The Rendering Pipeline - Practical Rendering and Computation with Direct3D 11 - page 199

Figure 3.48. The change from one coordinate space to another.

range in the post- W -divide range. Thus, we have two different ways to express the post-
projection coordinates—before and after the W -divide. We will refer to the pre-divide coor-
dinates as residing in clip space, and we will refer to the post-divide coordinates simply as
normalized device coordinates. This distinction is very important, since both coordinates
describe the same point, but their values will vary significantly between the two. The vari-
ous coordinate spaces and the operations that produce them are shown in Figure 3.48.
As we noted above, the position received by the rasterizer stage in the SV_Position
system value semantic should be the result of the projection transformation, and hence
should be in clip space. The rasterizer stage performs the W -divide later in its sequence
of processing, so the shader program that performs the projection transformation doesn't
need to manually execute the division. 2 7 In

many cases, it can often be easier to visualize
the post-projection coordinates in terms of the
normalized device coordinates when consider-
ing whether a particular vertex will be visible or
not. In these normalized device coordinates, a
vertex must reside within the cube between the
points [1,1,1] and [-1,-1,0]. This range of coor-
dinates is depicted in Figure 3.49.
As we can see in Figure 3.49, the positive
X-axis points to the right, the positive 7-axis
points upward, and the positive Z-axis points

Figure 3.49. A visualization of the region
where vertices are within the current view-
ing area.

2 7

This doesn't mean that the shader can't perform the W-divide if it needs to for further calculations. If so, the
rasterizer stage will simply divide the other coordinates by 1, which will of course produce the same result.