Formula 2.A.

Le Temps (Looking Glass 2)

Now consider that you move to a new position: a straight line drawn from this position to the intersection point of all three planes xz, xy, and yz (the 0 coordinate for all 3 axes of x, y & z) now forms a 30 and 60 degree angle with the z and x axis, respectively. (Figure 7) Now the system of vanishing points for the floor plane xz will drastically alter. In addition to this, consider that the lines of the vertical axis y are also foreshortened. “Looking Glass 2” is done with the formula for this new situation. What we have here is like the wide-angle photograph. The formula I've discovered for this standpoint of the artist (wide-angle linear perspective) can be explicated by comparison with the previous standpoint.

Figure 7

Figure 8

Consider Figure 8. When the standpoint (and line of sight) of the artist cuts the xz plane exactly in half (45 & 45 degree: Formula 1.B.), the y axis in the 2-D linear perspective also intersects the horizon line exactly at the middle (y @ 1/2 h; remember that in the foreshortening the y axis is always perpendicular to the horizon line). In addition, the vanishing point for the diagonals of the floor plane xz (x/z) coincides with the intersection point between the y axis and the horizon line. Moving 15 degree leftward from this standpoint (now at 30 - 60 degree) means that the y axis has to shift leftward from its original midpoint position on the horizon line by 1/3 of the total length of the horizon line (h = the length from the leftmost vanishing point for lines of x axis to the right most vanishing point for lines of z axis) -- as 15 degree is 1/3 of the original 45 degree -- and the distance of the intersection point between the y axis and the horizon line from the left most vanishing point for lines of x axis is now 1/6 of the total length of the horizon line, as 15 degree is 1/6 of the total 90 degree. In addition, the vanishing point for the diagonals of the floor plane xz (x/z) no longer coincides with the intersection point between the y axis and the horizon line. Rather, it shifts leftward only by 1/10 of the total length of the horizon line. If h is 90 (as marked in Figure 8) in length (the left most vanishing point for lines of x axis being the starting point 0), then the intersection point between the y axis and the horizon line (y) is now at 15, and the vanishing point for the diagonals of the floor plane xz (x/z) is now at 36 (45 - [90/10] = 36).

In this way the foreshortening of the floor plane xz can now be had. (Figure 10: here the length of the horizon line is marked out in centimeters to convey the positions of y & x/z.) The vanishing point for the lines of the y axis, as before, is arbitrarily chosen somewhere on the y axis below the horizon line. Just like before, the further you plot the vanishing point for the y-axis lines away from the horizon line, the lesser the foreshortening of the height; the closer, the greater the foreshortening.

Figure 9

Now the vanishing point for the diagonals of the vertical wall plane yz is found just as in the previous: draw a straight line (1) that is perpendicular to the straight line connecting the vanishing point for lines of z axis with the vanishing point for lines of y axis and (2) which passes through the point of intersection between all 3 planes of space (plane xz, yz, and xy; this point is the 0 coordinate for all 3 x, y, and z axes). This straight line will be the first diagonal for the plane yz and its intersection with the straight line connecting the vanishing point for lines of z axis with the vanishing point for lines of y axis will be the vanishing point for the diagonals of the plane yz. (Figure 10; the diagonals of the vertical wall plane yz are marked red this time.)

Figure 10

In addition to "Le Temps" "Anamnesis" (1999) is also done with Formula 2.A. (30 /60). As you can see it develop:

L. C. Chin. 2004.