OpenGL why I got three different projection matrices from same parameters - opengl

Question

my question is why I got three different matrices, and what is the difference, which is the correct one for converting coordinates from clip to eye space.
Details:
I am trying to get projection matrix of OpenGL to implement a virtual scanner, I use this matrix to convert coordinates from clip to eye space.
I found three ways to get it:
glGetFloatv (GL_PROJECTION_MATRIX, projection_tmp);
glm::mat4 Proj = glm::perspective(
fov,
aspect,
zNear, zFar);
compute it manually through the method given by this page: gluperspective source code
Parameters passed to these three method follows:
const double zNear = 1;
const double zFar = 10001;//for computational convenience
const double fov = _model.getCamera().getFieldOfViewAngle();//60
//w(523)h(489)
const double aspect = static_cast<double>(w) / static_cast<double>(h);
Then I get three different matrices:
glGetFloatv:
1.61945 0 0 0
0 1.73205 0 0
0 0 -1.0002 -1
0 0 -2.0002 0
GLM:
-0.145971 0 0 0
0 -0.15612 0 0
0 0 -1.0002 -1
0 0 -2.0002 0
Manual:
0.504724 0 0 0
0 0.57735 0 0
0 0 -1.0002 1
0 0 -2.0002 0
Thanks!

Answer 1

The glGetFloatv version is the only correct one among the three.
The GLM version expects the angle to be in radians, so you should correct the fovy by a factor of tau/360.
The third version is not exactly the one from the linked answer. The code in the linked answer writes negative one to m[11] whereas you posted a positive one. Let's assume that it's a typo and look at the other numbers. Here that code is simply wrong: it multiplies by tan(fov/2) instead of dividing by it. This is why it gets 0.57735 = 1/1.73205.
I don't know why people have trouble implementing it. Just take the formula from the gluPerspective specification and write it in code:
void gluPerspectivInRadians(double m[16],
double fovy, double aspect, double zNear, double zFar)
{
double f = 1/tan(fovy/2);
m[0] = f/aspect; m[1] = 0; m[2] = 0; m[3] = 0;
m[4] = 0; m[5] = f; m[6] = 0; m[7] = 0;
m[8] = 0; m[9] = 0; m[10] = (zFar+zNear)/(zNear-zFar); m[11] = -1;
m[12] = 0; m[13] = 0; m[14] = 2*zFar*zNear/(zNear-zFar); m[15] = 0;
}