Vector Analysis for Computer Graphics

This second edition of the book provides a complete introduction to vector analysis, from its origins in Hamilton's quaternions to its use in solving geometric problems. It is divided into eleven chapters, with new chapters on the history, differential operators, and tangent and normal vectors. The original chapters have been reworked and illustrated.

Format: Hardback
Length: 246 pages
Publication date: 02 June 2021
Publisher: Springer London Ltd

This second edition of the book has undergone a complete restructuring, resulting in a captivating account of vector analysis, spanning from its initial emergence as a byproduct of Hamilton's quaternions to its application in solving geometric problems. The result offers readers with diverse backgrounds a comprehensive introduction to vector analysis. The author elucidates the rationale behind vectors' immense utility and guides readers in developing analytical proficiency in manipulating vector algebra. Through the use of over 150 full-color illustrations, the author showcases in detailed worked examples how this relatively young branch of mathematics has evolved into a formidable and indispensable tool for describing and resolving a wide array of geometric challenges. These challenges may manifest in the form of lines, surfaces, and volumes, which may interact, collide, intersect, or cast shadows upon complex surfaces.

The book is organized into eleven chapters, each dedicated to exploring different aspects of vector analysis. The historical background of vector analysis is covered in depth, providing a foundation for the subsequent chapters. Linear equations form the core of this section, laying the groundwork for the subsequent discussions. Vector algebra is introduced, building upon the concepts of linear equations and introducing the fundamental operations of vector addition, subtraction, and multiplication. Vector products are explored, enabling the calculation of the cross-product and the dot product of vectors. Differentiating vector-valued functions is a crucial step in understanding the behavior of vector-based quantities. Vector differential operators are introduced, allowing for the analysis of vector-valued functions and the solution of differential equations. Tangent and normal vectors are discussed, providing insights into the geometry of curves and surfaces. Straight lines, planes, intersections, and rotating vectors are explored, extending the concepts of vector analysis to three-dimensional spaces.

In addition to the restructuring of the original chapters, several new chapters have been added to this edition. These chapters focus on the history of vector analysis, the differentiation of vector-valued functions, differential operators, and tangent and normal vectors. The original chapters have been reworked and illustrated to enhance their clarity and understanding.

Overall, this second edition of Vector Analysis: A Comprehensive Introduction offers readers a thorough and up-to-date exploration of vector analysis, from its historical origins to its contemporary applications. With its extensive illustrations, detailed explanations, and practical examples, the book provides a valuable resource for students, researchers, and practitioners in the fields of mathematics, engineering, and physics.

Weight: 542g
Dimension: 160 x 241 x 22 (mm)
ISBN-13: 9781447175049
Edition number: 2nd ed. 2021