Transformation: What would be the quaternion to characterize a chamber pose if the YYZ axis are inverse?

GitHub dialogue: https://github.com/colmap/glomap/points/161#issuecomment-2641739710

Focus 1:

When altering the digital camera coordinate system, we alter the transformation of a 3D level from the world body to the digital camera body. The unique transformation of the world to the unique digital camera is:

$$ p_ {oc} = r cdot pw + t $$

The transformation of the unique digital camera to the Habitat Chamber is:

$$ P_ {HC} = Start {pmatrix} 1 & 0 0 & −1 & 0 0 & 0 & −1 finish {pmatrix} P_ {oc} = r_x ( pi) p_ { oc} $$

By combining the above transformations, the interpretation $$ (t_x, t_y, t_z) $$ will change to $$ (t_x, – t_, – t_z) $$ Rotation R will change Arx (180 °) r, and within the type of quaternion: i ⋅ (W + xi + yj + zk) = – x + wi – zj + yk. Right here, it represents a 180 diploma rotation across the X axis.

APPROACH 2:

The identical is a 180 diploma rotation across the X axis. Then the angle axis is:

$$ ( textual content {angle, axis}) = ( start {pmatrix} 1 0 0 finish {pmatrix}, pi) $$

If we make it quaternion, it must be

$$ q = start {pmatrix} cos ( pi / 2) with out ( pi / 2) cos ( pi / 2) cos ( pi / 2) finish { Pmatrix} = start {pmatrix} 0 1 0 0 finish {pmatrix} $$

So the consequence will likely be $$ qpq^{-1} = (0 1 0 0) (wxyz) (0 1 0 0)^{-1} = (wx -y -Z) $$

Which is appropriate and why is the opposite evil?