The problem with carrying a vector with you is, you can't really concatenate tra...

creata · on Nov 30, 2020

I'm not sure what you mean. Let Ax mean rotating x by A (which is a rotation matrix, quaternion, rotor, whatever). Then, the composition of Ax + b and Cx + d is

    C(Ax + b) + d = (CA)x + (Cb + d).

hohohmm · on Nov 30, 2020

yes but what about non-uniform scaling. Is it possible to handle it in this case?

creata · on Nov 30, 2020

Not with just a rotor (quaternion) and an offset, or with motors (dual quaternions). If you want nonuniform scaling, rotation and translation, then matrices are probably the nicest way to do that.

pfortuny · on Nov 30, 2020

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?

enkimute · on Nov 30, 2020

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)