Mathematics for Computer Graphics, Vince J., 2014

Mathematics for Computer Graphics, Vince J., 2014.   

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.




Background.
Over the centuries, mathematicians have realised that in order to progress, they must give precise definitions to their discoveries, ideas and concepts, so that they can be built upon and referenced by new mathematical inventions. In the event of any new discovery, these definitions have to be occasionally changed or extended. For example, once upon a time, integers, rational and irrational numbers, satisfied all the needs of mathematicians, until imaginary quantities were invented. Today, complex numbers have helped shape the current number system hierarchy. Consequently, there must be clear definitions for numbers, and the operators that act upon them. Therefore, we need to identify the types of numbers that exist, what they are used for, and any problems that arise when they are stored in a computer.

Contents.
1.Mathematics.
2.Numbers.
3.Algebra.
4.Trigonometry.
5.Coordinate Systems.
6.Vectors.
7.Transforms.
8.Interpolation.
9.Curves and Patches.
10.Analytic Geometry.
11.Barycentric Coordinates.
12.Geometric Algebra.
13.Calculus: Derivatives.
14.Calculus: Integration.
15.Worked Examples.
16.Conclusion.



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