I want to rotate a square around it's vertical center line (red).
Looking at it from above (top right circle on image) I can tell that the object should, after the rotation, appear shorter length-wise by d1=d2 on each half.
After arbitrarily deciding on the position of the new vanishing point I drew the new, rotated square.
However, in the past I learned that the center point/line of any rectangle can be found using the crossing of it's diagonals. I drew those in (cross1) for a quick check and found that the apparent center of the rotated object completely deviated from the center line I intended to rotate it around.
Have I made a mistake in my construction, or is it not true that the diagonals mark the center of any rectangle? Or possibly both?
If relevant: The length of the original square is 2units, the desired degree of rotation is 30°, thus each half of the new, rotated object should be 1*cos(30°)= ~0.86 long horizontally, relatively speaking.