How to create perspective projection matrix, given focal points and camera principal center

Question

I managed to acquire camera's intrinsic and extrinsic parameters using OpenCV, thus I have fx, fy, cx and cy. And I also have the screen / image's width and height.

But how do I create an OpenGL perspective projection matrix from these parameters?

glFrustrum shows how to create projection matrix, given Z near, Z far and the image width and height. But how do I include focal points and camera centers in this matrix?

Answer 1

You can check the following links

Kyle Simek's explanation

My explanation

Answer 2

Here is the code to obtain the OpenGL projection matrix equivalent to a computer vision camera with camera matrix K=[fx, s, cx; 0, fy, cy; 0, 0, 1] and image size [W, H]:

glMatrixMode(GL_PROJECTION); // Select The Projection Matrix
glLoadIdentity();            // Reset The Projection Matrix
GLdouble perspMatrix[16]={2*fx/W,0,0,0,2*s/W,2*fy/H,0,0,2*(cx/W)-1,2*(cy/H)-1,(zmax+zmin)/(zmax-zmin),1,0,0,2*zmax*zmin/(zmin-zmax),0};
glMultMatrixd(perspMatrix);

NB: zmin and zmax represent the near and far Z clipping planes. This formulation assumes that the OpenGL world coordinate frame is chosen as follows:

The OpenGL camera is assumed to be located at the origin, looking towards positive Z axis, with a down vector collinear and towards the positive Y axis.