going deep

In the world of flat geometry, a right isosceles triangle has equal sized legs and a 45º angle. One can divide a vertically-striped plane into a grid of equal squares using the 45º diagonal.This same plane's set of parallel lines, when laid down into the geometry of linear perspective, appear as rays that converge as they recede. Their convergence is governed by the central vanishing point C in this diagram based on Kevin Forseth's useful book on perspective: Since we're no longer in flat space, a diagonal line is at a virtual 45º. A protractor laid on the drawing will not measure 45º.
The rate at which equal intervals diminish in size as they recede is a affected by how far the measured field/back wall/picture plane is from the observer. This process of representing space fixes the viewer's distance from the virtual scene. The distance between the viewer(SP) and the viewed object (in this case, the back wall) is related to the distance between C, the center of vision and the vpD, or diagonal vanishing point. A perspectivist can slide the back wall forward to make the viewer feel closer to it. 

Increasing the distance (on the HL) between the vpD and C, would flatten the virtual 45º diagonal, compress the receding intervals into a smaller space on the page, and give the impression that the scene is farther from the observer. Note that the size of the back wall is the same as in the drawing above. By moving the vpD away from the central VP, the "measured" distance, or depth, between that wall and the observer appears more compressed.