[ 0.945175 -0.303886 0.11957 0
  0.314851 0.945175 -0.0866755 0
  -0.0866755 0.11957 0.989035 0 ]
[1 1 3]ᵀ
[0.11957 -0.0866755 0.989035]ᵀ
[1 1 3]ᵀ

transform:
[ 1 0 0 0
  0 0.707107 -0.707107 0
  0 0.707107 0.707107 10 ]
plane: [0 0.707107 0.707107 2.12132]ᵀ
ray: [0 -0.707107 0.707107]ᵀ @ [0 0 10]ᵀ
dist = -4.94975, align = 5.96046e-08
hit: [-0 0.707107 -0.707107 5.96046e-08]ᵀ
Const: {0 0.707107 0.707107 2.12132}
Original:
[ 1 6 7
  2 5 2
  3 4 7 ]
Inverted:
[ -0.385714 0.2 0.328571
  0.114286 0.2 -0.171429
  0.1 -0.2 0.1 ]
[ 1 0 0 -0
  0 1 0 -0
  0 0 1 -0 ]
Check:
-0.385714 0.200000 0.328571 
0.114286 0.200000 -0.171429 
0.100000 -0.200000 0.100000 

fmat::TRANSFORMS
[ 0.612372 -0.353553 0.707107 -3.24264
  0.5 0.866025 0 -1
  -0.612372 0.353553 0.707107 2.58579 ]
[2.64765 6.69615 6.59499]ᵀ
[2.64765 6.69615 6.59499 1]ᵀ

fmat::MATRIX<4,4>
[ 0.612372 -0.353553 0.707107 -3.24264
  0.5 0.866025 0 -1
  -0.612372 0.353553 0.707107 2.58579
  0 0 0 1 ]
[2.64765 6.69615 6.59499 1]ᵀ
[2.64765 6.69615 6.59499 1]ᵀ

NEWMAT
0.612372 -0.353553 0.707107 -3.242640 
0.500000 0.866025 0.000000 -1.000000 
-0.612372 0.353553 0.707107 2.585786 
0.000000 0.000000 0.000000 1.000000 

2.647649 
6.696152 
6.594992 
1.000000 

fmat 4x4: 14.043786
[ 1 2 3 4
  5 6 7 8
  9 10 11 12
  0 0 0 1 ]
[2.68435e+08 5.36871e+08 1.07374e+09 1.67772e+07]ᵀ

fmat Transform: 8.579473
[ 1 2 3 4
  5 6 7 8
  9 10 11 12 ]
[2.68435e+08 5.36871e+08 1.07374e+09]ᵀ


IDEAL:{0.939693 0.0914087 0.182817 0.274226}
[ 0.782756 -0.481954 0.393718 2.47259
  0.548799 0.832889 -0.0715255 4.55081
  -0.293451 0.272059 0.916444 1.47526 ]
fmat Transform: 5.739530
[ 0.587968 -0.356665 0.233832 1.7445
  0.352691 0.584223 -0.124099 2.91679
  -0.240202 0.11212 0.579519 0.541539 ]
norms:
0.726494 0.693612 0.637119
0.726357 0.693619 0.637267
error:
[ -0.194788 0.125289 -0.159885 -0.728096
  -0.196108 -0.248666 -0.0525733 -1.63402
  0.0532491 -0.159939 -0.336926 -0.933722 ]
fmat Quaternion: 8.847564
{0.940105 0.0903639 0.182063 0.273661} [2.47455 4.54958 1.47509]ᵀ
norm: 1
q err: [0.000412226 -0.00104482 -0.000754461 -0.000565261]ᵀ
p err: [0.00195622 -0.00123358 -0.0001719]ᵀ

fmat 4x4: 11.104806
[ 1.07374e+09 1.07374e+09 1.07374e+09 1.07374e+09
  4.29497e+09 4.29497e+09 4.29497e+09 4.29497e+09
  8.58993e+09 8.58993e+09 8.58993e+09 8.58993e+09
  0 0 0 1.67772e+07 ]

fmat Transform: 7.907647
[ 1.07374e+09 1.07374e+09 1.07374e+09 1.07374e+09
  4.29497e+09 4.29497e+09 4.29497e+09 4.29497e+09
  8.58993e+09 8.58993e+09 8.58993e+09 8.58993e+09 ]

Unrolled: 2.742927
1.07374e+09 1.07374e+09 1.07374e+09 1.07374e+09 
4.29497e+09 4.29497e+09 4.29497e+09 4.29497e+09 
8.58993e+09 8.58993e+09 8.58993e+09 8.58993e+09 
0 0 0 1.67772e+07