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