Here is my reasoning:
- openGL draws everything within a 2x2x2 cube
- the x,y values inside this cube determine where the point is drawn on the screen. The z value is used for other stuff...
if you want the z value to have some effect on perspective you need to mutate the scene (usually with a matrix) so that it gives an illusion of distant objects being smaller.
the z values of the cube go from -1 to 1.
Now I want it so that objects that are at z = 1 are infinitely zoomed, and objects that are at z = 0 are normal size, and objects that are at z = -1 are 1/2 size.
When I say an object is zoomed, I mean that the (x,y) coordinates of its points are multiplied by scaler zoom factor, which is based on its z coordinate.
If a point lies outside the 2x2x2 cube I want the calculations to still be done on it if it is between z = 1 and z = -1. Since the z value doesn't change I don't care what happens to any points that are not within this range, as long as their z value is not changed.
Generalized point transformation:
If I have a point P = (x, y, z), and -1 <= z <= 1 then:
the Zoom Factor, S = 1 / (1 - z)
so the translation is as follows:
(x, y, z) ==> (x * S, y * S, z)
Creating the matrix?
This is where I am having issues. I don't know how to create a matrix so that it will transform a generalized point to have the desired effect.
I am considering not using a matrix and applying this transformation via a function in glsl...
If someone has insight on how to create such a matrix I would like to know.
