This semester I both took a computer vision and a computer graphics seminar. But only now before the exams I realize that there seems to be a fundamental difference between projection in both topics.
In computer vision we learned the math to map an object point from 3D to a plane using a 4x3 matrix, which seems logical to me:
|u| |p_11 p_12 p_13 p_14| |X|
|v| = |p_21 p_22 p_23 p_24| x |Y|
|w| |p_31 p_32 p_33 p_34| |Z|
However in computer graphics one usually uses a 4x4-matrix. The very nice explanation on Coding Labs has a picture depicting the outcome of said transformation: it depicts a unit-cube containing the transformed objects (distorted according to the projection).
But a unit-cube certainly isn't what is rendered on to the flat 2D screen. Is there something going on internally that just isn't mentioned? Why is this done?