Describe how to "squish" the frustum into a cuboid(n->n,f->f)

To "squish" a frustum into a cuboid, you would need to perform a process called perspective projection. This involves taking each point in the frustum and projecting it onto a flat plane that represents the cuboid.

The steps to do this are as follows:

1. Define the parameters of the frustum: the near plane distance (n), the far plane distance (f), the field of view angle (FOV), and the aspect ratio of the viewport.

2. Calculate the dimensions of the frustum. This involves using trigonometry to calculate the height and width of the near plane based on the FOV angle and aspect ratio, and then using similar triangles to calculate the height and width of the far plane.

3. Create a projection matrix. This is a 4x4 matrix that will be used to transform points in the frustum into the cuboid. The projection matrix can be created using the following formula:

P = [ 2n/(r-l)    0       (r+l)/(r-l)     0     ]
    [   0       2n/(t-b)  (t+b)/(t-b)     0     ]
    [   0         0       -(f+n)/(f-n)  -2fn/(f-n)]
    [   0         0          -1            0     ]

where l, r, b, and t are the coordinates of the left, right, bottom, and top edges of the near plane, respectively.

4. Apply the projection matrix to each point in the frustum. This involves multiplying each point by the projection matrix. The resulting points will be in homogenous coordinates, which can be converted to Cartesian coordinates by dividing by the fourth coordinate.

5. Map the resulting points onto the cuboid. To do this, you will need to define the dimensions of the cuboid (e.g. width, height, and depth). You can then map the x, y, and z coordinates of the transformed points to the corresponding ranges of the cuboid (e.g. x=-1 corresponds to the left side of the cuboid, x=1 corresponds to the right side, etc.)

6. Render the "squished" frustum. Once you have mapped the transformed points onto the cuboid, you can render the resulting scene as if it were a normal 3D scene. The "squishing" effect will be apparent due to the perspective projection.