# Calculating orthographic matrix parameters from perspective matrix

I have the following two matrix creation methods:

GLK_INLINE GLKMatrix4 GLKMatrix4MakePerspective(float fovyRadians, float aspect, float nearZ, float farZ)
{
float cotan = 1.0f / tanf(fovyRadians / 2.0f);

``````GLKMatrix4 m = { cotan / aspect, 0.0f, 0.0f, 0.0f,
0.0f, cotan, 0.0f, 0.0f,
0.0f, 0.0f, (farZ + nearZ) / (nearZ - farZ), -1.0f,
0.0f, 0.0f, (2.0f * farZ * nearZ) / (nearZ - farZ), 0.0f };

return m;
``````

}

GLK_INLINE GLKMatrix4 GLKMatrix4MakeOrtho(float left, float right,
float bottom, float top,
float nearZ, float farZ)
{
float ral = right + left;
float rsl = right - left;
float tab = top + bottom;
float tsb = top - bottom;
float fan = farZ + nearZ;
float fsn = farZ - nearZ;

``````GLKMatrix4 m = { 2.0f / rsl, 0.0f, 0.0f, 0.0f,
0.0f, 2.0f / tsb, 0.0f, 0.0f,
0.0f, 0.0f, -2.0f / fsn, 0.0f,
-ral / rsl, -tab / tsb, -fan / fsn, 1.0f };

return m;
``````

}

Is there a good way to create an Orthographic matrix from a given perspective matrix so that the transition will be as smooth as possible?

For very small FoV angles the two projections are (somewhat) similar. That suggests to me you want to keep near/far planes at the same world space position and move the eye point further and further away (making the FoV angle smaller in the process).