Suppose, I have defined a model view matrix as follows:

|1 0 0.0 -0.5cos(theta) 0|
|0.0 1.0 -0.5cos(alpha) 0|
|0.0 0.0 1.0 0|
|0.0 0.0 0.0 1.0|

where theta and alpha are some angles less that 90 degree.
What transformation actually this matrix does? Is it about some foreshortening along x and y direction?
Any clarification will be highly appreciated.

That matrix performs an oblique projection, but I’m unsure as to what theta and alpha are meant to represent.

Oblique projections are normally expressed as

``````
[1 0 a*cos(phi) 0]
[0 1 a*sin(phi) 0]
[0 0          1 0]
[0 0          0 1]

``````

where a=1/tan(alpha).

With that construction, alpha is the angle between the projection lines and the projection plane (45° for a cavalier projection, arctan(2) ~= 63.4° for a cabinet projection; 90° gives an orthographic projection, a=0), while phi is the angle between the projected Z axis and the X axis.(typically 30° or 45°).

[QUOTE=GClements;1280355] I’m unsure as to what theta and alpha are meant to represent.

[/QUOTE]

Thank you so much! Now I understand. Actually ‘theta’ and ‘phi’ are angles of projection with the x and y axes respectively.