How to calculate depth coordinate of the 3D rectangle?

Question

I have 3D rectangle, as shown in the image.

Here I know depth distance and x and y coordinates of the one end. Based on these two values I would like calculate coordinates at the other end.

For clear view, I have attached a screen.

Answer 1

If you don't know the relation between 2D and 3D (ie the projection formulas used) then you can't apply the depth.

That said, if you make the following assumptions:

• the projection type is orthographic
• a depth line is projected as a 45 degrees line
• the length of a 45 degrees line is the same as if it was a normal line

... then you could calculate it with Pythagoras' theorem as follows:

The red lines are equal (in case of a 45 degree line), so:

x1 = 100  +  50 * (1 / sqrt(2))
y1 = 50   -  50 * (1 / sqrt(2))