I notice in the derivation of the OpenGL orthographic projection matrix, as detailed in either Angel-Shreiner text or Akenine-Moller (Real Time Rendering), the z-component ends up having a negative sign, which has result of a mirror-reflection of the model about the z=0 plane.

Moller comments that this “converts from the right-handed viewing coordinate system (looking down the negative z-axis to left-handed normalized device coordinates.”

This serves to confuse the crap out of me.

Does the orthographic matrix contain the Z-coordinate mirror-reflection to “undo” another reflection which is built into the graphics HW pipeline?

Why is the “canonical view cube” mirror reflected w.r.t. z-coordinate?

We are taught to think of the camera as looking by default from the origin in direction of the negative-Z axis, but does this take into account this reflection?? After the reflection are we looking from origin in direction of +Z axis?

Can someone please explain what is going on here and why?