I am sure some people are hitting their heads trying to solve this simple problem when doing augmented reality with OpenCV and OpenGL:

How to get the proper OpenGL projection matrix from the OpenCV camera calibration values?

For the simple common case where the OpenCV camera matrix has the form:

``````|fx  0 cx|
|0  fy cy|
|0  0   1|
``````

The corresponding OpenGL projection matrix can be computed like this:

``````m[0][0] = 2.0 * fx / width;
m[0][1] = 0.0;
m[0][2] = 0.0;
m[0][3] = 0.0;

m[1][0] = 0.0;
m[1][1] = -2.0 * fy / height;
m[1][2] = 0.0;
m[1][3] = 0.0;

m[2][0] = 1.0 - 2.0 * cx / width;
m[2][1] = 2.0 * cy / height - 1.0;
m[2][2] = (zfar + znear) / (znear - zfar);
m[2][3] = -1.0;

m[3][0] = 0.0;
m[3][1] = 0.0;
m[3][2] = 2.0 * zfar * znear / (znear - zfar);
m[3][3] = 0.0;
``````

Where `height` and `width` are the size of the captured image ; `znear` and `zfar` are the clipping value for the projection.

It took me a lot of time to get it right, since we have to be careful of the difference in referential between OpenGL and OpenCV.