# Obtaining projection Matrix, from Intrinsic Matrix

Hello,

I need help in constructing Projection Matrix from Camera Calibration data.

I have rendered a scene after setting the perspective using gluPerspective() with some values after few trial and errors…and I am able to get a pretty decent rendering.

However I would like to get the ‘correct’ rendering using the camera calibration file data.

In that file, the Intrinsic Matrix [3x3] is given as:

``````
1914.070000     0.343703     564.645000
0.0       1918.500000     428.422000
0.0          0.0            1.0

``````

Also the Rotation Matrix from the camera is as follows:

``````
0.989230       0.003946       0.146295       -7.784865
-0.004391       0.999983       0.002724       -0.431597
-0.146283      -0.003337       0.989230        1.392058

``````

My question is:
How can I create a projection Matrix [4x4], projMatrx which I can use as an argument to

``````
glMatrixMode(GL_PROJECTION);

``````

I looked at lots of resources for the matrix calculations, but cannot figure out how do I get [4x4] from these values.

I am sure it is a routine thing for the experts out there…please help me out here.

I am no expert in camera calibration, but the GL_PROJECTION matrix in principle does the projection only and not the camera rotation you described, which is extrinsic and should be rather applied to the modelview matrix.

The intrinsic matrix is a 2d homgeous transformation, so I think it has not much to do with the projection (which is 3d homogenous), but rather with the viewport transformation (look for glViewport, glDepthRange). Setting the viewport will allow you to set the principal point ((564,428) in your case) and a scaling, I think. I am not sure about this, but you might want to try s.th. like

``````
glViewport(564-(1914/2), 428-(1918/2), 1914, 1918)

``````

As for the skew 0.34 … i am not sure how to integrate this, but i am pretty sure it can’t be done in the viewport transform since it is not a freely definable matrix.

Maybe you should use a vertex shader to accomplish the task - this way you might also be able to do nonlinear lens undistort and so on if that is sth you want to do.

BTW: 0.34 for skew - isn’t that quite large?

Hello x57, thanks a lot for your reply…i will try on your suggested lines and will post what I get, soon…