Question

I have a box defined by 8 points. From those points, I calculate axes and create rotation matrix as follows:

axis[0], axis[1], axis[2]
mat = 
{
  axis[0].x axis[1].x axis[2].x 0
  axis[0].y axis[1].y axis[2].y 0
  axis[0].z axis[1].z axis[2].z 0
  0         0         0         1
}

I have particular rotation matrix:

{
  -1  0  0  0
   0  0  1  0 
   0 -1  0  0
   0  0  0  1
}

As best of my knowledge, this is a valid rotation matrix. Its inversion is equal to its transposition.

Now I would like to store this matrix as a quaternion. But later, I need rotation matrix to be recreated from this quaternion. I believe that convertsion from matrix to quaternion and back to matrix should be an identity transform and I should get the same matrix that I had in the beginning (maybe with very small numerical errors).

But this seems not to be the case. Both SlimDX (C#) and my propertiary math library (C++) return invalid matrix.

First, quaternion that I receive:

C#:  0, 0, 0.70710676908493, 0
C++: 0, -0.707107, 0, 0

And matrix created from this quaternion:

C#:

0 0 0 0
0 0 0 0
0 0 1 0
0 0 0 1

C++:

0 0 0 0 
0 1 0 0
0 0 0 0
0 0 0 1

Why is this wrong?

I’ve also tried this: http://cache-www.intel.com/cd/00/00/29/37/293748_293748.pdf but it gave me bad results as well.

Answer 1

The matrix you gave isn’t a rotation matrix, it’s a reflection matrix because its determinant is -1. See the definition on Wikipedia. You can tell something isn’t right because you should get a unit quaternion, and yet the one you’re getting back only has length 1/sqrt(2).