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If you have a rotation quaternion q=(x,y,z,w), then -q=(-x,-y,-z,-w) describes the same rotation (quaternions are invariant under sign change), so you cannot rely on z being positive.

A quaternion is essentially a rotation axis (x,y,z) and an amount of rotation w (I avoid the word angle because it's not an angle in the usual sense). If you change the sign on w, you reverse the rotation direction. The same thing happens if you mirror the rotation axis to (-x,-y,-z). So if you do both, these effects cancel each other out.

If you have a rotation quaternion q=(x,y,z,w), then -q=(-x,-y,-z,-w) describes the same rotation (quaternions are invariant under sign change), so you cannot rely on z (or any other component) being positive.

A quaternion is essentially a rotation axis (x,y,z) and an amount of rotation w (I avoid the word angle because it's not an angle in the usual sense). If you change the sign on w, you reverse the rotation direction. The same thing happens if you mirror the rotation axis to (-x,-y,-z). So if you do both, these effects cancel each other out.

If you have a rotation quaternion q=(x,y,z,w), then -q=(-x,-y,-z,-w) describes the same rotation (quaternions are invariant under sign change), rotation, so you cannot rely on z (or any other component) being positive.

A quaternion is essentially a rotation axis (x,y,z) and an amount of rotation w (I avoid the word angle because it's not an angle in the usual sense). If you change the sign on w, you reverse the rotation direction. The same thing happens if you mirror the rotation axis to (-x,-y,-z). So if you do both, these effects cancel each other out.

If you have a rotation quaternion q=(x,y,z,w), then -q=(-x,-y,-z,-w) describes the same rotation, so you cannot rely on z (or any other component) being positive.

A rotation quaternion is essentially a rotation axis (x,y,z) and an amount of rotation w (I avoid the word angle because it's not an angle in the usual sense). sense), scaled to unit length (|q|=1). If you change the sign on w, you reverse the rotation direction. The same thing happens if you mirror the rotation axis to (-x,-y,-z). So if you do both, these effects cancel each other out.

If you have a rotation quaternion q=(x,y,z,w), then -q=(-x,-y,-z,-w) describes the same rotation, so you cannot rely on z (or any other component) being positive.

A rotation quaternion is essentially a rotation axis (x,y,z) and an amount of rotation w (I avoid the word angle because it's not an angle in the usual sense), scaled to unit length (|q|=1). If you change the sign on of w, you reverse the rotation direction. The same thing happens if you mirror the rotation axis to (-x,-y,-z). So if you do both, these effects cancel each other out.