Original point matrix:
[1 0 0 0 ;
0 1 0 0 ;
0 0 1 0]
Recovered point matrix:
[ -0.656929 -0.148709 0.701511 0.104128 ;
-0.232861 0.293848 -0.428608 0.367621 ;
-0.449133 0.760946 -0.108067 -0.203746 ]
Visualization (original is orange, recovered is blue):