Avoids nasty code all over where such math is required, and
compilers can easily deal with such situation.
Don't prefer questionable micro-optimization which comes with
a cost of nasty actual logic code.
In some heavy rigs matrix inverse can be 10% of computation time. This
reduces it to 2% by using Eigen's optimized 4x4 matrix inverse and SSE
matrix multiplication.
- Remove 'rotate_m2', unlike 'rotate_m4' it created a new matrix
duplicating 'angle_to_mat2' - now used instead.
(better avoid matching functions having different behavior).
- Add 'axis_angle_to_mat4_single',
convenience wrapper for 'axis_angle_to_mat3_single'.
- Replace 'unit_m4(), rotate_m4()' with a single call to 'axis_angle_to_mat4_single'.
mul_m4_m4m4(R, A, B) gives us R = AB in general. Existing code assumed the worst, that A and B both alias the output R. For safety it makes internal copies of A and B before calculating & writing R.
This is the least common case. Usually all 3 matrices differ. Often we see M = AM or M = MB, but never M = MM.
With this revision mul_m4_m4m4 is called in exactly the same way but copies inputs only when needed. If you know the inputs are independent of the output use the "uniq" variant to skip the saftety checks.
mat3_polar_decompose gives the right polar decomposition of given matrix,
as a pair (U, P) of matrices.
interp_m3_m3m3 uses that polar decomposition to perform a correct matrix interpolation,
even with non-uniformly scaled ones (where blend_m3_m3m3 would fail).
interp_m4_m4m4 just adds translation interpolation to the _m3 variant.
`BLI_space_transform_from_matrices()` defines a 'global-invariant' transform
(same point in global space, two different coordinates in local and target spaces).
New `BLI_space_transform_global_from_matrices()` is kind of opposite, it defines
a 'local-invariant' transform (two different points in global space, same coordinates in local and target spaces).
Useful to 'match' meshes.
That's really annoying that multiplication order is flipped
comparing mat3 and mat4 cases, but for the purposes of not
breaking all the branches which might use this stuff we'd
better keep order consistent with old version for now.
Suggestion here would be to make order consistent but rename
this functions to mult_* to make compilation fail instead
of failing and using wrong order silently.
