Opengl：给定 Z 的值，将四边形拟合到屏幕上

Question

Short Version of the question:

I will put a quad. I know the width and height of the screen in window coordinates, i know the Z-coordinates of the quad in 3D. I know the FOVY, I know the aspect. The quad will be put along Z-axis, My camera doesn't move (placed at 0, 0, 0). I want to find out the width and height of the quad IN 3D COORDINATES that will fit exactly onto my screen.

Long Version of the question:

I would like to put a quad along the Z-axis at the specified offset Z , I would like to find out the width and height of the quad that will exactly fill the entire screen.

I used to have a post on gamedev.net that uses a formula similar to the following:

*dist = Z * tan ( FOV / 2 )*

Now I can never find the post! Though it's similar, it is still different, because I remembered in that working formula, they do make use of screenWidth and screenHeight, which are the width and height of the screen in window coordinates.

I am not really familiar with concepts like frustum, fov and aspect so that's why I can't work out the formula on my own. Besides, I am sure I don't need gluUnproject (I tried it, but the results are way off). It's not some gl calls, it's just a math formula that can find out the width and height in 3D space that can fill the entire screen, IF Z offset, width in window coordinates, and height in window coordinates, are known.

Answer 1

假设 FOV 在 YZ 平面上测量，则：

Height = Z * tan(fov/2)

width = height * aspect_ratio