## Musing about Deferred Shading.

One of the subjects which fascinate me is, Computer-Generated Images, CGI, specifically, that render a 3D scene to a 2D perspective. But that subject is still rather vast. One could narrow it by first suggesting an interest in the hardware-accelerated form of CGI, which is also referred to as “Raster-Based Graphics”, and which works differently from ‘Ray-Tracing’. And after that, a further specialization can be made, into a modern form of it, known a “Deferred Shading”.

What happens with Deferred Shading is, that an entire scene is Rendered To Texture, but in such a way that, in addition to surface colours, separate output images also hold normal-vectors, and a distance-value (a depth-value), for each fragment of this initial rendering. And then, the resulting ‘G-Buffer’ can be put through post-processing, which results in the final 2D image. What advantages can this bring?

• It allows for a virtually unlimited number of dynamic lights,
• It allows for ‘SSAO’ – “Screen Space Ambient Occlusion” – to be implemented,
• It allows for more-efficient reflections to be implemented, in the form of ‘SSR’s – “Screen-Space Reflections”.
• (There could be more benefits.)

One fact which people should be aware of, given traditional strategies for computing lighting, is, that by default, the fragment shader would need to perform a separate computation for each light source that strikes the surface of a model. An exception to this has been possible with some game engines in the past, where a virtually unlimited number of static lights can be incorporated into a level map, by being baked in, as additional shadow-maps. But when it comes to computing dynamic lights – lights that can move and change intensity during a 3D game – there have traditionally been limits to how many of those may illuminate a given surface simultaneously. This was defined by how complex a fragment shader could be made, procedurally.

(Updated 1/15/2020, 14h45 … )

## Observations about the Z-Buffer

Any game-engine currently on the market, uses the GPU of your computer – or your tablet – to do most of the work of rendering 3D scenes to a 2D screen, that also represents a virtual camera-position. There are two constants about this process which the game-engine defines, which are the closest distance at which fragments are allowed to be rendered, which I will name ‘clip-near’, and the maximum distance rendering is to be extended to, which I will name ‘clip-far’.

Therefore, what some users might expect, is that the Z-buffer, which determines the final outcome of the occlusion of the fragments, should contain a simple value from [ clip-near … clip-far ) . However, this is not truly how the Z-buffer works. And the reason why has to do with its origins. The Z-buffer belonging to the earliest rendering-hardware was only a 16-bit value, associated with each output pixel! And so a system needed to be developed that could use this extremely low resolution, according to which distances closer to (clip-near) would be spaced closer together, and according to which distance closer to (clip-far) could receive a smaller number of Z-values, since at that distance, the ability of the player even to distinguish differences in distances, was also diminished.

And so the way hardware-rendering began, was in this Z-buffer-value representing a fractional value between [ 0.0 … 1.0 ) . In other words, it was decided early-on, that these 16 bits followed a decimal point – even though they were ones and zeros – and that while (0) could be reached exactly, (1.0) could never be reached. And, because game-engine developers love to use 4×4 matrices, there could exist a matrix which defines conversion from the model-view matrix to the model-view-projection matrix, just so that a single matrix could minimally be sent to the graphics card for any one model to render, which would do all the necessary work, including to determine screen-positions and to determine Z-buffer-values.

The rasterizer is given a triangle to render, and rasterizes the 2D space between, to include all the pixels, and to interpolate all the parameters, according to an algorithm which does not need to be specialized, for one sort of parameter or another. The pixel-coordinates it generates are then sent to any Fragment Shader (in modern times), and three main reasons their number does not actually equal the number of screen-pixels are:

1. Occlusion obviates the need for many FS-calls.
2. Either Multi-Sampling or Super-Sampling tampers with the true number of fragments that need to be computed, and in the case of Multi-Sampling, in a non-constant way.
3. Alpha Entities“, whose textures have an Alpha channel in addition to R, G, B per texel, are translucent and do not write the Z-buffer, thereby requiring that Entities behind them additionally be rendered.

And so there exists a projection-matrix which I can suggest which will do this (vertex-related) work:


| 1.0 0.0 0.0 0.0 |
| 0.0 1.0 0.0 0.0 |
| 0.0 0.0 1.0 0.0 |
| 0.0 0.0  a   b  |

a = clip-far / (clip-far - clip-near)
b = - (clip-far * clip-near) / (clip-far - clip-near)




One main assumption I am making, is that a standard, 4-component position-vector is to be multiplied by this matrix, which has the components named X, Y, Z and W, and the (W) component of which equals (1.0), just as it should. But as you can see, now, the output-vector has a (W) component, which will no longer equal (1.0).

The other assumption which I am making here, is that the rasterizer will divide (W) by (Z), once for every output fragment. This last request is not unreasonable. In the real world, when objects move further away from us, they seem to get smaller in the distance. Well in the game-world, we can expect the same thing. Therefore by default, we would already be dividing (X) and (Y) by (Z), to arrive at screen-coordinates from ( -1.0 … +1.0 ), regardless of what the real-world distances from the camera were, that also led to (Z) values.

This gives the game-engine something which photographic cameras fail to achieve at wide angles: Flat Field. The position from the center of the screen, becomes the tangent-function, of a view-angle from the Z-coordinate.

Well, to divide (X) by (Z), and then to divide (Y) by (Z), would actually be two GPU-operations, where to scalar-multiply the entire output-vector, including (X, Y, Z, W) by (1 / Z), would only be one GPU-operation.

Well in the example above, as (Z -> clip-far), the operation would compute:



W = a * Z + b

= (clip-far * clip-far) / (clip-far - clip-near) -
(clip-far * clip-near) / (clip-far - clip-near)

= clip-far * (clip-far - clip-near) /
(clip-far - clip-near)

= clip-far

Therefore,
(W / Z) = (W / clip-far) = 1.0




And, when (Z == clip-near), the operation would compute:



W = a * Z + b

= (clip-far * clip-near) / (clip-far - clip-near) -
(clip-far * clip-near) / (clip-far - clip-near)

= 0.0




Of course I understand that a modern graphics card will have a 32-bit Z-buffer. But then all that needs to be done, for backwards-compatibility with the older system, is to receive a fractional value that has 32 bits instead of 16.

Now, there are two main derivations of this approach, which some game engines offer as features, but which can be achieved just by feeding in a slightly different set of constants to a matrix, which the GPU can work with in an unchanging way:

• Rendering to infinite world coordinates,
• Orthogonal camera-views.

The values that are needed for the same matrix will be: