opengl,graphics,3d , Why Z is affected by the perscpective division?

## Question:

Tag: opengl,graphics,3d

I recently realized that OpenGL performs perspective division not only for `x` and `y`, but for `z` too.

In my understanding `x /= w;` and `y /= w;` would be enough. Of course, then we would need different projection matrixes.

So, why OpenGL does `z /= w;`? To make z-buffer more precise on short distances but less precise on long ones?

Mathematically, dividing all components is the correct way. That way, interpolating `z` in screen space linearily (perspective correct interpolation is not done for position data, as it is supposed to be interpolated in screen space). The linear interpolation in sceen space of course means that looking at this in eye or object space, it appears nonlinear. It simply means for an object not parallel to the image plane, going one pixel to the left on the screen does mean going a variable amount along + or -z, depending on the distance - so the perspecitve actually does distort the z axis, too.

The side effect is that Z buffer precision is highest at the near plane, and that is actually a good thing for most scenes.

Using an "undivided" Z for depth test is called W buffer. But that means that the linear interpolation can't be used any more. However, with modern GPUs, that is not a too big issue.

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