Mathematics for Computer Graphics

Mathematics for Computer Graphics is a comprehensive textbook that covers a wide range of mathematical techniques and problem-solving strategies used in computer graphics, including computer games, animation, special effects, virtual reality, CAD, and more. It includes chapters on number sets, algebra, trigonometry, coordinate systems, determinants, vectors, matrix algebra, complex numbers, geometric transforms, quaternion algebra, quaternions in space, interpolation, curves and patches, analytical geometry, and barycentric coordinates. The sixth edition has been revised and expanded and includes over 330 color illustrations and 150 worked examples.

Format: Paperback / softback
Length: 564 pages
Publication date: 06 May 2022
Publisher: Springer London Ltd

In this extensively revised and expanded sixth edition, John Vince delves into a comprehensive array of mathematical techniques and problem-solving strategies that are intertwined with computer games, computer animation, special effects, virtual reality, CAD, and various other domains of computer graphics. The book commences with a foundational introduction, encompassing number sets, algebra, trigonometry, and coordinate systems, which serve as the building blocks for subsequent chapters on determinants, vectors, matrix algebra, complex numbers, geometric transforms, quaternion algebra, quaternions in space, interpolation, curves and patches, analytical geometry, and barycentric coordinates.

Subsequently, the reader is introduced to the relatively recent field of geometric algebra, followed by two chapters that delve into differential and integral calculus. The culmination of the book is a chapter dedicated to worked examples, offering practical insights and applications of the mathematical concepts discussed throughout.

Mathematics for Computer Graphics encompasses a vast range of essential topics within the discipline, including:

Number Sets: This foundational chapter explores the concepts and operations related to sets, which form the basis of mathematical reasoning and problem-solving.

Algebra: Algebra is a fundamental branch of mathematics that deals with the study of variables, equations, and expressions. It encompasses topics such as linear equations, quadratic equations, polynomials, and matrices.

Trigonometry: Trigonometry is a branch of mathematics that deals with the relationships between angles, lengths, and heights. It provides the foundation for understanding geometric shapes, trigonometric functions, and their applications in computer graphics.

Complex Numbers: Complex numbers are a mathematical extension of real numbers that involves the addition and multiplication of complex numbers. They are essential in fields such as physics, engineering, and computer graphics, where complex equations and transformations are commonly used.

Coordinate Systems: Coordinate systems are a framework for representing and manipulating points, lines, and shapes in two or three dimensions. They provide a systematic way to describe and analyze geometric objects and their relationships.

Determinants: Determinants are mathematical objects that are used to calculate the determinant of a matrix. They play a crucial role in matrix algebra, which is fundamental in computer graphics for modeling and manipulating 3D objects.

Vectors: Vectors are mathematical quantities that have both magnitude and direction. They are used to represent physical quantities such as displacement, velocity, and force and are essential in computer graphics for defining and manipulating geometric objects.

Quaternions: Quaternions are a mathematical extension of complex numbers that are used to represent rotations in three dimensions. They are particularly useful in computer graphics for simulating complex animations and generating realistic visual effects.

Matrix Algebra: Matrix algebra is a branch of mathematics that deals with the manipulation and analysis of matrices. Matrices are a fundamental tool in computer graphics for modeling and manipulating 3D objects, as well as for performing geometric transformations.

Geometric Transformations: Geometric transformations are mathematical operations that transform points, lines, and shapes in a geometric space. They are used in computer graphics to create animations, render 3D scenes, and perform image processing tasks.

Interpolation: Interpolation is a technique used to estimate unknown values between given data points. It is widely used in computer graphics for generating smooth curves, surfaces, and animations.

Curves and Patches: Curves and patches are geometric objects that are used to represent and manipulate shapes in computer graphics. They can be defined using mathematical equations and are essential for creating realistic 3D models and animations.

Analytic Geometry: Analytic geometry is a branch of mathematics that deals with the study of geometric shapes and their properties using algebraic equations. It is used in computer graphics for defining and manipulating geometric objects in a precise and efficient manner.

Barycentric Coordinates: Barycentric coordinates are a system of coordinates that is used to represent points, lines, and surfaces in three dimensions. They are particularly useful in computer graphics for defining and manipulating objects in a non-linear and hierarchical manner.

Geometric Algebra: Geometric algebra is a branch of mathematics that combines the principles of geometry and algebra. It is used in computer graphics for representing and manipulating geometric objects in a more concise and efficient manner.

Differential Calculus: Differential calculus is a branch of mathematics that deals with the study of rates of change and the integration of functions. It is used in computer graphics for modeling and simulating physical phenomena such as motion, fluid dynamics, and heat transfer.

Integral Calculus: Integral calculus is a branch of mathematics that deals with the integration of functions and the evaluation of infinite sums. It is used in computer graphics for modeling and simulating complex systems and processes.

This sixth edition of Mathematics for Computer Graphics boasts an extensive collection of approximately 150 meticulously worked examples and over 330 vibrant color illustrations, which serve as the focal points of the author's descriptive writing style. These visual aids enhance the reader's understanding and comprehension of the mathematical concepts presented, fostering a deeper grasp of the subject matter.

Mathematics for Computer Graphics serves as an invaluable resource for individuals seeking to gain a solid foundation in the mathematics required for computer graphics software development and for those embarking on further exploration of advanced books and technical research papers in the field. By providing a comprehensive and coherent treatment of the subject, this book equips readers with the necessary tools to excel in the dynamic and rapidly evolving world of computer graphics.

Weight: 890g
Dimension: 235 x 155 (mm)
ISBN-13: 9781447175193
Edition number: 6th ed. 2022