Mathematics for Computer Graphics
3rd Edition
Published on 26. February 2010
Book
Paperback/Softback
XV, 293 pages
978-1-84996-022-9 (ISBN)
Description
John Vince explains a wide range of mathematical techniques and problem-solving strategies associated with computer games, computer animation, virtual reality, CAD, and other areas of computer graphics.
Covering all the mathematical techniques required to resolve geometric problems and design computer programs for computer graphic applications, each chapter explores a specific mathematical topic prior to moving forward into the more advanced areas of matrix transforms, 3D curves and surface patches. Problem-solving techniques using vector analysis and geometric algebra are also discussed.
All the key areas are covered including: Numbers, Algebra, Trigonometry, Coordinate geometry, Transforms, Vectors, Curves and surfaces, Barycentric coordinates, Analytic geometry.
Plus - and unusually in a student textbook - a chapter on geometric algebra is included.
Reviews / Votes
From the reviews of the third edition:
"Slim volume could be a computer graphics student's (and professor's) next best friend. . the style of writing is crisp and the approach is practical. Although the theory is light, rigorous detailed derivations on each topic, sometimes from more than one approaches are plentiful and characterize the author's approach throughout the entire book. It is surprising to find really practical mathematics packaged in fewer than 300 pages. For those studying or teaching computer graphics, this book will be a valuable companion to have on hand." (Anthony J. Duben, ACM Computing Reviews, September, 2010)More details
Series
Edition
3rd ed. 2010
Language
English
Place of publication
London
United Kingdom
Target group
Professional and scholarly
Lower undergraduate
Edition type
Revised edition
Product notice
Paperback (trade)
Illustrations
14 s/w Tabellen
14 black & white tables, biography
Dimensions
Height: 23.5 cm
Width: 15.5 cm
Thickness: 16 mm
Weight
970 gr
ISBN-13
978-1-84996-022-9 (9781849960229)
DOI
10.1007/978-1-84996-023-6
Schweitzer Classification
Other editions
New editions
John Vince
Mathematics for Computer Graphics
Book
07/2025
7th Edition
Springer
€80.24
Shipment within 15-20 days
John Vince
Mathematics for Computer Graphics
Book
04/2022
6th Edition
Springer
€64.19
Article exhausted; check for reprint
John Vince
Mathematics for Computer Graphics
Book
09/2017
5th Edition
Springer
€64.19
Article exhausted; check for reprint
Additional editions
John A. Vince
Mathematics for Computer Graphics
E-Book
01/2010
3rd Edition
Springer
€29.99
Available for download
Previous edition
John Vince
Mathematics for Computer Graphics
Book
11/2005
2nd Edition
Springer
€37.40
Article exhausted; check for reprint
Person
John Vince has been writing books for 25 years. Previous publications with Springer include:
Geometric Algebra: An Algebraic System for Computer Games and Animation Springer, 2009, ISBN 978-1-84882-378-5
Vector Analysis for Computer Graphics
Springer, 2007, ISBN 978-1-84628-803-6
Mathematics for Computer Graphics
Springer, 2006, ISBN 1-84628-034-6
Introduction to Virtual Reality
Springer, 2004, ISBN 1-85233-739-7
More information can be found at http://www.johnvince.co.uk/
Content
