Titlebook: Rethinking Quaternions; Ron Goldman Book 2010 Springer Nature Switzerland AG 2010

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Clifford Algebras and Quaternions only the sum, but also the product of every two elements in the algebra is defined. Let .,…,. be an orthonormal basis for .. Then the 2. canonical generators (basis vectors) of the Clifford algebra for . are denoted by the products:.Notice that there are . products with exactly . factors, so there

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operands and operators—Mass-Points and Quaternions of the even dimensional elements, the quaternions ., and one consisting of the odd dimensional elements, the duals . of the quaternions. Let.) = the Clifford algebra of .). = the even dimensional elements of . (R.) ≅ .). = the odd dimensional element of .(R.) ≅ ..

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Goals and Motivationation so that we can solve linear equations (see Section 4, especially Exercises 4.9-4.12). This void makes the study of transformations in higher dimensions more cumbersome than in lower dimensions; typically we need to resort to matrix methods rather than rely on direct manipulation of vector products.

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Book 2010tions: to increase speed and reduce storage for calculations involving rotations, to avoid distortions arising from numerical inaccuracies caused by floating point computations with rotations, and to interpolate between two rotations for key frame animation. Yet while the formal algebra of quaternio

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978-3-031-79548-0Springer Nature Switzerland AG 2010

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