Gaussian Kernel Generator

This page was made to generate a reasonably-ideal 1D gaussian filter for a given kernel size. Additionally, it generates optimized coefficients for linear filtered texture sampling.

Kernel size:

Coefficient Graph

Generated sigma (σ) value:

Standard 1D Coefficients

Optimized Coefficients For Bilinear Filtering

This is a set of coefficients and offsets for use with linear texture sampling, to do less actual texture samples (roughly half) by taking advantage of the linear filtering.

The coefficients list is how much to scale each texture sample.
The offsets list is a list of offsets from the center of the filter (in texels).

Note that for even-coefficient-count filters, the center will be situated between texels, not directly on one.

Coefficients

Offsets

Sample HLSL Code

Below is some (untested) sample code that uses the optimized coefficients and offsets computed above to blur an image in a given direction.

Texture2D<unorm float4> g_sourceTex;

// This must be set up for bilinear filtering for this to work
sampler g_sampler;

static const uint k_sampleCount =
     /* number of optimized coefficients */;
static const float k_coeffs[k_sampleCount] =
    { /* optimized coefficients calcualted above */ };
static const float k_offsets[k_sampleCount] =
    { /* offsets calculated above */ };

// Blur a texture along the blur direction (for a horizontal blur, use
// [1, 0] and for vertical use [0, 1]), centered at "centerTexCoord"
// (which is in standard [0..1] texture space).
float4 Blur(float2 centerTexCoord, float2 blurDirection)
{
    uint2 dim;
    g_sourceTex.GetDimensions(dim.x, dim.y);

    float4 v = float4(0, 0, 0, 0);
    for (uint i = 0; i < k_sampleCount; i++)
    {
        float2 c = centerTexCoord
            + blurDirection / float2(dim) * k_offsets[i];
        v += g_sourceTex.Sample(g_sampler, c) * k_coeffs[i];
    }

    return v;
}