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OpenGL Order of pixel operations - pixel shader/depth test

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I've heard that performing a "Pre-Z" depth only rendering pass can improve performance when you're executing complex pixel shaders for potentially occluded objects, the idea being (I think) that occluded pixels will be rejected by the depth test before having to execute their pixel shaders. This makes sense, and judging by my searches of gamedev and google, this technique seems to be fairly well known, even having been recommended in a couple of presentations I saw from ATI. However, according to the OpenGL and Direct3D documentation, the depth test in both API's is not performed until after the pixel shader is executed (this makes sense too, since the pixel shader could potentially modify a fragment's depth). So does a "Pre-Z" pass actually do anything? If so, what am I missing? Direct3D pipeline diagram, from Gamasutra: Direct3D9 pipeline

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If the pixel shader doesn't modify the depth then the pixel/fragment can be culled before the pixel shader is even run (early-z). If the pixel shader does modify the depth then the early depth test can not be performed and the pixel shader must be ran before the depth test can be done.

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The z-test is conceptually performed after the pixel shader is modified. The APIs require the hardware to behave 'as if' the test is performed at that point. In actual hardware though there is a fair bit of silicon dedicated to optimizing things so that in the common case of the pixel shader not modifying depth the hardware can do an early reject of the fragments and never run the pixel shader. Most hardware uses some kind of hierarchical z buffer to optimize this early z rejection and this often allows large numbers of fragments to be discarded early in the pipeline.

Certain things tend to disable this fast path though - modifying z in the pixel shader is an obvious one. Alpha testing and texkill can also disable this optimization on some hardware. This is the main reason you'll generally see hardware vendors recommend against changing depth in the pixel shader as it can have a large performance penalty by disabling all this valuable optimization.

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You're missing the point of the Z prepass though.

Lets say your Z prepass shader is simple, which is what you want. The vertex shader just transforms position, and the pixel shader does nothing. Lets say this takes 1 cycle/pixel to run.

Now lets assume you have heavy shaders, using multiple textures, complex per pixel lighting, taking 100 cycles/pixel to run.

Lets assume the average overdraw in your scene is 2. Overdraw is inevitable unless you have perfect Z sorting, which never happens. Some pixel tend to be shaded 3 times, some twice, some once, but on average, every pixel is drawn to twice.

Lets further assume that when a Z test fails, it takes a cycle/pixel to process.

Regular render: Cost = 200 cycles/pixel on average.
Z prepass render: 103 cycles/pixel on average.

The Z prepass is 2 draws/pixel of the quick Z only render, followed by a full render which will shade this pixel once, for the nearest depth, and Z fail once.

Lets assume random Z ordering of those heavy passes during regular rendering, Half the pixels will be drawn twice (200 cycles/pixel), and half will be drawn once and Z failed once (101 cycles/pixel), for an average of 150.5 cycles/pixel.

More realistic regular render = 150.5 cycles/pixel
Z prepass render: 103 cycles/pixel on average.

There are so many things which can change the balance of this that you need to test your app to see if it's a win for you, but the theory behind doing a Z pre-pass is quite sound.

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