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

You can check the following links

Kyle Simek's explanation

My explanation

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.

In relation to the AldurDisciple answer this is the formulation you need to use if the world coordinate frame is choosen with inverted z axe

glMatrixMode(GL_PROJECTION); // Select The Projection Matrix
glLoadIdentity();            // Reset The Projection Matrix
GLdouble perspMatrix[16]={2*fx/w,0,0,0,0,2*fy/h,0,0,2*(cx/w)-1,2*(cy/h)-1,-(far+near)/(far-near),-1,0,0,-2*far*near/(far-near),0};
glMultMatrixd(perspMatrix);