Making sense of the orthographic projection?

[dyamanoha_1]

Can someone help understand the components of the orthographic projection? Unity’s projection matrix doesn’t seem to align with any standard documentation on how they’re put together. For example, a camera with a size of 2, near plane 0 and far plane 1000 generates this projection matrix

0.28125	0.00000	0.00000	0.00000
0.00000	0.50000	0.00000	0.00000
0.00000	0.00000	-0.00200	-1.00000
0.00000	0.00000	0.00000	1.00000

Just consider the first column – it’s supposed to be 2/(right-left) but instead it’s the aspect ratio of my display resolution divided by the projection size. The y-axis column is just 1/size.

Now, this does make some sense – the x-axis is scaled to respect the aspect ratio, the y-axis is left alone. And then scale down both the x and y axes to project a larger space based on ‘size’.

I get that the z-column is being scaled to fit in a range of 2, and then the z-component of the translation column is making that between -1 and 1. This is all based on the near/far plane.

I don’t understand is what’s going on the the x and y-components of the translation column. Why are they zero? Shouldn’t there be some sort of size/2 component to shift the space to the center of the camera?

Thanks ahead of time, I’m sure I’m just being dense.

[unity_I8FaTX-tZFc4lA]

You might find whatever information your missing here : Unity - Scripting API: Matrix4x4.Ortho
OpenGL Projection Matrix

The value of left, right and bottom, top might not be what you are expecting.