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Sometimes you need to calculate the weights of a Gaussian blur kernel yourself. For example if you want to calculate weights for a kernel where the center of the Gaussian curve is not exactly in the "center of the kernel" but has a sub-pixel offset. These "shifted" Gaussian kernels can be used if you want to blur-and-upscale an image in a single pass, e.g. if you are adding a low-res raytraced reflection buffer to your high-res rasterized scene. It is also needed for the fake ambient occlusion (AO) term as used in this shader.
The Gaussian weights for a blur kernel can be calculated, either by numerical integration, or by directly calculating the value of the Gauss error funtion, as shown below.
In this shader I calculate a fake ambient occlusion (AO) term for each sample point. The AO-term is based on the weighted average of fake AO-terms for all cells in a 7x7 grid around the sample point, corresponding with a 7x7 Gaussian kernel with the sample point as its center. The AO-term for a single cell in this weighted average is simply given by the difference in height of the cell and that of the sample point.
You can find (the full source of) Gaussian Weights and Fake AO on Shadertoy.