Proof of geometric perspective?

Question

So I'm struggling to draw squares in perspective. I came across this technique where the method used is by dividing in half the angle made by the vertices of the lowest horizontal line parallel to horizon and the lines connecting it to the vanishing point, you can draw the diagonals that would determine the upper side of the resultant square. I can kinda see it intuitively, since the halves made by a the diagonals of a square are congruent, so I'm assuming the degree to which they are foreshortened would be the same for both halves as well? Can this be proved, and if it can, can it be used for other vanishing points?

Link to technique: http://pekkanen.brinkster.net/circle/index.htm

Answer 1

While it is true that the images of a square’s diagonals intersect at the image of its center, it’s not generally true that the images of those diagonals are the angle bisectors of the images of the square’s sides, even when a pair of sides parallels the horizon. If you have a square that’s positioned symmetrically within the scene as in the linked writeup, as it moves further from the viewpoint, its image becomes more and more foreshortened, with the angle between the horizontal sides of the square and its diagonals tending to zero.

Answer 2

There are many accurate methods to draw a square or any other objects even houses in perspective whether it's one point-, two point- or three point perspective. Here's a method that doesn't care about vanishing points but rather uses Cartesian coordinate system. And here's another one using the same technique but with one little change, that's the mirror location as vertical. Cheers