Vector Analysis for Computer Graphics

ISBN-13: 9781447175070 / Angielski / Miękka / 2022

John Vince

Opis

In my last book, Geometry for Computer Graphics, I employed a mixture of algebra and vector analysis to prove many of the equations used in computer graphics. At the time, I did not make any distinction between the two methodologies, but slowly it dawned upon me that I had had to discover, for the first time, how to use vector analysis and associated strategies for solving geometric problems. I suppose that mathematicians are taught this as part of their formal mathematical training, but then, I am not a mathematician! After some deliberation, I decided to write a book that would introduce the beginner to the world of vectors and their application to the geometric problems encountered in computer graphics. I accepted the fact that there would be some duplication of formulas between this and my last book; however, this time I would concentrate on explaining how problems are solved. The book contains eleven chapters: The first chapter distinguishes between scalar and vector quantities, which is reasonably straightforward. The second chapter introduces vector repres- tation, starting with Cartesian coordinates and concluding with the role of direction cosines in changes in axial systems. The third chapter explores how the line equation has a natural vector interpretation and how vector analysis is used to resolve a variety of line-related, geometric problems. Chapter 4 repeats Chapter 3 in the context of the plane.

Recenzje

"Each chapter presents some topic from vector analysis and contains a well-developed derivation and mathematical demonstration that makes following the topic easier. ... The book is written in a very accessible fashion. The author gives many examples presenting the notations and problems considered, making study easier. The book is suitable for undergraduate students of computer science, mathematics, and engineering, and is an ideal reference for researchers and professionals in computer graphics." (Krzysztof Gdawiec, zbMATH 1478.68008, 2022)

Spis treści

Preface.- History of Vector Analysis.- Linear Equations.- Vector Algebra.- Products of Vectors.- Differentiating Vector-Valued Functions.- Vector Differential Operators.- Tangent and Normal Vectors.- Straight Lines.- The Plane.- Intersections.- Rotating Vectors.- Index.

O autorze

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 45 books on computer graphics, computer animation, computer science and virtual reality, including the following Springer titles:

• Mathematics for Computer Graphics, 5^th edition (2017)

• Calculus for Computer Graphics, 2^nd edition (2019)

• Imaginary Mathematics for Computer Science, (2018)

• Foundation Mathematics for Computer Science, 2^nd edition (2015)

• 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)

• Geometric Algebra: An Algebraic System for Computer Animation and Games (2009)

• Geometric Algebra for Computer Graphics (2008)

Blurb

This second edition has been completely restructured, resulting in a compelling description of vector analysis from its first appearance as a byproduct of Hamilton’s quaternions to the use of vectors in solving geometric problems.  The result provides readers from different backgrounds with a complete introduction to vector analysis. The author shows why vectors are so useful and how it is possible to develop analytical skills in manipulating vector algebra.

Using over 150 full-colour illustrations, the author demonstrates in worked examples how this relatively young branch of mathematics has become a powerful and central tool in describing and solving a wide range of geometric problems. These may be in the form of lines, surfaces and volumes, which may touch, collide, intersect, or create shadows upon complex surfaces.

The book is divided into eleven chapters covering the history of vector analysis, linear equations, vector algebra, vector products, differentiating vector-valued functions, vector differential operators, tangent and normal vectors, straight lines, planes, intersections and rotating vectors. The new chapters are about the history, differentiating vector-valued functions, differential operators and tangent and normal vectors.  The original chapters have been reworked and illustrated.