Game Engine Architecture

444 10. The Rendering Engine

using them as our depth measure achieves uniform precision across the en-

tire depth range. This technique is called w-buff ering , because the view-space

z-coordinate conveniently appears in the w-component of our homogeneous

clip-space coordinates. (Recall from Equation (10.1) that pHw=−pVz.)

The terminology can be a very confusing here. The z- and w-buff ers store

coordinates that are expressed in clip space. But in terms of view-space coordi-

nates, the z-buff er stores 1/z (i.e., 1/pVz) while the w-buff er stores z (i.e., pVz)!

We should note here that the w-buff ering approach is a bit more expen-

sive than its z-based counterpart. This is because with w-buff ering, we cannot

linearly interpolate depths directly. Depths must be inverted prior to interpo-

lation and then re-inverted prior to being stored in the w-buff er.

10.2 The Rendering Pipeline

Now that we’ve completed our whirlwind tour of the major theoretical and

practical underpinnings of triangle rasterization, let’s turn our att ention to

how it is typically implemented. In real-time game rendering engines, the

high-level rendering steps described in Section 10.1 are implemented using

a soft ware/hardware architecture known as a pipeline. A pipeline is just an or-

dered chain of computational stages, each with a specifi c purpose, operating

on a stream of input data items and producing a stream of output data.

Each stage of a pipeline can typically operate independently of the other

stages. Hence, one of the biggest advantages of a pipelined architecture is that

it lends itself extremely well to parallelization. While the fi rst stage is chewing

on one data element, the second stage can be processing the results previously

produced by the fi rst stage, and so on down the chain.

Parallelization can also be achieved within an individual stage of the

pipeline. For example, if the computing hardware for a particular stage is du-

Figure 10.38. A plot of the function 1/pVz, showing how most of the precision lies close to

the camera.

ΔpHz

ΔpVz ΔpVz

ΔpHz

pHz= 1/pVz pHz= 1/pVz