Mathematics.- Introduction.- Is Mathematics Difficult?.- Who Should Read this book?.- Aims and Objectives of this Book.- Assumptions Made in this Book.- How to use the Book.- Numbers.- Introduction.- Natural Numbers.- Prime Numbers.- Integers.- Rational Numbers.- Irrational Numbers.- Real Numbers.- The Number Line.- Complex Numbers.- Summary.- Algebra.- Introduction.- Notation.- Algebraic Laws.- Associative Law.- Commutative Law.- Distributive Law.- Solving the Roots of a Quadratic Equation.- Indices.- Laws of Indices.- Examples.- Logarithms.- Further Notation.- Summary.- Trigonometry.- Introduction.- The Trigonometric Ratios.- Example.- Inverse Trigonometric Ratios.- Trigonometric Relationships.- The Sine Rule.- The Cosine Rule.- Compound Angles.- Perimeter Relationships.- Summary.- Cartesian Coordinates.- Introduction.- The Cartesian xy-plane.- Function Graphs.- Geometric Shapes.- Polygonal Shapes.- Areas of Shapes.- Theorem of Pythagoras in 2D.- 3D Coordinates.- Theorem of Pythagoras in 3D.- 3D polygons.- Euler's Rule.- Summary.- Vectors.- Introduction.- 2D Vectors.- Vector Notation.- Graphical Representation of Vectors.- Magnitude of a Vector.- 3D Vectors.- Vector Manipulation.- Multiplying a Vector by a Scalar.- Vector Addition and Subtraction.- Position Vectors.- Unit Vectors.- Cartesian Vectors.- Vector Multiplication.- Scalar Product.- Example of the Scalar Product.- The Dot Product in Lightening Calculations.- The Scalar Product in Back-Face Detection.- The Vector Product.- The Right-Hand Rule.- Deriving a Unit Normal Vector for a Triangle.- Areas.- Calculating 2D Areas.- Summary.- Transforms.- Introduction.- 2D Transforms.- Translation.- Scaling.- Reflection.- Matrices.- Systems of Notation.- The Determinant of a Matrix.- Homogeneous Coordinates.- 2D Translation.- 2D Scaling.- 2D Reflections.- 2D Shearing.- 2D Rotation.- 2DScaling.- 2D Reflection.- 2D Rotation about an Arbitrary Point.- 3D Transforms.- 3D Translation.- 3D Scaling.- 3D Rotation.- Gimbal Lock.- Rotating about an Axis.- 3D Reflections.- Change of Axes.- 2D Change of Axes.- Direct Cosines.- 3D Change of Axes.- Positioning on the Virtual Camera.- Direction Cosines.- Euler Angles.- Rotating a point about an Arbitrary Axis.- Matrices.- Quaternions.- Adding and Subtracting Quaternions.- Multiplying Quaternions.- Pure Quaternion.- The Inverse Quaternion.- Unit Quaternion.- Rotating Points about an Axis.- Roll, Pitch and Yaw Quaternions.- Quaternions in Matrix Form.- Frames of Reference.- Transforming Vectors.- Determinants.- Perspective Projection.- Summary.- Interpolation.- Introduction.- Linear Interpolation.- Non-Linear Interpolation.- Trigonometric Interpolation.- Cubic Interpolation.- Interpolating Vectors.- Interpolating Quaternions.- Summary.- Curves and Patches.- Introduction.- The Circle.- The Ellipse.- Bezier Curves.- Bernstein Polynomials.- Quadratic Bezier Curves.- Cubic Bernstein Polynominals.- A Recursive Bezier Formula.- Bezier Curves Using Matrices.- Linear Interpolation.- B-Splines.- Continuity.- Non-Uniform B-Splines.- Non-Uniform Rational B-Splines.- Surface Patches.- Planar Surface Patch.- Quadratic Bezier Surface Patch.- Cubic Bezier Surface Patch.- Summary.- Analytical Geometry.- Introduction.- Review of Geometry.- Angles.- Intercept Theorems.- Golden Section.- Triangles.- Centre of Gravity of a Triangle.- Isosceles Triangle.- Equilateral Triangle.- Right Triangle.- Theorem of Thales.- Theorem of Pythagoras.- Quadrilaterals.- Trapezoid.- Parallelogram.- Rhombus.- Regular Polygon (n-gon).- Circle.- 2D Analytical Geometry.- Equation of a Straight Line.- The Hessian Normal Form.- Space Partitioning.- The Hessian Normal Form From Two Points.- Intersection Points.- Intersection Point of Two Straight Lines.- Intersection Point of Two Line Segments.- Point Insi