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In Implementing Cameras, the following is written:
The primary objective of perspective projection is to transform this trapezoidal frustum into a cuboid
Followed by:
This resulting cuboid exists in what we call Normalized Device Coordinates (NDC).
Then followed by:

Even though:

I think here you confused NDC and the clip coordinates (note the inconsistency in the last two images). The projection matrix doesn't output the vertex positions in NDC, instead it outputs them in homogeneous clip coordinates, which then through perspective-divide (i.e. divide by w) become coordinates in the NDC space. So it should be: LOCAL -> WORLD -> VIEW -> CLIP -> NDC -> VIEWPORT.
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