Plot 2d point on 3D plane drawn in 2d

Question

I am attempting to draw a point from a 2d plane on a 3d plane that is drawn in 2d. I'm not sure how to adjust the y position based on the angle of the perspective. As you can see in the image linked below (Stack Overflow won't let me include the image because I just signed up), if the point is at the center point of the rectangle, it would need to be shifted up slightly when viewed from an angle to account for distance from the viewer. Can anyone provide an equation to help?

Answer 1

Say the point in the rectangle is given by (x,y), and the coordinates we're looking for in the second image are (x', y').

w = y + y ₀
y' = k atan(w/h)
r = sqrt(h ² + w ² )
x' = k atan(x/r)

where k is a scaling factor for the whole image, h is "altitude of the viewpoint above the plane" and y ₀ is, roughly, distance to the object.