The resulting concentrated matrix was basically a function of both projector properties and vertex eye positions.
By using those two matrices, a few instructions are sufficient to output the transformed eye space vertex position and a projective texture coordinate.
According to the used texture wrap mode various artifacts may occur but it's obvious a shift and scale operation is definitely necessary to get the expected result.
This artifact has historically been avoided by using a special black and white texture to cut away unnecessary projecting contributions.
Using pixel shaders a different approach can be used: a coordinate check is sufficient to discriminate between forward (correct) contributions and backward (wrong, to be avoided) ones.