Dual Quaternions and Their Associated Clifford Algebras

Part I. Dual Quaternions, 1.1. Algebras and Dual Algebras, 1.2. Algebra, 1.3. Geometry, 1.4. Rigid Motions, 1.5. Rigid Motions as Rotations in 8-Dimensions, 1.6. Screw Linear Interpolation (ScLERP), 1.7. Perspective and Pseudo-Perspective, 1.8. Visualizing Quaternions and Dual Quaternions, 1.9. Matrices versus Dual Quaternions, 1.10. Insights, 1.11. Formulas, Part II. Clifford Algebras for Dual Quaternions, 1. A Brief Review of Clifford Algebra, 2. The Plane Model of Clifford Algebra for Dual Quaternions, 3. The Point Model of Clifford Algebra for Dual Quaternions

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Computer graphics;Clifford Algebra;graphics;Dual Quaternions;Quaternion Algebra;Hyperbolic Numbers;Dual Algebra;Pure Quaternion;Unit Quaternions;Violate;Rigid Motion;Unit Normal Vector;Perspective Projection;Quaternion Multiplication;Normal Vectors;Quaternion Products;Commutative Subalgebra;Floating Point Arithmetic;Dot Product;Vector Space;Shearing Vectors;Translation Vector;Quaternions Representing;Incidence Relations;Basis Vectors;Wedge Product;Linear Isometries