the techniques needed to build VR applications for mobile and standalone head-mounted displays (HMDs) using the Unreal Engine. This book covers the entire VR ecosystem including production tools, Unreal engine, workflows, performance and optimization, and presents two fully-developed projects to reinforce what you've learned. Media designers, CG artists and other creatives will be able to take advantage of real-time engine techniques and easy-to-learn visual scripting logic to turn their creations into immersive and interactive VR worlds. Gear VR, the Oculus Go and other Android based VR HMDs are becoming exciting new platforms for immersive business presentations, entertainment and educational solutions. The Unreal engine, one of the world's most powerful and popular game engines, is now free to use and has become increasingly popular for real-time visualizations and enterprise solutions in recent years. With Unreal's powerful blueprint visual scripting system, non-coders can now design blueprints in Unreal, unlock the power of rapid prototyping, and create complex interactions without a line of code. Get your copy of Unreal for Mobile and Standalone VR today and begin using this powerful tool-set to create high-end VR apps for a wide range of applications from games, B2B, to education. What You'll Learn Explore the VR ecosystem, including history, recent trends and future outlook Review tool set, graphics and animation pipeline (Blender, Zbrush, Substance Painter and others) Examine graphics optimization techniques Set up a project and the target platform Design interaction with Unreal blueprints Deployments, testing, further optimization Who This Book Is For Multimedia designers, CG artists, producers, app developers. No coding experience is required.