7 ms·
The problem with carrying a vector with you is, you can't really concatenate transform. Maybe I am missing something?
by hohohmm 6y ago
The problem with carrying a vector with you is, you can't really concatenate transform. Maybe I am missing something?
- pfortuny 6y agoYou 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 6y agoa 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)
- deleted 6y ago[deleted]
- creata 6y agoI'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 6y agoyes but what about non-uniform scaling. Is it possible to handle it in this case?
- creata 6y agoNot 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.