1//! A library containing a 1D Gaussian blur kernel.
2//!
3//! This is used by depth of field, but you can also use it in custom
4//! postprocessing passes.
5
6/// Performs a single direction of the separable Gaussian blur kernel.
7///
8/// * `color_texture` is the texture to blur.
9///
10/// * `color_texture_sampler` is a sampler to sample the texture. It must have
11///   linear filtering for both minification and magnification.
12///
13/// * `frag_coord` is the screen-space pixel coordinate of the fragment (i.e. the
14///   `position` input to the fragment).
15///
16/// * `coc` is the diameter (not the radius) of the circle of confusion for this
17///   fragment.
18///
19/// * `frag_offset` is the vector, in screen-space units, from one sample to the
20///   next. For a horizontal blur this will be `vec2(1.0, 0.0)`; for a vertical
21///   blur this will be `vec2(0.0, 1.0)`.
22///
23/// Returns the resulting color of the fragment.
24fn gaussian_blur(color_texture: texture_2d<f32>, color_texture_sampler: sampler, frag_coord: vec4<f32>, coc: f32, frag_offset: vec2<f32>) -> vec4<f32> {
25    // Usually σ (the standard deviation) is half the radius, and the radius is
26    // half the CoC. So we multiply by 0.25.
27    let sigma = coc * 0.25;
28
29    // 1.5σ is a good, somewhat aggressive default for support—the number of
30    // texels on each side of the center that we process.
31    let support = i32(ceil(sigma * 1.5));
32    let uv = frag_coord.xy / vec2<f32>(textureDimensions(color_texture));
33    let offset = frag_offset / vec2<f32>(textureDimensions(color_texture));
34
35    // The probability density function of the Gaussian blur is (up to constant factors) `exp(-1 / 2σ² *
36    // x²). We precalculate the constant factor here to avoid having to
37    // calculate it in the inner loop.
38    let exp_factor = -1.0 / (2.0 * sigma * sigma);
39
40    // Accumulate samples on both sides of the current texel. Go two at a time,
41    // taking advantage of bilinear filtering.
42    var sum = textureSampleLevel(color_texture, color_texture_sampler, uv, 0.0).rgb;
43    var weight_sum = 1.0;
44    for (var i = 1; i <= support; i += 2) {
45        // This is a well-known trick to reduce the number of needed texture
46        // samples by a factor of two. We seek to accumulate two adjacent
47        // samples c₀ and c₁ with weights w₀ and w₁ respectively, with a single
48        // texture sample at a carefully chosen location. Observe that:
49        //
50        //     k ⋅ lerp(c₀, c₁, t) = w₀⋅c₀ + w₁⋅c₁
51        //
52        //                              w₁
53        //     if k = w₀ + w₁ and t = ───────
54        //                            w₀ + w₁
55        //
56        // Therefore, if we sample at a distance of t = w₁ / (w₀ + w₁) texels in
57        // between the two texel centers and scale by k = w₀ + w₁ afterward, we
58        // effectively evaluate w₀⋅c₀ + w₁⋅c₁ with a single texture lookup.
59        let w0 = exp(exp_factor * f32(i) * f32(i));
60        let w1 = exp(exp_factor * f32(i + 1) * f32(i + 1));
61        let uv_offset = offset * (f32(i) + w1 / (w0 + w1));
62        let weight = w0 + w1;
63
64        sum += (
65            textureSampleLevel(color_texture, color_texture_sampler, uv + uv_offset, 0.0).rgb +
66            textureSampleLevel(color_texture, color_texture_sampler, uv - uv_offset, 0.0).rgb
67        ) * weight;
68        weight_sum += weight * 2.0;
69    }
70
71    return vec4(sum / weight_sum, 1.0);
72}