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Quaternions for Computer Graphics / by John Vince
Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: SpringerLink BücherPublisher: London : Springer-Verlag London Limited, 2011Description: Online-Ressource (XIV, 140p. 33 illus, digital)ISBN:- 9780857297600
- 006.60151
- QA76.9.C62
- T385
Contents:
Summary: John VinceSummary: Sir William Rowan Hamilton was a genius, and will be remembered for his significant contributions to physics and mathematics. The Hamiltonian, which is used in quantum physics to describe the total energy of a system, would have been a major achievement for anyone, but Hamilton also invented quaternions, which paved the way for modern vector analysis. Quaternions are one of the most documented inventions in the history of mathematics, and this book is about their invention, and how they are used to rotate vectors about an arbitrary axis. Apart from introducing the reader to the features of quaternions and their associated algebra, the book provides valuable historical facts that bring the subject alive. Quaternions for Computer Graphics introduces the reader to quaternion algebra by describing concepts of sets, groups, fields and rings. It also includes chapters on imaginary quantities, complex numbers and the complex plane, which are essential to understanding quaternions. The book contains many illustrations and worked examples, which make it essential reading for students, academics, researchers and professional practitioners.PPN: PPN: 1650964943Package identifier: Produktsigel: ZDB-2-SCS
""Quaternions for Computer Graphics""; ""Preface""; ""Contents""; ""Chapter 1: Introduction""; ""1.1 Rotation Transforms""; ""1.2 The Reader""; ""1.3 Aims and Objectives of This Book""; ""1.4 Mathematical Techniques""; ""1.5 Assumptions Made in This Book""; ""Chapter 2: Number Sets and Algebra""; ""2.1 Introduction""; ""2.2 Number Sets""; ""2.2.1 Natural Numbers""; ""2.2.2 Real Numbers""; ""2.2.3 Integers""; ""2.2.4 Rational Numbers""; ""2.3 Arithmetic Operations""; ""2.4 Axioms""; ""2.5 Expressions""; ""2.6 Equations""; ""2.7 Ordered Pairs""; ""2.8 Groups, Rings and Fields""
""2.8.1 Groups""""2.8.2 Abelian Group""; ""2.8.3 Rings""; ""2.8.4 Fields""; ""2.8.5 Division Ring""; ""2.9 Summary""; ""2.9.1 Summary of Definitions""; ""Chapter 3: Complex Numbers""; ""3.1 Introduction""; ""3.2 Imaginary Numbers""; ""3.3 Powers of i""; ""3.4 Complex Numbers""; ""3.5 Adding and Subtracting Complex Numbers""; ""3.6 Multiplying a Complex Number by a Scalar""; ""3.7 Complex Number Products""; ""3.7.1 Square of a Complex Number""; ""3.8 Norm of a Complex Number""; ""3.9 Complex Conjugate""; ""3.10 Quotient of Two Complex Numbers""; ""3.11 Inverse of a Complex Number""
""3.12 Square-Root of i""""3.13 Field Structure""; ""3.14 Ordered Pairs""; ""3.14.1 Multiplying by a Scalar""; ""3.14.2 Complex Conjugate""; ""3.14.3 Quotient""; ""3.14.4 Inverse""; ""3.15 Matrix Representation of a Complex Number""; ""3.15.1 Adding and Subtracting""; ""3.15.2 The Product""; ""3.15.3 The Square of the Norm""; ""3.15.4 The Complex Conjugate""; ""3.15.5 The Inverse""; ""3.15.6 Quotient""; ""3.16 Summary""; ""3.16.1 Summary of Operations""; ""3.17 Worked Examples""; ""Chapter 4: The Complex Plane""; ""4.1 Introduction""; ""4.2 Some History""; ""4.3 The Complex Plane""
""4.4 Polar Representation""""4.5 Rotors""; ""4.6 Summary""; ""4.6.1 Summary of Operations""; ""4.7 Worked Examples""; ""Chapter 5: Quaternion Algebra""; ""5.1 Introduction""; ""5.2 Some History""; ""5.3 Defining a Quaternion""; ""5.3.1 The Quaternion Units""; ""5.3.2 Example of Quaternion Products""; ""5.4 Algebraic Definition""; ""5.5 Adding and Subtracting Quaternions""; ""5.6 Real Quaternion""; ""5.7 Multiplying a Quaternion by a Scalar""; ""5.8 Pure Quaternion""; ""5.9 Unit Quaternion""; ""5.10 Additive Form of a Quaternion""; ""5.11 Binary Form of a Quaternion""; ""5.12 The Conjugate""
""5.13 Norm of a Quaternion""""5.14 Normalised Quaternion""; ""5.15 Quaternion Products""; ""5.15.1 Product of Pure Quaternions""; ""5.15.2 Product of Two Unit-Norm Quaternions""; ""5.15.3 Square of a Quaternion""; ""5.15.4 Norm of the Quaternion Product""; ""5.16 Inverse Quaternion""; ""5.17 Matrices""; ""5.17.1 Orthogonal Matrix""; ""5.18 Quaternion Algebra""; ""5.19 Summary""; ""5.19.1 Summary of Operations""; ""5.20 Worked Examples""; ""Chapter 6: 3D Rotation Transforms""; ""6.1 Introduction""; ""6.2 3D Rotation Transforms""; ""6.3 Rotating About a Cartesian Axis""
""6.4 Rotate About an Off-Set Axis""
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