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Thread: How does this simple fragment shader function work?

  1. #1
    Junior Member Newbie
    Join Date
    Jan 2009

    How does this simple fragment shader function work?

    This code is used in a DoF blur fragment shader I found online (I am trying to make one of my own):

    Code :
    uniform sampler2D gdepth; //<- the depth buffer? How/where is this set?
    float getDepth(vec2 coord)
        return 2.0 * near * far / (far + near - (2.0 * texture2D(gdepth, coord).x - 1.0) * (far - near)); //is gdepth equivalent to gl_FragCoord.z?

    How do the mathematics in this depth retrieval function work? I assume it's converting from screen to world space. The terms look strikingly like those found in the projection matrix I ended up using in my CPU-side code:

    Code :
    public static Matrix4 getProjectionMatrix(float fovYDeg, float aspectRatio, float near, float far)
        Matrix4 result = new Matrix4();
        float fovYRad = fovYDeg * (float)PI / 180f; 
        float e = 1f/(float)(tan(fovYRad / 2)); //focal length
        result.val[Matrix4.M00] = e / aspectRatio;
        result.val[Matrix4.M11] = e;
        result.val[Matrix4.M22] = (far + near) / (near - far);
        result.val[Matrix4.M23] = (2 * far * near) / (near - far);
        result.val[Matrix4.M32] = -1f;
        result.val[Matrix4.M33] = 0f;
        return result;

    I really can't just keep letting this stuff go over my head.

    PS. The original shader code is here.
    Last edited by Nick Wiggill; 10-01-2012 at 02:32 PM.

  2. #2
    Senior Member OpenGL Guru Dark Photon's Avatar
    Join Date
    Oct 2004
    Quote Originally Posted by Nick Wiggill View Post
    Code :
    2.0 * near * far / (far + near - (2.0 * texture2D(gdepth, coord).x - 1.0) * (far - near));

    How do the mathematics in this depth retrieval function work?
    This computes the negative of eye-space Z (so +near..+far) from window-space Z (0..1) with the assumptions: 1) a perspective projection was used for rendering, 2) glDepthRange == 0..1, and 3) w_eye == 1 (true for a point). Add a leading negative to it and it computes eye-space Z (i.e. -near..-far).

    (No, I didn't just figure that out -- have read that and done it before :-)

    Yeah, you can get this from the perspective projection matrix, which takes you from eye-space to clip-space. To get from clip-space to NDC space, divide by w. To get from NDC to window-space, shift/scale -1..1 to 0..1.

    Here's the jist of it:

    Code :
    // First, multiply (0,0,z_eye,1) by projection matrix to get z_clip and w_clip), then just plug them into
    //    the following equation, as we'll do below:
    z_ndc = z_clip / w_clip
    z_ndc = [ z_eye*gl_ProjectionMatrix[2].z + gl_ProjectionMatrix[3].z ] / -z_eye

    Solve the above for z_eye, and you get:

    Code :
    float z_eye = gl_ProjectionMatrix[3].z/(-z_ndc - gl_ProjectionMatrix[2].z);

    Typically your glDepthRange is 0..1, so z_ndc = z_window * 2 - 1, so plugging that in...

    Code :
    float z_eye = gl_ProjectionMatrix[3].z/(z_window * -2.0 + 1.0 - gl_ProjectionMatrix[2].z);

    Substitute the terms from the projection matrix, and there you go.
    Last edited by Dark Photon; 10-02-2012 at 05:48 AM.

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