# 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):

``````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:

``````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.

[QUOTE=Nick Wiggill;1243023]

``````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? [/QUOTE]

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:

``````
// 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:

``````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…

``````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.

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