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A comment on Geometric Algebra (2012). Parent comment

Re:Geometric Algebra (2012) by pfortuny on Monday November 30, 2020 @03:39AM (#25251881)
You work with 4x4 (in 3D space) matrices, with a specific form (a row/columb of 1’s). The affine part of a projective transformation.

All this GA stuff is OK but what is the problem with matrices of affine transformations?

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Re:Geometric Algebra (2012) by enkimute on Monday November 30, 2020 @04:18AM (#25252078)
a selection:

- no closed form exponential/logarithm (i.e. cant interpolate)

- no numerical stability for subgroups (i.e. need Gramm-Shmidt, SVD)

- no covariant transformations (i.e. need adjugate to transform axial vectors)

- no geometric construction. (e.g. in GA product of two elements is (square of) versor between them)

- costly inverses (just some sign swaps in GA)

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