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copied!<p>From <a href="http://web.archive.org/web/20130416194336/http://olivers.posterous.com/linear-depth-in-glsl-for-real" rel="nofollow noreferrer">http://web.archive.org/web/20130416194336/http://olivers.posterous.com/linear-depth-in-glsl-for-real</a></p> <pre><code>// == Post-process frag shader =========================================== uniform sampler2D depthBuffTex; uniform float zNear; uniform float zFar; varying vec2 vTexCoord; void main(void) { float z_b = texture2D(depthBuffTex, vTexCoord).x; float z_n = 2.0 * z_b - 1.0; float z_e = 2.0 * zNear * zFar / (zFar + zNear - z_n * (zFar - zNear)); } </code></pre> <p>[edit] So here's the explanation (with 2 mistakes, see Christian's comment below) :</p> <p>An OpenGL perspective matrix looks like this : <img src="https://i.stack.imgur.com/mN7ke.png" alt="from songho.ca"></p> <p>When you multiply this matrix by an homogeneous point [x,y,z,1], it gives you: [don't care, don't care, Az+B, -z] (with A and B the 2 big components in the matrix).</p> <p>OpenGl next does the perspective division: it divides this vector by its w component. This operation is not done in shaders (except special cases like shadowmapping) but in hardware; you can't control it. w = -z, so the Z value becomes -A/z -B.</p> <p>We are now in Normalized Device Coordinates. The Z value is between 0 and 1. For some stupid reason, OpenGL requires that it should be moved to the [-1,1] range (just like x and y). A scaling and offset is applied.</p> <p>This final value is then stored in the buffer.</p> <p>The above code does the exact opposite : </p> <ul> <li>z_b is the raw value stored in the buffer</li> <li>z_n linearly transforms z_b from [-1,1] to [0,1]</li> <li>z_e is the same formula as z_n=-A/z_e -B, but solved for z_e instead. It's equivalent to z_e = -A / (z_n+B). A and B should be computed on the CPU and sent as uniforms, btw.</li> </ul> <p>The opposite function is :</p> <pre><code>varying float depth; // Linear depth, in world units void main(void) { float A = gl_ProjectionMatrix[2].z; float B = gl_ProjectionMatrix[3].z; gl_FragDepth = 0.5*(-A*depth + B) / depth + 0.5; } </code></pre>

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